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Puzzles for CUET General Aptitude

About 10 min to learn · 65 questions

A puzzle in CUET's General Aptitude Test gives a short passage of clues and then asks three to five questions about the same arrangement. The marks go to whoever builds the table first and solves it once; after that each question takes seconds. This lesson covers matching people to attributes, floors and stacked boxes, schedules across a week, splitting into cases, arrangements that are only partly fixed, and removable clues, with worked examples and traps.

Syllabus area
Logical and Analytical Reasoning
On this page · 8 sections
  1. 01The core idea
  2. 02The method
  3. 03Floors, boxes and days
  4. 04Cases and uncertainty
  5. 05Exam shortcuts
  6. 06Common mistakes
  7. 07Quick revision
  8. 08Check your understanding

The core idea

Solve the puzzle once, in a table, before you read the questions. If you answer each question straight from the clues, you solve the whole puzzle again every time, and that is where the minutes go. A clean table answers four or five questions in the time a guess answers one.

Every puzzle falls to the same four moves: build the grid, place the direct clues, eliminate, and split into cases only when you are stuck. Seating in rows and circles has its own chapter, seating arrangement, and "taller than" chains are in ranking and ordering.

The method

How do you start a puzzle in the exam?

Draw the table first, then fill it clue by clue, starting with the clues that fix something outright.

  1. Build the grid. People down the side and attributes across the top; for floors, boxes and days, positions down the side.
  2. Direct clues first. "Tenzin is from Shillong", "Dolma lives on the top floor".
  3. Linked clues next. "The person from Madurai plays badminton" ties two columns; place it as soon as either half is known.
  4. Negative clues last. "Kabir drinks neither tea nor lassi" crosses cells out. When a row or column has one cell left, that cell is the answer.

Watch out

Read the convention line every time. In this bank, floor 1 is the ground floor, box 1 is the bottom box, and "above" means anywhere above unless the passage says "immediately above".

How do you draw the grid for an attribute-matching puzzle?

Make a table with one row per person and one column per attribute. With two or more attributes, keep a list of linked pairs beside it, such as "tea = gardening".

Example 1 · Drinks and hobbies

Kabir, Leela, Mustafa and Nisha each drink a different drink (tea, coffee, lassi, nimbu pani) and have a different hobby (reading, cycling, painting, gardening). Leela drinks coffee. The tea drinker likes gardening. Kabir drinks neither tea nor lassi. Nisha likes reading. Leela does not like cycling. Match everyone.

  1. Leela has coffee. Kabir cannot have tea, lassi or coffee, so he has nimbu pani.

  2. Tea and lassi are left for Mustafa and Nisha. The tea drinker gardens, but Nisha reads, so Nisha has lassi and Mustafa tea and gardening.

  3. Cycling and painting are left for Kabir and Leela. Leela does not cycle, so she paints, and Kabir cycles.

Answer
PersonDrinkHobby
KabirNimbu paniCycling
LeelaCoffeePainting
MustafaTeaGardening
NishaLassiReading

Exam shortcut

Read linked clues in reverse too. "The tea drinker likes gardening" also means "someone who does not garden is not the tea drinker", and that reverse reading removes more options than the forward one.

Floors, boxes and days

What does "above" mean, and how is it different from "immediately above"?

"Above" means anywhere higher; "immediately above" means the very next floor. The first gives only a direction, the second fixes a gap of exactly one. Confusing them is the commonest error in floor and box puzzles.

PhraseWhat it tells you
X lives above YX's floor is higher, by any gap
X lives immediately above YX's floor is Y's plus 1
Exactly two people live between X and YThe floors differ by 3, either way
X lives on an even-numbered floorFloor 2, 4 or 6; usually a case split

Example 2 · A six-storey building

A six-storey building has one person on each floor, floor 1 at the ground. Uma lives on floor 4. Tariq lives immediately above Uma. Ravi lives above Sunita but below Uma. Wangmo lives on an even-numbered floor. Vinod lives immediately below Ravi. Who lives where?

  1. Uma 4, Tariq 5. Ravi and Sunita are both below 4, Sunita lower.

  2. Wangmo on 2: Ravi and Sunita take 1 and 3, so Ravi is 3 and Vinod must be 2, which Wangmo has. This case fails.

  3. Wangmo on 6: Ravi, Sunita and Vinod take 1 to 3, with Vinod just under Ravi and Sunita below Ravi, so Ravi 3, Vinod 2, Sunita 1.

Answer
FloorPerson
6Wangmo
5Tariq
4Uma
3Ravi
2Vinod
1Sunita

Watch out

"Between" counts only the floors strictly between: floors 1 and 5 have 3 people between them, not 4. Between is the difference minus 1.

How do you handle a stack of boxes?

Treat a stack exactly like a building: position 1 is the bottom, and "on top of" means immediately above. The only new skill is switching ends: position from the top is the total minus the position from the bottom, plus 1.

Example 3 · Five boxes

Boxes of rice, dal, sugar, salt and tea are stacked in one pile. The sugar box is second from the top. Exactly one box lies between rice and sugar. Tea is immediately below rice. Salt is above dal. Find the order.

  1. Second from the top of 5 is position 4, so sugar is at 4.

  2. Rice is two places from sugar: position 2, since 6 does not exist. Tea is directly under it, at 1.

  3. Dal and salt take 3 and 5, with salt higher.

Answer

From the top: salt, sugar, dal, rice, tea

How do you solve a scheduling puzzle across the days of a week?

Write the days in a column in order and treat each day as a position, exactly like a floor. "Before" means any earlier day, "immediately before" the previous day, and "between" counts only the days strictly in between.

Example 4 · Six exams

Six exams, Hindi, English, Maths, Physics, Chemistry and Biology, are held from Monday to Saturday, one a day. Maths is on Wednesday. Exactly one exam is held between Maths and Biology. English is the day after Hindi. Physics is on some day before Hindi. Chemistry is the day after Maths. Find the schedule.

  1. Maths Wednesday, Chemistry Thursday. Biology is two days from Wednesday: Monday or Friday.

  2. Biology Friday leaves Monday, Tuesday and Saturday. Hindi and English need two days in a row, so Monday and Tuesday, and then Physics has no day before Hindi. This case fails.

  3. Biology Monday leaves Tuesday, Friday and Saturday. Hindi and English take Friday and Saturday, and Physics Tuesday.

Answer

Monday Biology, Tuesday Physics, Wednesday Maths, Thursday Chemistry, Friday Hindi, Saturday English

Watch out

Check whether the week runs Monday to Saturday or Monday to Sunday. With fewer events than days, one day is empty: it counts in "days between" but not in "how many exams after". Time slots work the same way: 10, 11, 12, 1 and 2 o'clock are positions 1 to 5.

Cases and uncertainty

When should you split a puzzle into cases?

When a clue leaves exactly two or three possibilities and nothing else moves. Write each case as its own short column, follow it until it breaks a clue or completes, and keep the one that survives.

  • Good clues to split on: "exactly one between X and Y", "X is on an even floor", "X and Y in some order", or a fixed item with two options.
  • Pick the clue with the fewest cases. Six cases means another clue should have been placed first.
  • A case usually dies within two steps, when it collides with a fixed item. Look for that collision.

What if a puzzle has more than one arrangement?

A question can still have one answer, as long as the asked fact is the same in every arrangement. If it differs, the answer is "cannot be determined".

Example 5 · Two arrangements

Asha, Bilal, Chitra and Dinesh give talks at 9, 10, 11 and 12 o'clock, one each. Bilal speaks immediately after Asha. Chitra speaks before Asha. Dinesh does not speak at 12. Who speaks at 12, and who at 9?

  1. Asha and Bilal are a pair with Chitra before them. Dinesh is not last, so Bilal is: Asha 11, Bilal 12.

  2. Chitra and Dinesh take 9 and 10 in either order, and both fit every clue.

Answer

Bilal speaks at 12; the 9 o'clock speaker cannot be determined

How do you answer "which clue could be removed"?

Solve the puzzle and note which clues you used. A clue the solution never needed is the candidate; check it by trying to build a second arrangement without it. In Example 4, the Chemistry clue is needed: without it, three schedules fit, with Chemistry on Tuesday, Thursday or Saturday.

Exam shortcut

Once the table is complete, every question is a look-up: immediately above X is X's position plus 1; the number above X is the total minus X's position; a matched pair must match in every part; and some sets ask for the false statement.

Exam shortcuts

  • Table first. Spend the first minute drawing, not reading options.
  • Direct, linked, negative. In that order.
  • Reverse readings. Every linked clue works both ways.
  • Fewest cases. Split on the clue with the fewest possibilities.
  • Check once. Run every clue against the finished table.

Common mistakes

  • "Above" read as "immediately above".
  • Counting the ends as "between".
  • The wrong end of a stack. Convert with total − position + 1.
  • Forgetting the empty day.
  • Missing a reverse reading.
  • Half-matched pairs. One wrong part makes the whole option wrong.
  • Missing the word "false".
  • Answering from one case. Finish every case.
  • The wrong week. Monday to Saturday or to Sunday.

Quick revision

Method

  • Grid, direct clues, linked clues, negative clues
  • Split on the clue with the fewest cases
  • Check every clue against the finished table

Positions

  • Floor 1 ground, box 1 bottom
  • Above: any gap. Immediately above: gap 1
  • Between = difference − 1
  • From the top = total − position + 1

Uncertainty

  • Same in every arrangement: answer it
  • Differs: cannot be determined
  • Removable clue: the one the solution never needed

Puzzles reward the same draw-it habit as blood relations and direction sense.

Next · 07Quick revision

Check your understanding

65 questions, grouped by type, easy to hard. Pick an answer and check it. The worked solution opens when you ask for it.

Matching people to attributesQ1 of 65Q1

Matching people to attributes

24 questions

Question 1

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Four friends, Ishaan, Mehak, Tenzin and Revathi, meet at a sports camp. Each comes from a different city (Pune, Shillong, Madurai or Bhopal) and each plays a different sport (chess, badminton, kabaddi or swimming). The following is known:

1. Tenzin is from Shillong.

2. The person from Madurai plays badminton.

3. Mehak plays neither kabaddi nor chess.

4. Neither Ishaan nor Revathi is from Pune.

5. The chess player is from neither Bhopal nor Madurai.

6. Ishaan does not play badminton.

At the sports camp, which sport does Tenzin play?

Options for question 1

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AnswerB · chess

  1. Clue 1 gives Tenzin = Shillong. Clue 4 rules Pune out for Ishaan and Revathi, so Mehak = Pune.

  2. Clue 5: the chess player is from Pune or Shillong. Mehak (Pune) does not play chess (clue 3), so Tenzin plays chess.

  3. So Tenzin plays chess.

Worth noting

Clue 5 does the work: once the chess player is limited to Pune or Shillong, clue 3 removes Mehak.

Question 2

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Four friends, Ishaan, Mehak, Tenzin and Revathi, meet at a sports camp. Each comes from a different city (Pune, Shillong, Madurai or Bhopal) and each plays a different sport (chess, badminton, kabaddi or swimming). The following is known:

1. Tenzin is from Shillong.

2. The person from Madurai plays badminton.

3. Mehak plays neither kabaddi nor chess.

4. Neither Ishaan nor Revathi is from Pune.

5. The chess player is from neither Bhopal nor Madurai.

6. Ishaan does not play badminton.

Revathi, one of the four friends at the camp, comes from which city?

Options for question 2

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AnswerC · Madurai

  1. Clue 1 gives Tenzin = Shillong. Clue 4 rules Pune out for Ishaan and Revathi, so Mehak = Pune.

  2. Clue 5: the chess player is from Pune or Shillong. Mehak (Pune) does not play chess (clue 3), so Tenzin plays chess.

  3. Badminton belongs to the Madurai person (clue 2), and Mehak is from Pune, so Mehak cannot play badminton either: Mehak swims.

  4. Kabaddi and badminton are left for Ishaan and Revathi. Ishaan does not play badminton (clue 6), so Ishaan plays kabaddi and Revathi plays badminton, which makes Revathi = Madurai and Ishaan = Bhopal.

  5. Revathi is from Madurai.

Question 3

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Five students, Farhan, Gurpreet, Nandini, Joseph and Lalremsiami, each take a different elective (Physics, History, Economics, Biology or Geography) and each keep their notes in a notebook of a different colour (red, blue, green, yellow or white). The following is known:

1. The student who takes History uses the blue notebook.

2. Gurpreet's notebook is red.

3. The Physics student's notebook is white.

4. Farhan takes neither History nor Geography, and his notebook is neither yellow nor white.

5. Joseph's notebook is neither blue nor white, and he does not take Biology.

6. Nandini does not take History.

7. The Biology student and the Geography student are Gurpreet and Joseph, in some order.

Which elective does Lalremsiami take?

Options for question 3

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AnswerB · History

  1. Clue 7 says Biology and Geography go to Gurpreet and Joseph; Joseph does not take Biology (clue 5), so Joseph takes Geography and Gurpreet takes Biology.

  2. Farhan does not take History (clue 4), and not Physics either, because the Physics notebook is white (clue 3) and Farhan's is not white. So Farhan takes Economics.

  3. Physics and History are left for Nandini and Lalremsiami. Nandini does not take History (clue 6), so Nandini takes Physics (white notebook) and Lalremsiami takes History (blue notebook, clue 1).

  4. Lalremsiami takes History.

Question 4

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Five students, Farhan, Gurpreet, Nandini, Joseph and Lalremsiami, each take a different elective (Physics, History, Economics, Biology or Geography) and each keep their notes in a notebook of a different colour (red, blue, green, yellow or white). The following is known:

1. The student who takes History uses the blue notebook.

2. Gurpreet's notebook is red.

3. The Physics student's notebook is white.

4. Farhan takes neither History nor Geography, and his notebook is neither yellow nor white.

5. Joseph's notebook is neither blue nor white, and he does not take Biology.

6. Nandini does not take History.

7. The Biology student and the Geography student are Gurpreet and Joseph, in some order.

What colour is the notebook Nandini uses for her elective?

Options for question 4

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AnswerC · white

  1. Clue 7 says Biology and Geography go to Gurpreet and Joseph; Joseph does not take Biology (clue 5), so Joseph takes Geography and Gurpreet takes Biology.

  2. Farhan does not take History (clue 4), and not Physics either, because the Physics notebook is white (clue 3) and Farhan's is not white. So Farhan takes Economics.

  3. Physics and History are left for Nandini and Lalremsiami. Nandini does not take History (clue 6), so Nandini takes Physics (white notebook) and Lalremsiami takes History (blue notebook, clue 1).

  4. Nandini takes Physics, so her notebook is white.

Worth noting

The colour follows from the subject: clue 3 ties Physics to white.

Question 5

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Five colleagues, Kavya, Rohit, Sana, Anirudh and Pooja, each work in a different department (Legal, Design, Accounts, Sales or HR) and each reach the office by a different mode (metro, bicycle, car, bus or scooter). The following is known:

1. The colleague in Design cycles to work.

2. Sana comes by car, but she does not work in Sales.

3. Kavya comes by neither bus nor bicycle, and she works in neither HR nor Accounts.

4. The colleague in Sales takes the bus.

5. Pooja rides a scooter.

6. Anirudh does not cycle to work.

7. Sana does not work in HR.

How does Kavya travel to the office?

Options for question 5

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AnswerC · by metro

  1. Sana comes by car (clue 2) and Pooja by scooter (clue 5).

  2. Kavya uses neither the bus nor the bicycle (clue 3), so Kavya takes the metro. Bus and bicycle are left for Rohit and Anirudh; Anirudh does not cycle (clue 6), so Anirudh takes the bus and Rohit cycles.

  3. Kavya travels by metro.

Question 6

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Five colleagues, Kavya, Rohit, Sana, Anirudh and Pooja, each work in a different department (Legal, Design, Accounts, Sales or HR) and each reach the office by a different mode (metro, bicycle, car, bus or scooter). The following is known:

1. The colleague in Design cycles to work.

2. Sana comes by car, but she does not work in Sales.

3. Kavya comes by neither bus nor bicycle, and she works in neither HR nor Accounts.

4. The colleague in Sales takes the bus.

5. Pooja rides a scooter.

6. Anirudh does not cycle to work.

7. Sana does not work in HR.

Anirudh works in which department of the office?

Options for question 6

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AnswerD · Sales

  1. Sana comes by car (clue 2) and Pooja by scooter (clue 5).

  2. Kavya uses neither the bus nor the bicycle (clue 3), so Kavya takes the metro. Bus and bicycle are left for Rohit and Anirudh; Anirudh does not cycle (clue 6), so Anirudh takes the bus and Rohit cycles.

  3. The cyclist works in Design (clue 1), so Rohit is in Design; the bus user is in Sales (clue 4), so Anirudh is in Sales.

  4. Anirudh is in Sales.

Question 7

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Four friends, Ishaan, Mehak, Tenzin and Revathi, meet at a sports camp. Each comes from a different city (Pune, Shillong, Madurai or Bhopal) and each plays a different sport (chess, badminton, kabaddi or swimming). The following is known:

1. Tenzin is from Shillong.

2. The person from Madurai plays badminton.

3. Mehak plays neither kabaddi nor chess.

4. Neither Ishaan nor Revathi is from Pune.

5. The chess player is from neither Bhopal nor Madurai.

6. Ishaan does not play badminton.

From which city is the friend who plays kabaddi?

Options for question 7

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AnswerD · Bhopal

  1. Clue 1 gives Tenzin = Shillong. Clue 4 rules Pune out for Ishaan and Revathi, so Mehak = Pune.

  2. Clue 5: the chess player is from Pune or Shillong. Mehak (Pune) does not play chess (clue 3), so Tenzin plays chess.

  3. Badminton belongs to the Madurai person (clue 2), and Mehak is from Pune, so Mehak cannot play badminton either: Mehak swims.

  4. Kabaddi and badminton are left for Ishaan and Revathi. Ishaan does not play badminton (clue 6), so Ishaan plays kabaddi and Revathi plays badminton, which makes Revathi = Madurai and Ishaan = Bhopal.

  5. The kabaddi player is Ishaan, who is from Bhopal.

Worth noting

Madurai is tempting if you pair Ishaan with the only city left before using clue 2; the Madurai person must play badminton.

Question 8

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Four friends, Ishaan, Mehak, Tenzin and Revathi, meet at a sports camp. Each comes from a different city (Pune, Shillong, Madurai or Bhopal) and each plays a different sport (chess, badminton, kabaddi or swimming). The following is known:

1. Tenzin is from Shillong.

2. The person from Madurai plays badminton.

3. Mehak plays neither kabaddi nor chess.

4. Neither Ishaan nor Revathi is from Pune.

5. The chess player is from neither Bhopal nor Madurai.

6. Ishaan does not play badminton.

Which one of the following friend, city and sport combinations is correct?

Options for question 8

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AnswerA · Mehak, Pune, swimming

  1. Clue 1 gives Tenzin = Shillong. Clue 4 rules Pune out for Ishaan and Revathi, so Mehak = Pune.

  2. Clue 5: the chess player is from Pune or Shillong. Mehak (Pune) does not play chess (clue 3), so Tenzin plays chess.

  3. Badminton belongs to the Madurai person (clue 2), and Mehak is from Pune, so Mehak cannot play badminton either: Mehak swims.

  4. Kabaddi and badminton are left for Ishaan and Revathi. Ishaan does not play badminton (clue 6), so Ishaan plays kabaddi and Revathi plays badminton, which makes Revathi = Madurai and Ishaan = Bhopal.

  5. Only Mehak, Pune, swimming matches the grid.

Worth noting

Tenzin is from Shillong, but he plays chess, not kabaddi. A combination is correct only if every part of it is correct.

Question 9

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Five students, Farhan, Gurpreet, Nandini, Joseph and Lalremsiami, each take a different elective (Physics, History, Economics, Biology or Geography) and each keep their notes in a notebook of a different colour (red, blue, green, yellow or white). The following is known:

1. The student who takes History uses the blue notebook.

2. Gurpreet's notebook is red.

3. The Physics student's notebook is white.

4. Farhan takes neither History nor Geography, and his notebook is neither yellow nor white.

5. Joseph's notebook is neither blue nor white, and he does not take Biology.

6. Nandini does not take History.

7. The Biology student and the Geography student are Gurpreet and Joseph, in some order.

Among the five students, who keeps notes in the green notebook?

Options for question 9

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AnswerD · Farhan

  1. Clue 7 says Biology and Geography go to Gurpreet and Joseph; Joseph does not take Biology (clue 5), so Joseph takes Geography and Gurpreet takes Biology.

  2. Farhan does not take History (clue 4), and not Physics either, because the Physics notebook is white (clue 3) and Farhan's is not white. So Farhan takes Economics.

  3. Physics and History are left for Nandini and Lalremsiami. Nandini does not take History (clue 6), so Nandini takes Physics (white notebook) and Lalremsiami takes History (blue notebook, clue 1).

  4. Gurpreet has red (clue 2). Green and yellow are left for Farhan and Joseph; Farhan's is not yellow, so Farhan has green and Joseph has yellow.

  5. The green notebook belongs to Farhan.

Worth noting

Joseph is the tempting answer if clue 4's colour condition is overlooked.

Question 10

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Five students, Farhan, Gurpreet, Nandini, Joseph and Lalremsiami, each take a different elective (Physics, History, Economics, Biology or Geography) and each keep their notes in a notebook of a different colour (red, blue, green, yellow or white). The following is known:

1. The student who takes History uses the blue notebook.

2. Gurpreet's notebook is red.

3. The Physics student's notebook is white.

4. Farhan takes neither History nor Geography, and his notebook is neither yellow nor white.

5. Joseph's notebook is neither blue nor white, and he does not take Biology.

6. Nandini does not take History.

7. The Biology student and the Geography student are Gurpreet and Joseph, in some order.

The student with the yellow notebook takes which elective?

Options for question 10

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AnswerA · Geography

  1. Clue 7 says Biology and Geography go to Gurpreet and Joseph; Joseph does not take Biology (clue 5), so Joseph takes Geography and Gurpreet takes Biology.

  2. Farhan does not take History (clue 4), and not Physics either, because the Physics notebook is white (clue 3) and Farhan's is not white. So Farhan takes Economics.

  3. Physics and History are left for Nandini and Lalremsiami. Nandini does not take History (clue 6), so Nandini takes Physics (white notebook) and Lalremsiami takes History (blue notebook, clue 1).

  4. Gurpreet has red (clue 2). Green and yellow are left for Farhan and Joseph; Farhan's is not yellow, so Farhan has green and Joseph has yellow.

  5. The yellow notebook is Joseph's, and Joseph takes Geography.

Question 11

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Five colleagues, Kavya, Rohit, Sana, Anirudh and Pooja, each work in a different department (Legal, Design, Accounts, Sales or HR) and each reach the office by a different mode (metro, bicycle, car, bus or scooter). The following is known:

1. The colleague in Design cycles to work.

2. Sana comes by car, but she does not work in Sales.

3. Kavya comes by neither bus nor bicycle, and she works in neither HR nor Accounts.

4. The colleague in Sales takes the bus.

5. Pooja rides a scooter.

6. Anirudh does not cycle to work.

7. Sana does not work in HR.

Which colleague works in HR?

Options for question 11

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AnswerA · Pooja

  1. Sana comes by car (clue 2) and Pooja by scooter (clue 5).

  2. Kavya uses neither the bus nor the bicycle (clue 3), so Kavya takes the metro. Bus and bicycle are left for Rohit and Anirudh; Anirudh does not cycle (clue 6), so Anirudh takes the bus and Rohit cycles.

  3. The cyclist works in Design (clue 1), so Rohit is in Design; the bus user is in Sales (clue 4), so Anirudh is in Sales.

  4. Kavya is not in HR or Accounts (clue 3), so Kavya is in Legal. Sana is not in HR (clue 7), so Sana is in Accounts and Pooja is in HR.

  5. Pooja works in HR.

Worth noting

Clue 7 is small but decisive: without it, Sana and Pooja could swap Accounts and HR.

Question 12

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Five colleagues, Kavya, Rohit, Sana, Anirudh and Pooja, each work in a different department (Legal, Design, Accounts, Sales or HR) and each reach the office by a different mode (metro, bicycle, car, bus or scooter). The following is known:

1. The colleague in Design cycles to work.

2. Sana comes by car, but she does not work in Sales.

3. Kavya comes by neither bus nor bicycle, and she works in neither HR nor Accounts.

4. The colleague in Sales takes the bus.

5. Pooja rides a scooter.

6. Anirudh does not cycle to work.

7. Sana does not work in HR.

The colleague who works in Accounts comes to the office by which mode?

Options for question 12

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AnswerB · car

  1. Sana comes by car (clue 2) and Pooja by scooter (clue 5).

  2. Kavya uses neither the bus nor the bicycle (clue 3), so Kavya takes the metro. Bus and bicycle are left for Rohit and Anirudh; Anirudh does not cycle (clue 6), so Anirudh takes the bus and Rohit cycles.

  3. The cyclist works in Design (clue 1), so Rohit is in Design; the bus user is in Sales (clue 4), so Anirudh is in Sales.

  4. Kavya is not in HR or Accounts (clue 3), so Kavya is in Legal. Sana is not in HR (clue 7), so Sana is in Accounts and Pooja is in HR.

  5. Sana is in Accounts, and she comes by car.

Question 13

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Five colleagues, Kavya, Rohit, Sana, Anirudh and Pooja, each work in a different department (Legal, Design, Accounts, Sales or HR) and each reach the office by a different mode (metro, bicycle, car, bus or scooter). The following is known:

1. The colleague in Design cycles to work.

2. Sana comes by car, but she does not work in Sales.

3. Kavya comes by neither bus nor bicycle, and she works in neither HR nor Accounts.

4. The colleague in Sales takes the bus.

5. Pooja rides a scooter.

6. Anirudh does not cycle to work.

7. Sana does not work in HR.

Which one of the following colleague and department pairs is correct?

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AnswerC · Rohit, Design

  1. Sana comes by car (clue 2) and Pooja by scooter (clue 5).

  2. Kavya uses neither the bus nor the bicycle (clue 3), so Kavya takes the metro. Bus and bicycle are left for Rohit and Anirudh; Anirudh does not cycle (clue 6), so Anirudh takes the bus and Rohit cycles.

  3. The cyclist works in Design (clue 1), so Rohit is in Design; the bus user is in Sales (clue 4), so Anirudh is in Sales.

  4. Kavya is not in HR or Accounts (clue 3), so Kavya is in Legal. Sana is not in HR (clue 7), so Sana is in Accounts and Pooja is in HR.

  5. Of the pairs given, only Rohit, Design matches.

Question 14

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Six friends, Arjun, Bindu, Deepak, Esha, Harish and Jyoti, attend the same music class. Each plays a different instrument (tabla, veena, harmonium, flute, violin or sitar) and each has a different favourite fruit (guava, lychee, mango, jamun, papaya or orange). The following is known:

1. The friend who likes mango plays the harmonium.

2. Jyoti plays the sitar, and Esha plays the flute.

3. Arjun likes guava. He plays neither the veena nor the violin.

4. The friend who plays the violin likes papaya.

5. Bindu does not like papaya, and Harish likes neither mango nor lychee.

6. Neither Esha nor Jyoti likes lychee or mango.

7. The flute player does not like orange, and Deepak does not play the veena.

In the music class, which instrument does Arjun play?

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AnswerD · tabla

  1. Jyoti plays the sitar and Esha the flute (clue 2). Arjun likes guava, so he cannot play the harmonium (that player likes mango, clue 1); he is barred from veena and violin (clue 3), so Arjun plays the tabla.

  2. Arjun plays the tabla.

Worth noting

Harmonium looks open for Arjun until clue 1 is read the other way: the harmonium player likes mango, and Arjun likes guava.

Question 15

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Six friends, Arjun, Bindu, Deepak, Esha, Harish and Jyoti, attend the same music class. Each plays a different instrument (tabla, veena, harmonium, flute, violin or sitar) and each has a different favourite fruit (guava, lychee, mango, jamun, papaya or orange). The following is known:

1. The friend who likes mango plays the harmonium.

2. Jyoti plays the sitar, and Esha plays the flute.

3. Arjun likes guava. He plays neither the veena nor the violin.

4. The friend who plays the violin likes papaya.

5. Bindu does not like papaya, and Harish likes neither mango nor lychee.

6. Neither Esha nor Jyoti likes lychee or mango.

7. The flute player does not like orange, and Deepak does not play the veena.

What is Jyoti's favourite fruit?

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AnswerA · orange

  1. Jyoti plays the sitar and Esha the flute (clue 2). Arjun likes guava, so he cannot play the harmonium (that player likes mango, clue 1); he is barred from veena and violin (clue 3), so Arjun plays the tabla.

  2. Veena, violin and harmonium are left for Bindu, Deepak and Harish. Harish does not like mango (clue 5), so he is not the harmonium player; Deepak does not play the veena (clue 7).

  3. Case Deepak = violin: then Harish = veena and Bindu = harmonium (mango). The fruits left for Esha, Jyoti and Harish are lychee, jamun and orange, but none of them may take lychee (clues 5 and 6). Impossible.

  4. So Deepak = harmonium (mango). Bindu cannot take the violin, whose player likes papaya (clues 4 and 5), so Bindu = veena and Harish = violin (papaya). Lychee, jamun and orange remain; Esha and Jyoti cannot take lychee, so Bindu likes lychee; the flute player Esha does not like orange (clue 7), so Esha likes jamun and Jyoti orange.

  5. Jyoti's favourite fruit is orange.

Question 16

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Six friends, Arjun, Bindu, Deepak, Esha, Harish and Jyoti, attend the same music class. Each plays a different instrument (tabla, veena, harmonium, flute, violin or sitar) and each has a different favourite fruit (guava, lychee, mango, jamun, papaya or orange). The following is known:

1. The friend who likes mango plays the harmonium.

2. Jyoti plays the sitar, and Esha plays the flute.

3. Arjun likes guava. He plays neither the veena nor the violin.

4. The friend who plays the violin likes papaya.

5. Bindu does not like papaya, and Harish likes neither mango nor lychee.

6. Neither Esha nor Jyoti likes lychee or mango.

7. The flute player does not like orange, and Deepak does not play the veena.

The friend whose favourite fruit is lychee plays which instrument?

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AnswerC · veena

  1. Jyoti plays the sitar and Esha the flute (clue 2). Arjun likes guava, so he cannot play the harmonium (that player likes mango, clue 1); he is barred from veena and violin (clue 3), so Arjun plays the tabla.

  2. Veena, violin and harmonium are left for Bindu, Deepak and Harish. Harish does not like mango (clue 5), so he is not the harmonium player; Deepak does not play the veena (clue 7).

  3. Case Deepak = violin: then Harish = veena and Bindu = harmonium (mango). The fruits left for Esha, Jyoti and Harish are lychee, jamun and orange, but none of them may take lychee (clues 5 and 6). Impossible.

  4. So Deepak = harmonium (mango). Bindu cannot take the violin, whose player likes papaya (clues 4 and 5), so Bindu = veena and Harish = violin (papaya). Lychee, jamun and orange remain; Esha and Jyoti cannot take lychee, so Bindu likes lychee; the flute player Esha does not like orange (clue 7), so Esha likes jamun and Jyoti orange.

  5. Bindu likes lychee and plays the veena.

Question 17

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Manoj, Nazia, Oindrila, Pranav and Rukmini live in five different cities (Nagpur, Kochi, Guwahati, Surat and Jaipur), work in five different professions (chef, doctor, teacher, lawyer and engineer) and keep five different pets (parrot, cat, rabbit, dog and fish), one each. The following is known:

1. The doctor lives in Kochi and keeps a cat.

2. Oindrila is a teacher. She lives in neither Jaipur nor Surat.

3. The person from Surat keeps a dog and is not an engineer.

4. Rukmini lives in Jaipur and keeps fish.

5. Manoj is neither the doctor nor the lawyer, and he does not live in Guwahati.

6. The chef keeps a parrot.

7. Nazia is not from Surat, and Pranav does not keep a rabbit.

In which city does Manoj live?

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AnswerA · Nagpur

  1. Rukmini: Jaipur, fish (clue 4). Oindrila is the teacher, so she is not in Kochi (the doctor's city); with clue 2 she is in Nagpur or Guwahati.

  2. Surat is not Oindrila's, Rukmini's or Nazia's (clue 7), so it is Manoj's or Pranav's. The Surat person keeps a dog (clue 3), so is not the chef (parrot, clue 6), the doctor (Kochi) or the engineer: the Surat person is the lawyer.

  3. Manoj is not the lawyer (clue 5), so Pranav = Surat, lawyer, dog. Manoj is not in Guwahati, and Kochi is the doctor's, so Manoj = Nagpur; then Oindrila = Guwahati and Nazia = Kochi, doctor, cat (clue 1).

  4. Manoj lives in Nagpur.

Question 18

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Manoj, Nazia, Oindrila, Pranav and Rukmini live in five different cities (Nagpur, Kochi, Guwahati, Surat and Jaipur), work in five different professions (chef, doctor, teacher, lawyer and engineer) and keep five different pets (parrot, cat, rabbit, dog and fish), one each. The following is known:

1. The doctor lives in Kochi and keeps a cat.

2. Oindrila is a teacher. She lives in neither Jaipur nor Surat.

3. The person from Surat keeps a dog and is not an engineer.

4. Rukmini lives in Jaipur and keeps fish.

5. Manoj is neither the doctor nor the lawyer, and he does not live in Guwahati.

6. The chef keeps a parrot.

7. Nazia is not from Surat, and Pranav does not keep a rabbit.

What is Rukmini's profession?

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AnswerC · engineer

  1. Rukmini: Jaipur, fish (clue 4). Oindrila is the teacher, so she is not in Kochi (the doctor's city); with clue 2 she is in Nagpur or Guwahati.

  2. Surat is not Oindrila's, Rukmini's or Nazia's (clue 7), so it is Manoj's or Pranav's. The Surat person keeps a dog (clue 3), so is not the chef (parrot, clue 6), the doctor (Kochi) or the engineer: the Surat person is the lawyer.

  3. Manoj is not the lawyer (clue 5), so Pranav = Surat, lawyer, dog. Manoj is not in Guwahati, and Kochi is the doctor's, so Manoj = Nagpur; then Oindrila = Guwahati and Nazia = Kochi, doctor, cat (clue 1).

  4. Chef and engineer are left for Manoj and Rukmini. Rukmini keeps fish, and the chef keeps a parrot, so Rukmini is the engineer and Manoj the chef (parrot). Oindrila keeps the rabbit.

  5. Rukmini is the engineer.

Worth noting

Chef is ruled out for Rukmini by her pet: the chef keeps a parrot and Rukmini keeps fish.

Question 19

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Five students, Farhan, Gurpreet, Nandini, Joseph and Lalremsiami, each take a different elective (Physics, History, Economics, Biology or Geography) and each keep their notes in a notebook of a different colour (red, blue, green, yellow or white). The following is known:

1. The student who takes History uses the blue notebook.

2. Gurpreet's notebook is red.

3. The Physics student's notebook is white.

4. Farhan takes neither History nor Geography, and his notebook is neither yellow nor white.

5. Joseph's notebook is neither blue nor white, and he does not take Biology.

6. Nandini does not take History.

7. The Biology student and the Geography student are Gurpreet and Joseph, in some order.

About the five students and their electives, which one of the following statements is true?

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AnswerB · The Economics student uses the green notebook

  1. Clue 7 says Biology and Geography go to Gurpreet and Joseph; Joseph does not take Biology (clue 5), so Joseph takes Geography and Gurpreet takes Biology.

  2. Farhan does not take History (clue 4), and not Physics either, because the Physics notebook is white (clue 3) and Farhan's is not white. So Farhan takes Economics.

  3. Physics and History are left for Nandini and Lalremsiami. Nandini does not take History (clue 6), so Nandini takes Physics (white notebook) and Lalremsiami takes History (blue notebook, clue 1).

  4. Gurpreet has red (clue 2). Green and yellow are left for Farhan and Joseph; Farhan's is not yellow, so Farhan has green and Joseph has yellow.

  5. Farhan takes Economics and uses green, so that statement is the true one.

Worth noting

Clue 7 alone allows Gurpreet to take Geography; only clue 5 settles which of the two takes Biology.

Question 20

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Six friends, Arjun, Bindu, Deepak, Esha, Harish and Jyoti, attend the same music class. Each plays a different instrument (tabla, veena, harmonium, flute, violin or sitar) and each has a different favourite fruit (guava, lychee, mango, jamun, papaya or orange). The following is known:

1. The friend who likes mango plays the harmonium.

2. Jyoti plays the sitar, and Esha plays the flute.

3. Arjun likes guava. He plays neither the veena nor the violin.

4. The friend who plays the violin likes papaya.

5. Bindu does not like papaya, and Harish likes neither mango nor lychee.

6. Neither Esha nor Jyoti likes lychee or mango.

7. The flute player does not like orange, and Deepak does not play the veena.

Who in the music class plays the harmonium?

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AnswerB · Deepak

  1. Jyoti plays the sitar and Esha the flute (clue 2). Arjun likes guava, so he cannot play the harmonium (that player likes mango, clue 1); he is barred from veena and violin (clue 3), so Arjun plays the tabla.

  2. Veena, violin and harmonium are left for Bindu, Deepak and Harish. Harish does not like mango (clue 5), so he is not the harmonium player; Deepak does not play the veena (clue 7).

  3. Case Deepak = violin: then Harish = veena and Bindu = harmonium (mango). The fruits left for Esha, Jyoti and Harish are lychee, jamun and orange, but none of them may take lychee (clues 5 and 6). Impossible.

  4. So Deepak = harmonium (mango). Bindu cannot take the violin, whose player likes papaya (clues 4 and 5), so Bindu = veena and Harish = violin (papaya). Lychee, jamun and orange remain; Esha and Jyoti cannot take lychee, so Bindu likes lychee; the flute player Esha does not like orange (clue 7), so Esha likes jamun and Jyoti orange.

  5. Deepak plays the harmonium.

Worth noting

Bindu survives every direct clue; only the case split in step 3 (it leaves no fruit for Harish) removes her.

Question 21

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Six friends, Arjun, Bindu, Deepak, Esha, Harish and Jyoti, attend the same music class. Each plays a different instrument (tabla, veena, harmonium, flute, violin or sitar) and each has a different favourite fruit (guava, lychee, mango, jamun, papaya or orange). The following is known:

1. The friend who likes mango plays the harmonium.

2. Jyoti plays the sitar, and Esha plays the flute.

3. Arjun likes guava. He plays neither the veena nor the violin.

4. The friend who plays the violin likes papaya.

5. Bindu does not like papaya, and Harish likes neither mango nor lychee.

6. Neither Esha nor Jyoti likes lychee or mango.

7. The flute player does not like orange, and Deepak does not play the veena.

Which one of the following statements about the six friends is FALSE?

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AnswerD · Bindu plays the harmonium

  1. Jyoti plays the sitar and Esha the flute (clue 2). Arjun likes guava, so he cannot play the harmonium (that player likes mango, clue 1); he is barred from veena and violin (clue 3), so Arjun plays the tabla.

  2. Veena, violin and harmonium are left for Bindu, Deepak and Harish. Harish does not like mango (clue 5), so he is not the harmonium player; Deepak does not play the veena (clue 7).

  3. Case Deepak = violin: then Harish = veena and Bindu = harmonium (mango). The fruits left for Esha, Jyoti and Harish are lychee, jamun and orange, but none of them may take lychee (clues 5 and 6). Impossible.

  4. So Deepak = harmonium (mango). Bindu cannot take the violin, whose player likes papaya (clues 4 and 5), so Bindu = veena and Harish = violin (papaya). Lychee, jamun and orange remain; Esha and Jyoti cannot take lychee, so Bindu likes lychee; the flute player Esha does not like orange (clue 7), so Esha likes jamun and Jyoti orange.

  5. Bindu plays the veena, so the statement that she plays the harmonium is the false one.

Worth noting

Read the question word FALSE before you start matching: three of these statements are true.

Question 22

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Manoj, Nazia, Oindrila, Pranav and Rukmini live in five different cities (Nagpur, Kochi, Guwahati, Surat and Jaipur), work in five different professions (chef, doctor, teacher, lawyer and engineer) and keep five different pets (parrot, cat, rabbit, dog and fish), one each. The following is known:

1. The doctor lives in Kochi and keeps a cat.

2. Oindrila is a teacher. She lives in neither Jaipur nor Surat.

3. The person from Surat keeps a dog and is not an engineer.

4. Rukmini lives in Jaipur and keeps fish.

5. Manoj is neither the doctor nor the lawyer, and he does not live in Guwahati.

6. The chef keeps a parrot.

7. Nazia is not from Surat, and Pranav does not keep a rabbit.

Which pet does the lawyer keep?

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AnswerB · dog

  1. Rukmini: Jaipur, fish (clue 4). Oindrila is the teacher, so she is not in Kochi (the doctor's city); with clue 2 she is in Nagpur or Guwahati.

  2. Surat is not Oindrila's, Rukmini's or Nazia's (clue 7), so it is Manoj's or Pranav's. The Surat person keeps a dog (clue 3), so is not the chef (parrot, clue 6), the doctor (Kochi) or the engineer: the Surat person is the lawyer.

  3. Manoj is not the lawyer (clue 5), so Pranav = Surat, lawyer, dog. Manoj is not in Guwahati, and Kochi is the doctor's, so Manoj = Nagpur; then Oindrila = Guwahati and Nazia = Kochi, doctor, cat (clue 1).

  4. The lawyer is Pranav, who keeps the dog.

Worth noting

The key step is seeing that the Surat person must be the lawyer: every other profession is tied to another city or pet.

Question 23

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Manoj, Nazia, Oindrila, Pranav and Rukmini live in five different cities (Nagpur, Kochi, Guwahati, Surat and Jaipur), work in five different professions (chef, doctor, teacher, lawyer and engineer) and keep five different pets (parrot, cat, rabbit, dog and fish), one each. The following is known:

1. The doctor lives in Kochi and keeps a cat.

2. Oindrila is a teacher. She lives in neither Jaipur nor Surat.

3. The person from Surat keeps a dog and is not an engineer.

4. Rukmini lives in Jaipur and keeps fish.

5. Manoj is neither the doctor nor the lawyer, and he does not live in Guwahati.

6. The chef keeps a parrot.

7. Nazia is not from Surat, and Pranav does not keep a rabbit.

Who keeps the rabbit, and in which city does that person live?

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AnswerD · Oindrila, Guwahati

  1. Rukmini: Jaipur, fish (clue 4). Oindrila is the teacher, so she is not in Kochi (the doctor's city); with clue 2 she is in Nagpur or Guwahati.

  2. Surat is not Oindrila's, Rukmini's or Nazia's (clue 7), so it is Manoj's or Pranav's. The Surat person keeps a dog (clue 3), so is not the chef (parrot, clue 6), the doctor (Kochi) or the engineer: the Surat person is the lawyer.

  3. Manoj is not the lawyer (clue 5), so Pranav = Surat, lawyer, dog. Manoj is not in Guwahati, and Kochi is the doctor's, so Manoj = Nagpur; then Oindrila = Guwahati and Nazia = Kochi, doctor, cat (clue 1).

  4. Chef and engineer are left for Manoj and Rukmini. Rukmini keeps fish, and the chef keeps a parrot, so Rukmini is the engineer and Manoj the chef (parrot). Oindrila keeps the rabbit.

  5. The rabbit is Oindrila's, and she lives in Guwahati.

Worth noting

Oindrila, Nagpur is what you get if you stop at clue 2, which leaves her two cities.

Question 24

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Manoj, Nazia, Oindrila, Pranav and Rukmini live in five different cities (Nagpur, Kochi, Guwahati, Surat and Jaipur), work in five different professions (chef, doctor, teacher, lawyer and engineer) and keep five different pets (parrot, cat, rabbit, dog and fish), one each. The following is known:

1. The doctor lives in Kochi and keeps a cat.

2. Oindrila is a teacher. She lives in neither Jaipur nor Surat.

3. The person from Surat keeps a dog and is not an engineer.

4. Rukmini lives in Jaipur and keeps fish.

5. Manoj is neither the doctor nor the lawyer, and he does not live in Guwahati.

6. The chef keeps a parrot.

7. Nazia is not from Surat, and Pranav does not keep a rabbit.

Which one of the following statements about the five people is true?

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AnswerA · The chef lives in Nagpur

  1. Rukmini: Jaipur, fish (clue 4). Oindrila is the teacher, so she is not in Kochi (the doctor's city); with clue 2 she is in Nagpur or Guwahati.

  2. Surat is not Oindrila's, Rukmini's or Nazia's (clue 7), so it is Manoj's or Pranav's. The Surat person keeps a dog (clue 3), so is not the chef (parrot, clue 6), the doctor (Kochi) or the engineer: the Surat person is the lawyer.

  3. Manoj is not the lawyer (clue 5), so Pranav = Surat, lawyer, dog. Manoj is not in Guwahati, and Kochi is the doctor's, so Manoj = Nagpur; then Oindrila = Guwahati and Nazia = Kochi, doctor, cat (clue 1).

  4. Chef and engineer are left for Manoj and Rukmini. Rukmini keeps fish, and the chef keeps a parrot, so Rukmini is the engineer and Manoj the chef (parrot). Oindrila keeps the rabbit.

  5. Manoj is the chef and lives in Nagpur, so that statement is the true one.

Floors and boxes

21 questions

Question 25

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Aditi, Balwinder, Chinmay, Dolma and Emmanuel live in a five-storey building, one person on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Dolma lives on the top floor.

2. Aditi lives immediately above Chinmay.

3. Emmanuel lives above Aditi but below Balwinder.

4. Emmanuel lives on an odd-numbered floor.

Who lives on floor 3 of the five-storey building?

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AnswerB · Emmanuel

  1. Dolma is on floor 5 (clue 1), so the other four fill floors 1 to 4.

  2. Clue 2 puts Chinmay directly under Aditi, and clue 3 puts Emmanuel above Aditi and Balwinder above Emmanuel.

  3. Upward order is therefore Chinmay, Aditi, Emmanuel, Balwinder on floors 1, 2, 3 and 4.

  4. Floor 3 is Emmanuel's.

Question 26

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Aditi, Balwinder, Chinmay, Dolma and Emmanuel live in a five-storey building, one person on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Dolma lives on the top floor.

2. Aditi lives immediately above Chinmay.

3. Emmanuel lives above Aditi but below Balwinder.

4. Emmanuel lives on an odd-numbered floor.

How many people live on the floors between Chinmay's floor and Dolma's floor?

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AnswerC · 3

  1. Dolma is on floor 5 (clue 1), so the other four fill floors 1 to 4.

  2. Clue 2 puts Chinmay directly under Aditi, and clue 3 puts Emmanuel above Aditi and Balwinder above Emmanuel.

  3. Upward order is therefore Chinmay, Aditi, Emmanuel, Balwinder on floors 1, 2, 3 and 4.

  4. Chinmay is on floor 1 and Dolma on floor 5. The floors in between are 2, 3 and 4, so 3 people.

Worth noting

4 is the difference 5−15 - 1. The number of floors strictly between two floors is the difference minus 1.

Question 27

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Aditi, Balwinder, Chinmay, Dolma and Emmanuel live in a five-storey building, one person on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Dolma lives on the top floor.

2. Aditi lives immediately above Chinmay.

3. Emmanuel lives above Aditi but below Balwinder.

4. Emmanuel lives on an odd-numbered floor.

Whose flat is immediately above Balwinder's?

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AnswerD · Dolma

  1. Dolma is on floor 5 (clue 1), so the other four fill floors 1 to 4.

  2. Clue 2 puts Chinmay directly under Aditi, and clue 3 puts Emmanuel above Aditi and Balwinder above Emmanuel.

  3. Upward order is therefore Chinmay, Aditi, Emmanuel, Balwinder on floors 1, 2, 3 and 4.

  4. Balwinder is on floor 4, so the person immediately above is Dolma on floor 5.

Worth noting

Emmanuel is immediately BELOW Balwinder; read the direction carefully.

Question 28

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Six people, Hemant, Ishita, Kuldeep, Lavanya, Moinuddin and Neha, live on the six floors of a building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. Each person comes from a different city: Agra, Imphal, Mysuru, Rajkot, Ranchi or Varanasi. The following is known:

1. The person from Ranchi lives on the top floor.

2. Ishita lives immediately below the person from Ranchi.

3. Exactly two people live between Hemant and Ishita.

4. Neha, who is from Agra, lives immediately above Hemant.

5. The person from Imphal lives below Hemant.

6. Moinuddin lives above Kuldeep, and Kuldeep lives above Lavanya.

7. The person from Varanasi lives immediately above Neha, and Hemant is not from Mysuru.

On which floor number does Kuldeep live?

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AnswerB · 4

  1. The Ranchi person is on floor 6 (clue 1), so Ishita is on floor 5 (clue 2). Two people between Hemant and Ishita puts Hemant on floor 2 (clue 3), and Neha of Agra on floor 3 (clue 4).

  2. Floors 1, 4 and 6 are left for Kuldeep, Lavanya and Moinuddin. Clue 6 (Moinuddin above Kuldeep above Lavanya) gives Lavanya 1, Kuldeep 4, Moinuddin 6.

  3. Kuldeep lives on floor 4.

Worth noting

Floor 6 would put Kuldeep on top, but clue 6 needs Moinuddin above him.

Question 29

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Six boxes, P, Q, R, S, T and U, are stacked one on top of another in a single pile. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. Each box is a different colour: black, white, red, green, blue or orange. The following is known:

1. Box S, which is black, is at the bottom.

2. Box Q is green, and it is immediately above the red box.

3. Exactly one box lies between box P and box Q, and P is below Q.

4. Box R is at the top, immediately above box T, which is blue.

5. The white box is immediately below box U.

What colour is box U in the stack?

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AnswerB · red

  1. Box S is at position 1 (clue 1). Box R is on top at position 6 with the blue box T at 5 (clue 4).

  2. Q is green and has the red box directly under it (clue 2). Q cannot be at 2, because position 1 is black, so Q is at 3 or 4.

  3. P is two places below Q (clue 3). If Q were at 3, P would be at 1, which is S. So Q is at 4 and P at 2, leaving U at 3.

  4. The white box is directly under U, so P is white; the red box is directly under Q, so U is red. R takes the last colour, orange.

  5. Box U is red.

Question 30

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Seven cartons in a godown are stacked in a single pile. Each holds something different: books, clothes, lamps, plates, shoes, tools or toys. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. The following is known:

1. The box of shoes is exactly in the middle of the stack.

2. The box of books is immediately above the box of tools.

3. Exactly two boxes lie between the box of books and the box of plates.

4. The box of clothes is above the box of toys, and the box of toys is above the box of plates.

5. The box of lamps is below the box of shoes.

Which carton is at the very top of the pile?

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AnswerD · clothes

  1. Shoes are at position 4, the middle of seven (clue 1). Books sit directly on tools (clue 2).

  2. Plates need two cartons above them (toys, then clothes, clue 4), so plates are at 5 or lower; plates are three places from books (clue 3).

  3. Try books at 2 (tools 1): plates at 5, toys 6, clothes 7, and lamps take 3, which is below shoes (clue 5). Everything fits.

  4. Books at 3 would push plates to 6 (too high); books at 6 or 7 would put plates at 3 or 4, and with tools at 5 or 6 there is no room above for both toys and clothes. So books at 2 is the only arrangement.

  5. Clothes are at position 7, the top.

Question 31

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Seven cartons in a godown are stacked in a single pile. Each holds something different: books, clothes, lamps, plates, shoes, tools or toys. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. The following is known:

1. The box of shoes is exactly in the middle of the stack.

2. The box of books is immediately above the box of tools.

3. Exactly two boxes lie between the box of books and the box of plates.

4. The box of clothes is above the box of toys, and the box of toys is above the box of plates.

5. The box of lamps is below the box of shoes.

What does the carton directly beneath the shoes hold?

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AnswerC · lamps

  1. Shoes are at position 4, the middle of seven (clue 1). Books sit directly on tools (clue 2).

  2. Plates need two cartons above them (toys, then clothes, clue 4), so plates are at 5 or lower; plates are three places from books (clue 3).

  3. Try books at 2 (tools 1): plates at 5, toys 6, clothes 7, and lamps take 3, which is below shoes (clue 5). Everything fits.

  4. Shoes are at 4, and the carton at 3 holds lamps.

Worth noting

Plates are directly ABOVE the shoes.

Question 32

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Seven cartons in a godown are stacked in a single pile. Each holds something different: books, clothes, lamps, plates, shoes, tools or toys. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. The following is known:

1. The box of shoes is exactly in the middle of the stack.

2. The box of books is immediately above the box of tools.

3. Exactly two boxes lie between the box of books and the box of plates.

4. The box of clothes is above the box of toys, and the box of toys is above the box of plates.

5. The box of lamps is below the box of shoes.

Counting from the TOP of the pile, at which position is the carton of books?

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AnswerD · 6

  1. Shoes are at position 4, the middle of seven (clue 1). Books sit directly on tools (clue 2).

  2. Plates need two cartons above them (toys, then clothes, clue 4), so plates are at 5 or lower; plates are three places from books (clue 3).

  3. Try books at 2 (tools 1): plates at 5, toys 6, clothes 7, and lamps take 3, which is below shoes (clue 5). Everything fits.

  4. Books at 3 would push plates to 6 (too high); books at 6 or 7 would put plates at 3 or 4, and with tools at 5 or 6 there is no room above for both toys and clothes. So books at 2 is the only arrangement.

  5. Books are 2nd from the bottom. From the top: 7−2+17 - 2 + 1 = 6th.

Worth noting

2 is the position from the bottom. Position from top = total − position from bottom + 1.

Question 33

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Aditi, Balwinder, Chinmay, Dolma and Emmanuel live in a five-storey building, one person on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Dolma lives on the top floor.

2. Aditi lives immediately above Chinmay.

3. Emmanuel lives above Aditi but below Balwinder.

4. Emmanuel lives on an odd-numbered floor.

Which one of the following clues could be taken out of the list, with every person's floor still fixed by the remaining clues?

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AnswerA · Emmanuel lives on an odd-numbered floor.

  1. Clues 1, 2 and 3 alone already give Chinmay 1, Aditi 2, Emmanuel 3, Balwinder 4, Dolma 5; the solving above never used clue 4.

  2. Without clue 1, Dolma need not be on top: Chinmay 1, Aditi 2, Emmanuel 3, Dolma 4, Balwinder 5 also fits.

  3. Without clue 2, Aditi 1, Chinmay 2, Emmanuel 3, Balwinder 4, Dolma 5 fits. Without clue 3, Emmanuel 1, Chinmay 2, Aditi 3, Balwinder 4, Dolma 5 fits.

  4. So only the clue about Emmanuel's odd-numbered floor can be removed.

Worth noting

A clue that the solution never used is the candidate; then check that every other clue really is needed.

Question 34

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Six people, Hemant, Ishita, Kuldeep, Lavanya, Moinuddin and Neha, live on the six floors of a building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. Each person comes from a different city: Agra, Imphal, Mysuru, Rajkot, Ranchi or Varanasi. The following is known:

1. The person from Ranchi lives on the top floor.

2. Ishita lives immediately below the person from Ranchi.

3. Exactly two people live between Hemant and Ishita.

4. Neha, who is from Agra, lives immediately above Hemant.

5. The person from Imphal lives below Hemant.

6. Moinuddin lives above Kuldeep, and Kuldeep lives above Lavanya.

7. The person from Varanasi lives immediately above Neha, and Hemant is not from Mysuru.

Moinuddin, one of the six residents, comes from which city?

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AnswerC · Ranchi

  1. The Ranchi person is on floor 6 (clue 1), so Ishita is on floor 5 (clue 2). Two people between Hemant and Ishita puts Hemant on floor 2 (clue 3), and Neha of Agra on floor 3 (clue 4).

  2. Floors 1, 4 and 6 are left for Kuldeep, Lavanya and Moinuddin. Clue 6 (Moinuddin above Kuldeep above Lavanya) gives Lavanya 1, Kuldeep 4, Moinuddin 6.

  3. Imphal is below Hemant (clue 5), so floor 1: Lavanya is from Imphal. Moinuddin on floor 6 is from Ranchi.

  4. Moinuddin is from Ranchi.

Question 35

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Six people, Hemant, Ishita, Kuldeep, Lavanya, Moinuddin and Neha, live on the six floors of a building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. Each person comes from a different city: Agra, Imphal, Mysuru, Rajkot, Ranchi or Varanasi. The following is known:

1. The person from Ranchi lives on the top floor.

2. Ishita lives immediately below the person from Ranchi.

3. Exactly two people live between Hemant and Ishita.

4. Neha, who is from Agra, lives immediately above Hemant.

5. The person from Imphal lives below Hemant.

6. Moinuddin lives above Kuldeep, and Kuldeep lives above Lavanya.

7. The person from Varanasi lives immediately above Neha, and Hemant is not from Mysuru.

Which resident of the building is from Mysuru?

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AnswerD · Ishita

  1. The Ranchi person is on floor 6 (clue 1), so Ishita is on floor 5 (clue 2). Two people between Hemant and Ishita puts Hemant on floor 2 (clue 3), and Neha of Agra on floor 3 (clue 4).

  2. Floors 1, 4 and 6 are left for Kuldeep, Lavanya and Moinuddin. Clue 6 (Moinuddin above Kuldeep above Lavanya) gives Lavanya 1, Kuldeep 4, Moinuddin 6.

  3. Imphal is below Hemant (clue 5), so floor 1: Lavanya is from Imphal. Moinuddin on floor 6 is from Ranchi.

  4. Varanasi is immediately above Neha, so floor 4: Kuldeep. Hemant is not from Mysuru, so Hemant is from Rajkot and Ishita from Mysuru.

  5. Ishita is from Mysuru.

Worth noting

Hemant is the tempting answer if the last part of clue 7 is missed.

Question 36

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Seven people, Om, Priyanka, Rehan, Shalini, Tushar, Ujjwala and Vikram, live in a seven-storey building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Om lives on an even-numbered floor, but not on floor 2.

2. Exactly two people live between Om and Shalini.

3. Rehan lives immediately above Ujjwala.

4. Tushar lives below Priyanka, and Priyanka lives below Vikram.

5. Ujjwala lives above Om.

6. Vikram lives below Om.

Who lives on the floor immediately above Om's?

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AnswerB · Ujjwala

  1. Clues 4 and 6 give Tushar below Priyanka below Vikram below Om, so at least three people live below Om. With clue 1, Om is on floor 4 or 6.

  2. If Om were on floor 6, Ujjwala (above Om, clue 5) would be on floor 7 and Rehan, immediately above her (clue 3), would have no floor. So Om is on floor 4.

  3. Tushar, Priyanka and Vikram take floors 1, 2 and 3 in that order. Shalini is three floors from Om (clue 2): floor 1 is taken, so she is on floor 7.

  4. Floors 5 and 6 remain for Ujjwala and Rehan, with Rehan immediately above: Ujjwala 5, Rehan 6.

  5. Om is on floor 4, so floor 5 is Ujjwala's.

Worth noting

Vikram is immediately BELOW Om.

Question 37

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Seven people, Om, Priyanka, Rehan, Shalini, Tushar, Ujjwala and Vikram, live in a seven-storey building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Om lives on an even-numbered floor, but not on floor 2.

2. Exactly two people live between Om and Shalini.

3. Rehan lives immediately above Ujjwala.

4. Tushar lives below Priyanka, and Priyanka lives below Vikram.

5. Ujjwala lives above Om.

6. Vikram lives below Om.

Priyanka lives on which floor of the seven-storey building?

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AnswerA · 2

  1. Clues 4 and 6 give Tushar below Priyanka below Vikram below Om, so at least three people live below Om. With clue 1, Om is on floor 4 or 6.

  2. If Om were on floor 6, Ujjwala (above Om, clue 5) would be on floor 7 and Rehan, immediately above her (clue 3), would have no floor. So Om is on floor 4.

  3. Tushar, Priyanka and Vikram take floors 1, 2 and 3 in that order. Shalini is three floors from Om (clue 2): floor 1 is taken, so she is on floor 7.

  4. Priyanka is on floor 2.

Worth noting

3 is Vikram's floor: 'Priyanka below Vikram' leaves only one floor, floor 2, once Tushar is under her.

Question 38

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Six boxes, P, Q, R, S, T and U, are stacked one on top of another in a single pile. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. Each box is a different colour: black, white, red, green, blue or orange. The following is known:

1. Box S, which is black, is at the bottom.

2. Box Q is green, and it is immediately above the red box.

3. Exactly one box lies between box P and box Q, and P is below Q.

4. Box R is at the top, immediately above box T, which is blue.

5. The white box is immediately below box U.

Which box rests directly on top of the green box?

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AnswerC · T

  1. Box S is at position 1 (clue 1). Box R is on top at position 6 with the blue box T at 5 (clue 4).

  2. Q is green and has the red box directly under it (clue 2). Q cannot be at 2, because position 1 is black, so Q is at 3 or 4.

  3. P is two places below Q (clue 3). If Q were at 3, P would be at 1, which is S. So Q is at 4 and P at 2, leaving U at 3.

  4. The green box Q is at position 4, so the box directly on it, at 5, is T.

Worth noting

U is directly UNDER the green box; R is above it but not directly.

Question 39

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Six boxes, P, Q, R, S, T and U, are stacked one on top of another in a single pile. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. Each box is a different colour: black, white, red, green, blue or orange. The following is known:

1. Box S, which is black, is at the bottom.

2. Box Q is green, and it is immediately above the red box.

3. Exactly one box lies between box P and box Q, and P is below Q.

4. Box R is at the top, immediately above box T, which is blue.

5. The white box is immediately below box U.

Counting only the boxes strictly between them, how many boxes separate box P from box R?

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AnswerB · 3

  1. Box S is at position 1 (clue 1). Box R is on top at position 6 with the blue box T at 5 (clue 4).

  2. Q is green and has the red box directly under it (clue 2). Q cannot be at 2, because position 1 is black, so Q is at 3 or 4.

  3. P is two places below Q (clue 3). If Q were at 3, P would be at 1, which is S. So Q is at 4 and P at 2, leaving U at 3.

  4. P is at 2 and R at 6; positions 3, 4 and 5 lie between them, so 3 boxes.

Worth noting

4 is the difference 6−26 - 2; the boxes between are one fewer.

Question 40

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Six boxes, P, Q, R, S, T and U, are stacked one on top of another in a single pile. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. Each box is a different colour: black, white, red, green, blue or orange. The following is known:

1. Box S, which is black, is at the bottom.

2. Box Q is green, and it is immediately above the red box.

3. Exactly one box lies between box P and box Q, and P is below Q.

4. Box R is at the top, immediately above box T, which is blue.

5. The white box is immediately below box U.

Which one of the following statements about the stack of six boxes is true?

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AnswerA · The orange box is at the top

  1. Box S is at position 1 (clue 1). Box R is on top at position 6 with the blue box T at 5 (clue 4).

  2. Q is green and has the red box directly under it (clue 2). Q cannot be at 2, because position 1 is black, so Q is at 3 or 4.

  3. P is two places below Q (clue 3). If Q were at 3, P would be at 1, which is S. So Q is at 4 and P at 2, leaving U at 3.

  4. The white box is directly under U, so P is white; the red box is directly under Q, so U is red. R takes the last colour, orange.

  5. R, at the top, is orange, so that statement is the true one.

Worth noting

P is two places below Q, not immediately below: one box, U, lies between them.

Question 41

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Seven cartons in a godown are stacked in a single pile. Each holds something different: books, clothes, lamps, plates, shoes, tools or toys. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. The following is known:

1. The box of shoes is exactly in the middle of the stack.

2. The box of books is immediately above the box of tools.

3. Exactly two boxes lie between the box of books and the box of plates.

4. The box of clothes is above the box of toys, and the box of toys is above the box of plates.

5. The box of lamps is below the box of shoes.

How many cartons are there between the carton of tools and the carton of toys?

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AnswerB · 4

  1. Shoes are at position 4, the middle of seven (clue 1). Books sit directly on tools (clue 2).

  2. Plates need two cartons above them (toys, then clothes, clue 4), so plates are at 5 or lower; plates are three places from books (clue 3).

  3. Try books at 2 (tools 1): plates at 5, toys 6, clothes 7, and lamps take 3, which is below shoes (clue 5). Everything fits.

  4. Books at 3 would push plates to 6 (too high); books at 6 or 7 would put plates at 3 or 4, and with tools at 5 or 6 there is no room above for both toys and clothes. So books at 2 is the only arrangement.

  5. Tools are at 1 and toys at 6; positions 2, 3, 4 and 5 lie between: 4 cartons.

Worth noting

5 is the difference 6−16 - 1, which counts one end as well.

Question 42

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Seven cartons in a godown are stacked in a single pile. Each holds something different: books, clothes, lamps, plates, shoes, tools or toys. Positions are counted from the bottom: the bottom box is position 1. 'Above' or 'below' means anywhere higher or lower in the stack; 'immediately above' means resting directly on top of it. The following is known:

1. The box of shoes is exactly in the middle of the stack.

2. The box of books is immediately above the box of tools.

3. Exactly two boxes lie between the box of books and the box of plates.

4. The box of clothes is above the box of toys, and the box of toys is above the box of plates.

5. The box of lamps is below the box of shoes.

Which two cartons are placed one directly on the other?

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AnswerA · plates and toys

  1. Shoes are at position 4, the middle of seven (clue 1). Books sit directly on tools (clue 2).

  2. Plates need two cartons above them (toys, then clothes, clue 4), so plates are at 5 or lower; plates are three places from books (clue 3).

  3. Try books at 2 (tools 1): plates at 5, toys 6, clothes 7, and lamps take 3, which is below shoes (clue 5). Everything fits.

  4. Books at 3 would push plates to 6 (too high); books at 6 or 7 would put plates at 3 or 4, and with tools at 5 or 6 there is no room above for both toys and clothes. So books at 2 is the only arrangement.

  5. Plates are at 5 and toys at 6, so they touch. Lamps and plates (3, 5), tools and lamps (1, 3) and shoes and toys (4, 6) each have one carton between them.

Question 43

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Six people, Hemant, Ishita, Kuldeep, Lavanya, Moinuddin and Neha, live on the six floors of a building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. Each person comes from a different city: Agra, Imphal, Mysuru, Rajkot, Ranchi or Varanasi. The following is known:

1. The person from Ranchi lives on the top floor.

2. Ishita lives immediately below the person from Ranchi.

3. Exactly two people live between Hemant and Ishita.

4. Neha, who is from Agra, lives immediately above Hemant.

5. The person from Imphal lives below Hemant.

6. Moinuddin lives above Kuldeep, and Kuldeep lives above Lavanya.

7. The person from Varanasi lives immediately above Neha, and Hemant is not from Mysuru.

How many people live between the person from Imphal and the person from Varanasi?

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AnswerA · 2

  1. The Ranchi person is on floor 6 (clue 1), so Ishita is on floor 5 (clue 2). Two people between Hemant and Ishita puts Hemant on floor 2 (clue 3), and Neha of Agra on floor 3 (clue 4).

  2. Floors 1, 4 and 6 are left for Kuldeep, Lavanya and Moinuddin. Clue 6 (Moinuddin above Kuldeep above Lavanya) gives Lavanya 1, Kuldeep 4, Moinuddin 6.

  3. Imphal is below Hemant (clue 5), so floor 1: Lavanya is from Imphal. Moinuddin on floor 6 is from Ranchi.

  4. Varanasi is immediately above Neha, so floor 4: Kuldeep. Hemant is not from Mysuru, so Hemant is from Rajkot and Ishita from Mysuru.

  5. Imphal is floor 1 and Varanasi floor 4; floors 2 and 3 lie between them, so 2 people.

Worth noting

3 is the plain difference 4−14 - 1. Count only the floors strictly between.

Question 44

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Seven people, Om, Priyanka, Rehan, Shalini, Tushar, Ujjwala and Vikram, live in a seven-storey building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Om lives on an even-numbered floor, but not on floor 2.

2. Exactly two people live between Om and Shalini.

3. Rehan lives immediately above Ujjwala.

4. Tushar lives below Priyanka, and Priyanka lives below Vikram.

5. Ujjwala lives above Om.

6. Vikram lives below Om.

How many of the seven residents live above Vikram?

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AnswerC · 4

  1. Clues 4 and 6 give Tushar below Priyanka below Vikram below Om, so at least three people live below Om. With clue 1, Om is on floor 4 or 6.

  2. If Om were on floor 6, Ujjwala (above Om, clue 5) would be on floor 7 and Rehan, immediately above her (clue 3), would have no floor. So Om is on floor 4.

  3. Tushar, Priyanka and Vikram take floors 1, 2 and 3 in that order. Shalini is three floors from Om (clue 2): floor 1 is taken, so she is on floor 7.

  4. Floors 5 and 6 remain for Ujjwala and Rehan, with Rehan immediately above: Ujjwala 5, Rehan 6.

  5. Vikram is on floor 3, so floors 4, 5, 6 and 7 are above him: 4 people.

Worth noting

3 counts only Om, Ujjwala and Rehan and forgets Shalini on the top floor.

Question 45

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Seven people, Om, Priyanka, Rehan, Shalini, Tushar, Ujjwala and Vikram, live in a seven-storey building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:

1. Om lives on an even-numbered floor, but not on floor 2.

2. Exactly two people live between Om and Shalini.

3. Rehan lives immediately above Ujjwala.

4. Tushar lives below Priyanka, and Priyanka lives below Vikram.

5. Ujjwala lives above Om.

6. Vikram lives below Om.

One clue in the list turns out to be unnecessary: the same arrangement follows without it. Which clue is it?

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AnswerD · Ujjwala lives above Om.

  1. Drop the clue 'Ujjwala lives above Om' and try Om on floor 6. Shalini must then be on floor 3 (clue 2), leaving floors 1, 2, 4, 5 and 7.

  2. Ujjwala and Rehan need two consecutive floors from these: 1 and 2, or 4 and 5. Either way only two floors below Om are left for Tushar, Priyanka and Vikram, who need three. So Om is on floor 4 even without the clue.

  3. With Om on floor 4, the rest follows exactly as before, so the Ujjwala clue can go.

  4. The other clues are all needed. Without the even-floor clue, Om 5 with Shalini 2 also fits; without the Rehan clue, Rehan and Ujjwala could swap floors 5 and 6; without 'Vikram lives below Om', Shalini 1, Tushar 2, Priyanka 3, Vikram 7 fits.

Worth noting

Hard questions of this type are about checking, not guessing: remove the clue and see whether a second arrangement appears.

Days and schedules

20 questions

Question 46

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A college holds six guest lectures in one week, one on each day from Monday to Saturday. The speakers are Ananya, Bhaskar, Charu, Devesh, Elango and Firdaus, and each speaks on a different topic: Astronomy, Banking, Law, Nutrition, Poetry or Robotics. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. The lecture on Astronomy is on Tuesday.

2. Ananya speaks on Poetry, on the day immediately after the Astronomy lecture.

3. Devesh gives the last lecture of the week, and his topic is not Robotics.

4. Exactly two lectures are held between Charu's lecture and Elango's lecture.

5. Bhaskar speaks on Law, on some day after Elango.

6. Charu speaks on neither Nutrition nor Robotics.

7. The Robotics lecture is held on the day immediately before the Law lecture.

On which day of the week does Firdaus give his guest lecture?

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AnswerB · Tuesday

  1. Astronomy is on Tuesday, so Ananya (Poetry) is on Wednesday (clues 1 and 2). Devesh is on Saturday (clue 3).

  2. Charu and Elango are three days apart on the free days Monday, Tuesday, Thursday and Friday: Monday and Thursday, or Tuesday and Friday. Bhaskar is after Elango (clue 5), so Elango is not on Friday.

  3. If Elango is on Tuesday, Bhaskar (Law) must be on Thursday, making Wednesday the Robotics day (clue 7), but Wednesday is Poetry. If Elango is on Monday and Charu on Thursday, Bhaskar is on Friday and Robotics falls on Thursday, Charu's day, against clue 6.

  4. So Charu is on Monday, Elango on Thursday (Robotics), Bhaskar on Friday (Law) and Firdaus on Tuesday (Astronomy). Charu does not take Nutrition, so Charu takes Banking and Devesh Nutrition.

  5. Firdaus speaks on Tuesday.

Question 47

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Seven friends, Gauri, Hriday, Ira, Jatin, Kiran, Lakshmi and Mohit, each visit a science museum on a different day of one week. The week runs from Monday to Sunday, and exactly one friend visits on each day. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. Exactly three friends visit before Mohit.

2. Hriday visits on the last day of the week.

3. Gauri visits on the day immediately before Mohit.

4. Exactly one friend visits between Ira and Gauri.

5. Kiran visits on the day immediately after Ira.

6. Lakshmi visits before Gauri, but not on Monday.

Which friend visits the museum on Monday?

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AnswerD · Jatin

  1. Three friends visit before Mohit, so Mohit visits on Thursday; Gauri is on Wednesday (clue 3) and Hriday on Sunday (clue 2).

  2. Lakshmi is before Gauri but not on Monday, so Lakshmi visits on Tuesday (clue 6).

  3. Ira is two days from Gauri: Monday or Friday. Ira on Monday would put Kiran on Tuesday, which is Lakshmi's day, so Ira is on Friday and Kiran on Saturday (clue 5).

  4. Jatin takes the one day left, Monday.

  5. Monday is Jatin's day.

Question 48

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Seven friends, Gauri, Hriday, Ira, Jatin, Kiran, Lakshmi and Mohit, each visit a science museum on a different day of one week. The week runs from Monday to Sunday, and exactly one friend visits on each day. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. Exactly three friends visit before Mohit.

2. Hriday visits on the last day of the week.

3. Gauri visits on the day immediately before Mohit.

4. Exactly one friend visits between Ira and Gauri.

5. Kiran visits on the day immediately after Ira.

6. Lakshmi visits before Gauri, but not on Monday.

Kiran goes to the museum on which day?

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AnswerC · Saturday

  1. Three friends visit before Mohit, so Mohit visits on Thursday; Gauri is on Wednesday (clue 3) and Hriday on Sunday (clue 2).

  2. Lakshmi is before Gauri but not on Monday, so Lakshmi visits on Tuesday (clue 6).

  3. Ira is two days from Gauri: Monday or Friday. Ira on Monday would put Kiran on Tuesday, which is Lakshmi's day, so Ira is on Friday and Kiran on Saturday (clue 5).

  4. Kiran visits on Saturday.

Worth noting

Tuesday is where Kiran would land if Ira went on Monday; that case clashes with Lakshmi.

Question 49

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Seven friends, Gauri, Hriday, Ira, Jatin, Kiran, Lakshmi and Mohit, each visit a science museum on a different day of one week. The week runs from Monday to Sunday, and exactly one friend visits on each day. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. Exactly three friends visit before Mohit.

2. Hriday visits on the last day of the week.

3. Gauri visits on the day immediately before Mohit.

4. Exactly one friend visits between Ira and Gauri.

5. Kiran visits on the day immediately after Ira.

6. Lakshmi visits before Gauri, but not on Monday.

After Lakshmi's visit, how many of the friends are still to visit the museum that week?

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AnswerD · 5

  1. Three friends visit before Mohit, so Mohit visits on Thursday; Gauri is on Wednesday (clue 3) and Hriday on Sunday (clue 2).

  2. Lakshmi is before Gauri but not on Monday, so Lakshmi visits on Tuesday (clue 6).

  3. Lakshmi visits on Tuesday; Wednesday to Sunday are five days, so 5 friends visit after her.

Question 50

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Seven friends, Gauri, Hriday, Ira, Jatin, Kiran, Lakshmi and Mohit, each visit a science museum on a different day of one week. The week runs from Monday to Sunday, and exactly one friend visits on each day. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. Exactly three friends visit before Mohit.

2. Hriday visits on the last day of the week.

3. Gauri visits on the day immediately before Mohit.

4. Exactly one friend visits between Ira and Gauri.

5. Kiran visits on the day immediately after Ira.

6. Lakshmi visits before Gauri, but not on Monday.

Who visits on the day immediately after Mohit?

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AnswerC · Ira

  1. Three friends visit before Mohit, so Mohit visits on Thursday; Gauri is on Wednesday (clue 3) and Hriday on Sunday (clue 2).

  2. Lakshmi is before Gauri but not on Monday, so Lakshmi visits on Tuesday (clue 6).

  3. Ira is two days from Gauri: Monday or Friday. Ira on Monday would put Kiran on Tuesday, which is Lakshmi's day, so Ira is on Friday and Kiran on Saturday (clue 5).

  4. Jatin takes the one day left, Monday.

  5. Mohit is on Thursday, so Friday's visitor, Ira, comes immediately after him.

Worth noting

Gauri comes immediately BEFORE Mohit.

Question 51

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A bank manager meets five clients, Nirmala, Omar, Pallavi, Raghav and Sukhmani, one after another on the same day, in the slots 10 am, 11 am, 12 noon, 1 pm and 2 pm. Each client comes about a different matter: a deposit, insurance, a loan, a locker or a pension. 'Before' or 'after' means any earlier or later slot; 'immediately after' means the next slot in this list. The following is known:

1. The pension meeting is the first of the day.

2. Sukhmani's meeting is immediately after Omar's.

3. Pallavi's meeting is at some time after Nirmala's, and Nirmala's is at some time after Raghav's.

4. The locker meeting is the last of the day.

5. Raghav's meeting is immediately after Sukhmani's. Neither Raghav nor Nirmala has come about a loan.

6. The insurance meeting is immediately after the deposit meeting.

At what time is Raghav's appointment with the manager?

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AnswerC · 12 noon

  1. Clues 2 and 5 chain Omar, Sukhmani and Raghav into three consecutive slots in that order, and clue 3 puts Nirmala after Raghav and Pallavi after Nirmala.

  2. Five people in the fixed order Omar, Sukhmani, Raghav, Nirmala, Pallavi fill 10 am, 11 am, 12 noon, 1 pm and 2 pm.

  3. Raghav is at 12 noon.

Question 52

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A bank manager meets five clients, Nirmala, Omar, Pallavi, Raghav and Sukhmani, one after another on the same day, in the slots 10 am, 11 am, 12 noon, 1 pm and 2 pm. Each client comes about a different matter: a deposit, insurance, a loan, a locker or a pension. 'Before' or 'after' means any earlier or later slot; 'immediately after' means the next slot in this list. The following is known:

1. The pension meeting is the first of the day.

2. Sukhmani's meeting is immediately after Omar's.

3. Pallavi's meeting is at some time after Nirmala's, and Nirmala's is at some time after Raghav's.

4. The locker meeting is the last of the day.

5. Raghav's meeting is immediately after Sukhmani's. Neither Raghav nor Nirmala has come about a loan.

6. The insurance meeting is immediately after the deposit meeting.

Which client has come about the locker?

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AnswerB · Pallavi

  1. Clues 2 and 5 chain Omar, Sukhmani and Raghav into three consecutive slots in that order, and clue 3 puts Nirmala after Raghav and Pallavi after Nirmala.

  2. Five people in the fixed order Omar, Sukhmani, Raghav, Nirmala, Pallavi fill 10 am, 11 am, 12 noon, 1 pm and 2 pm.

  3. Pension is at 10 am (Omar) and the locker at 2 pm (Pallavi). Deposit and insurance take two consecutive slots among 11 am, 12 noon and 1 pm, with deposit first; the loan takes the third.

  4. The 2 pm client, Pallavi, has the locker matter.

Question 53

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A community centre runs six one-day workshops in one week from Monday to Sunday: coding, dance, painting, photography, pottery and yoga. Each workshop is held on a different day, and on the remaining day no workshop is held. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. When counting the days between two workshops, count every day in between, including the day with no workshop. The following is known:

1. The day with no workshop comes immediately after the coding workshop.

2. Painting is held on the last day of the week.

3. Exactly two days lie between the yoga workshop and the pottery workshop.

4. Dance is held on the day immediately after pottery.

5. Photography is held on some day after dance, and coding on some day before pottery.

6. The yoga workshop is held before the coding workshop.

On which day does the community centre hold no workshop?

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AnswerC · Wednesday

  1. Yoga is before coding (clue 6), and the free day is immediately after coding (clue 1). Pottery is after coding (clue 5) but cannot be on the free day, so pottery is after the free day.

  2. Dance is immediately after pottery (clue 4) and photography after dance (clue 5), and painting is on Sunday (clue 2).

  3. So Monday to Saturday hold, in order: yoga, coding, the free day, pottery, dance, photography. That is yoga Monday, coding Tuesday, no workshop Wednesday, pottery Thursday, dance Friday, photography Saturday.

  4. The free day is Wednesday.

Question 54

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A community centre runs six one-day workshops in one week from Monday to Sunday: coding, dance, painting, photography, pottery and yoga. Each workshop is held on a different day, and on the remaining day no workshop is held. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. When counting the days between two workshops, count every day in between, including the day with no workshop. The following is known:

1. The day with no workshop comes immediately after the coding workshop.

2. Painting is held on the last day of the week.

3. Exactly two days lie between the yoga workshop and the pottery workshop.

4. Dance is held on the day immediately after pottery.

5. Photography is held on some day after dance, and coding on some day before pottery.

6. The yoga workshop is held before the coding workshop.

Which workshop is held on Friday?

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AnswerD · dance

  1. Yoga is before coding (clue 6), and the free day is immediately after coding (clue 1). Pottery is after coding (clue 5) but cannot be on the free day, so pottery is after the free day.

  2. Dance is immediately after pottery (clue 4) and photography after dance (clue 5), and painting is on Sunday (clue 2).

  3. So Monday to Saturday hold, in order: yoga, coding, the free day, pottery, dance, photography. That is yoga Monday, coding Tuesday, no workshop Wednesday, pottery Thursday, dance Friday, photography Saturday.

  4. Friday's workshop is dance.

Question 55

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A college holds six guest lectures in one week, one on each day from Monday to Saturday. The speakers are Ananya, Bhaskar, Charu, Devesh, Elango and Firdaus, and each speaks on a different topic: Astronomy, Banking, Law, Nutrition, Poetry or Robotics. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. The lecture on Astronomy is on Tuesday.

2. Ananya speaks on Poetry, on the day immediately after the Astronomy lecture.

3. Devesh gives the last lecture of the week, and his topic is not Robotics.

4. Exactly two lectures are held between Charu's lecture and Elango's lecture.

5. Bhaskar speaks on Law, on some day after Elango.

6. Charu speaks on neither Nutrition nor Robotics.

7. The Robotics lecture is held on the day immediately before the Law lecture.

What topic does Devesh speak on?

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AnswerD · Nutrition

  1. Astronomy is on Tuesday, so Ananya (Poetry) is on Wednesday (clues 1 and 2). Devesh is on Saturday (clue 3).

  2. Charu and Elango are three days apart on the free days Monday, Tuesday, Thursday and Friday: Monday and Thursday, or Tuesday and Friday. Bhaskar is after Elango (clue 5), so Elango is not on Friday.

  3. If Elango is on Tuesday, Bhaskar (Law) must be on Thursday, making Wednesday the Robotics day (clue 7), but Wednesday is Poetry. If Elango is on Monday and Charu on Thursday, Bhaskar is on Friday and Robotics falls on Thursday, Charu's day, against clue 6.

  4. So Charu is on Monday, Elango on Thursday (Robotics), Bhaskar on Friday (Law) and Firdaus on Tuesday (Astronomy). Charu does not take Nutrition, so Charu takes Banking and Devesh Nutrition.

  5. Devesh's topic is Nutrition.

Worth noting

Robotics is excluded for Devesh by clue 3 itself; Banking goes to Charu once Nutrition is barred for her.

Question 56

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A college holds six guest lectures in one week, one on each day from Monday to Saturday. The speakers are Ananya, Bhaskar, Charu, Devesh, Elango and Firdaus, and each speaks on a different topic: Astronomy, Banking, Law, Nutrition, Poetry or Robotics. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. The lecture on Astronomy is on Tuesday.

2. Ananya speaks on Poetry, on the day immediately after the Astronomy lecture.

3. Devesh gives the last lecture of the week, and his topic is not Robotics.

4. Exactly two lectures are held between Charu's lecture and Elango's lecture.

5. Bhaskar speaks on Law, on some day after Elango.

6. Charu speaks on neither Nutrition nor Robotics.

7. The Robotics lecture is held on the day immediately before the Law lecture.

Which speaker gives the lecture on Banking?

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AnswerA · Charu

  1. Astronomy is on Tuesday, so Ananya (Poetry) is on Wednesday (clues 1 and 2). Devesh is on Saturday (clue 3).

  2. Charu and Elango are three days apart on the free days Monday, Tuesday, Thursday and Friday: Monday and Thursday, or Tuesday and Friday. Bhaskar is after Elango (clue 5), so Elango is not on Friday.

  3. If Elango is on Tuesday, Bhaskar (Law) must be on Thursday, making Wednesday the Robotics day (clue 7), but Wednesday is Poetry. If Elango is on Monday and Charu on Thursday, Bhaskar is on Friday and Robotics falls on Thursday, Charu's day, against clue 6.

  4. So Charu is on Monday, Elango on Thursday (Robotics), Bhaskar on Friday (Law) and Firdaus on Tuesday (Astronomy). Charu does not take Nutrition, so Charu takes Banking and Devesh Nutrition.

  5. Charu gives the Banking lecture.

Question 57

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Seven friends, Gauri, Hriday, Ira, Jatin, Kiran, Lakshmi and Mohit, each visit a science museum on a different day of one week. The week runs from Monday to Sunday, and exactly one friend visits on each day. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. Exactly three friends visit before Mohit.

2. Hriday visits on the last day of the week.

3. Gauri visits on the day immediately before Mohit.

4. Exactly one friend visits between Ira and Gauri.

5. Kiran visits on the day immediately after Ira.

6. Lakshmi visits before Gauri, but not on Monday.

Which one of the following statements about the museum visits is true?

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AnswerA · Exactly two friends visit between Jatin and Mohit

  1. Three friends visit before Mohit, so Mohit visits on Thursday; Gauri is on Wednesday (clue 3) and Hriday on Sunday (clue 2).

  2. Lakshmi is before Gauri but not on Monday, so Lakshmi visits on Tuesday (clue 6).

  3. Ira is two days from Gauri: Monday or Friday. Ira on Monday would put Kiran on Tuesday, which is Lakshmi's day, so Ira is on Friday and Kiran on Saturday (clue 5).

  4. Jatin takes the one day left, Monday.

  5. Jatin is on Monday and Mohit on Thursday; Lakshmi and Gauri visit between them, so exactly two. The other statements fail.

Question 58

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A bank manager meets five clients, Nirmala, Omar, Pallavi, Raghav and Sukhmani, one after another on the same day, in the slots 10 am, 11 am, 12 noon, 1 pm and 2 pm. Each client comes about a different matter: a deposit, insurance, a loan, a locker or a pension. 'Before' or 'after' means any earlier or later slot; 'immediately after' means the next slot in this list. The following is known:

1. The pension meeting is the first of the day.

2. Sukhmani's meeting is immediately after Omar's.

3. Pallavi's meeting is at some time after Nirmala's, and Nirmala's is at some time after Raghav's.

4. The locker meeting is the last of the day.

5. Raghav's meeting is immediately after Sukhmani's. Neither Raghav nor Nirmala has come about a loan.

6. The insurance meeting is immediately after the deposit meeting.

What matter has Nirmala come to the bank about?

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AnswerC · insurance

  1. Clues 2 and 5 chain Omar, Sukhmani and Raghav into three consecutive slots in that order, and clue 3 puts Nirmala after Raghav and Pallavi after Nirmala.

  2. Five people in the fixed order Omar, Sukhmani, Raghav, Nirmala, Pallavi fill 10 am, 11 am, 12 noon, 1 pm and 2 pm.

  3. Pension is at 10 am (Omar) and the locker at 2 pm (Pallavi). Deposit and insurance take two consecutive slots among 11 am, 12 noon and 1 pm, with deposit first; the loan takes the third.

  4. Neither Raghav (12 noon) nor Nirmala (1 pm) has the loan, so Sukhmani has the loan at 11 am; then deposit is Raghav's at 12 noon and insurance Nirmala's at 1 pm.

  5. Nirmala has come about insurance.

Worth noting

Deposit is tempting, but clue 6 puts deposit BEFORE insurance, so the later of the two slots is insurance.

Question 59

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A bank manager meets five clients, Nirmala, Omar, Pallavi, Raghav and Sukhmani, one after another on the same day, in the slots 10 am, 11 am, 12 noon, 1 pm and 2 pm. Each client comes about a different matter: a deposit, insurance, a loan, a locker or a pension. 'Before' or 'after' means any earlier or later slot; 'immediately after' means the next slot in this list. The following is known:

1. The pension meeting is the first of the day.

2. Sukhmani's meeting is immediately after Omar's.

3. Pallavi's meeting is at some time after Nirmala's, and Nirmala's is at some time after Raghav's.

4. The locker meeting is the last of the day.

5. Raghav's meeting is immediately after Sukhmani's. Neither Raghav nor Nirmala has come about a loan.

6. The insurance meeting is immediately after the deposit meeting.

Whose meeting takes place in the slot just before the insurance meeting?

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AnswerD · Raghav

  1. Clues 2 and 5 chain Omar, Sukhmani and Raghav into three consecutive slots in that order, and clue 3 puts Nirmala after Raghav and Pallavi after Nirmala.

  2. Five people in the fixed order Omar, Sukhmani, Raghav, Nirmala, Pallavi fill 10 am, 11 am, 12 noon, 1 pm and 2 pm.

  3. Pension is at 10 am (Omar) and the locker at 2 pm (Pallavi). Deposit and insurance take two consecutive slots among 11 am, 12 noon and 1 pm, with deposit first; the loan takes the third.

  4. Neither Raghav (12 noon) nor Nirmala (1 pm) has the loan, so Sukhmani has the loan at 11 am; then deposit is Raghav's at 12 noon and insurance Nirmala's at 1 pm.

  5. Insurance is at 1 pm, so the slot just before it, 12 noon, is Raghav's (the deposit).

Question 60

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A bank manager meets five clients, Nirmala, Omar, Pallavi, Raghav and Sukhmani, one after another on the same day, in the slots 10 am, 11 am, 12 noon, 1 pm and 2 pm. Each client comes about a different matter: a deposit, insurance, a loan, a locker or a pension. 'Before' or 'after' means any earlier or later slot; 'immediately after' means the next slot in this list. The following is known:

1. The pension meeting is the first of the day.

2. Sukhmani's meeting is immediately after Omar's.

3. Pallavi's meeting is at some time after Nirmala's, and Nirmala's is at some time after Raghav's.

4. The locker meeting is the last of the day.

5. Raghav's meeting is immediately after Sukhmani's. Neither Raghav nor Nirmala has come about a loan.

6. The insurance meeting is immediately after the deposit meeting.

How many meetings come after the loan meeting that day?

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AnswerC · 3

  1. Clues 2 and 5 chain Omar, Sukhmani and Raghav into three consecutive slots in that order, and clue 3 puts Nirmala after Raghav and Pallavi after Nirmala.

  2. Five people in the fixed order Omar, Sukhmani, Raghav, Nirmala, Pallavi fill 10 am, 11 am, 12 noon, 1 pm and 2 pm.

  3. Pension is at 10 am (Omar) and the locker at 2 pm (Pallavi). Deposit and insurance take two consecutive slots among 11 am, 12 noon and 1 pm, with deposit first; the loan takes the third.

  4. Neither Raghav (12 noon) nor Nirmala (1 pm) has the loan, so Sukhmani has the loan at 11 am; then deposit is Raghav's at 12 noon and insurance Nirmala's at 1 pm.

  5. The loan meeting is at 11 am; 12 noon, 1 pm and 2 pm come after it: 3 meetings.

Question 61

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A community centre runs six one-day workshops in one week from Monday to Sunday: coding, dance, painting, photography, pottery and yoga. Each workshop is held on a different day, and on the remaining day no workshop is held. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. When counting the days between two workshops, count every day in between, including the day with no workshop. The following is known:

1. The day with no workshop comes immediately after the coding workshop.

2. Painting is held on the last day of the week.

3. Exactly two days lie between the yoga workshop and the pottery workshop.

4. Dance is held on the day immediately after pottery.

5. Photography is held on some day after dance, and coding on some day before pottery.

6. The yoga workshop is held before the coding workshop.

Which workshop takes place two days before the photography workshop?

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AnswerA · pottery

  1. Yoga is before coding (clue 6), and the free day is immediately after coding (clue 1). Pottery is after coding (clue 5) but cannot be on the free day, so pottery is after the free day.

  2. Dance is immediately after pottery (clue 4) and photography after dance (clue 5), and painting is on Sunday (clue 2).

  3. So Monday to Saturday hold, in order: yoga, coding, the free day, pottery, dance, photography. That is yoga Monday, coding Tuesday, no workshop Wednesday, pottery Thursday, dance Friday, photography Saturday.

  4. Photography is on Saturday; two days earlier is Thursday, the pottery day.

Worth noting

Dance is one day before photography, not two.

Question 62

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A college holds six guest lectures in one week, one on each day from Monday to Saturday. The speakers are Ananya, Bhaskar, Charu, Devesh, Elango and Firdaus, and each speaks on a different topic: Astronomy, Banking, Law, Nutrition, Poetry or Robotics. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. The lecture on Astronomy is on Tuesday.

2. Ananya speaks on Poetry, on the day immediately after the Astronomy lecture.

3. Devesh gives the last lecture of the week, and his topic is not Robotics.

4. Exactly two lectures are held between Charu's lecture and Elango's lecture.

5. Bhaskar speaks on Law, on some day after Elango.

6. Charu speaks on neither Nutrition nor Robotics.

7. The Robotics lecture is held on the day immediately before the Law lecture.

How many lectures are held between the Poetry lecture and the Law lecture?

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AnswerA · 1

  1. Astronomy is on Tuesday, so Ananya (Poetry) is on Wednesday (clues 1 and 2). Devesh is on Saturday (clue 3).

  2. Charu and Elango are three days apart on the free days Monday, Tuesday, Thursday and Friday: Monday and Thursday, or Tuesday and Friday. Bhaskar is after Elango (clue 5), so Elango is not on Friday.

  3. If Elango is on Tuesday, Bhaskar (Law) must be on Thursday, making Wednesday the Robotics day (clue 7), but Wednesday is Poetry. If Elango is on Monday and Charu on Thursday, Bhaskar is on Friday and Robotics falls on Thursday, Charu's day, against clue 6.

  4. So Charu is on Monday, Elango on Thursday (Robotics), Bhaskar on Friday (Law) and Firdaus on Tuesday (Astronomy). Charu does not take Nutrition, so Charu takes Banking and Devesh Nutrition.

  5. Poetry is on Wednesday and Law on Friday. Only Thursday lies between them, so 1 lecture.

Worth noting

2 is the gap Friday − Wednesday; the lectures strictly between are one fewer.

Question 63

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A college holds six guest lectures in one week, one on each day from Monday to Saturday. The speakers are Ananya, Bhaskar, Charu, Devesh, Elango and Firdaus, and each speaks on a different topic: Astronomy, Banking, Law, Nutrition, Poetry or Robotics. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. The following is known:

1. The lecture on Astronomy is on Tuesday.

2. Ananya speaks on Poetry, on the day immediately after the Astronomy lecture.

3. Devesh gives the last lecture of the week, and his topic is not Robotics.

4. Exactly two lectures are held between Charu's lecture and Elango's lecture.

5. Bhaskar speaks on Law, on some day after Elango.

6. Charu speaks on neither Nutrition nor Robotics.

7. The Robotics lecture is held on the day immediately before the Law lecture.

In what order are the topics taken from Thursday to Saturday?

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AnswerC · Robotics, Law, Nutrition

  1. Astronomy is on Tuesday, so Ananya (Poetry) is on Wednesday (clues 1 and 2). Devesh is on Saturday (clue 3).

  2. Charu and Elango are three days apart on the free days Monday, Tuesday, Thursday and Friday: Monday and Thursday, or Tuesday and Friday. Bhaskar is after Elango (clue 5), so Elango is not on Friday.

  3. If Elango is on Tuesday, Bhaskar (Law) must be on Thursday, making Wednesday the Robotics day (clue 7), but Wednesday is Poetry. If Elango is on Monday and Charu on Thursday, Bhaskar is on Friday and Robotics falls on Thursday, Charu's day, against clue 6.

  4. So Charu is on Monday, Elango on Thursday (Robotics), Bhaskar on Friday (Law) and Firdaus on Tuesday (Astronomy). Charu does not take Nutrition, so Charu takes Banking and Devesh Nutrition.

  5. Thursday Robotics, Friday Law, Saturday Nutrition.

Worth noting

Law, Robotics reverses clue 7: Robotics is the day BEFORE Law.

Question 64

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A community centre runs six one-day workshops in one week from Monday to Sunday: coding, dance, painting, photography, pottery and yoga. Each workshop is held on a different day, and on the remaining day no workshop is held. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. When counting the days between two workshops, count every day in between, including the day with no workshop. The following is known:

1. The day with no workshop comes immediately after the coding workshop.

2. Painting is held on the last day of the week.

3. Exactly two days lie between the yoga workshop and the pottery workshop.

4. Dance is held on the day immediately after pottery.

5. Photography is held on some day after dance, and coding on some day before pottery.

6. The yoga workshop is held before the coding workshop.

How many workshops are held after the coding workshop?

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AnswerB · 4

  1. Yoga is before coding (clue 6), and the free day is immediately after coding (clue 1). Pottery is after coding (clue 5) but cannot be on the free day, so pottery is after the free day.

  2. Dance is immediately after pottery (clue 4) and photography after dance (clue 5), and painting is on Sunday (clue 2).

  3. So Monday to Saturday hold, in order: yoga, coding, the free day, pottery, dance, photography. That is yoga Monday, coding Tuesday, no workshop Wednesday, pottery Thursday, dance Friday, photography Saturday.

  4. Coding is on Tuesday. Wednesday has no workshop, and Thursday to Sunday have pottery, dance, photography and painting: 4 workshops.

Worth noting

5 counts the days after Tuesday, including Wednesday, which has no workshop.

Question 65

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A community centre runs six one-day workshops in one week from Monday to Sunday: coding, dance, painting, photography, pottery and yoga. Each workshop is held on a different day, and on the remaining day no workshop is held. 'Before' or 'after' means on any earlier or later day; 'immediately before' or 'immediately after' means the previous or the next day. When counting the days between two workshops, count every day in between, including the day with no workshop. The following is known:

1. The day with no workshop comes immediately after the coding workshop.

2. Painting is held on the last day of the week.

3. Exactly two days lie between the yoga workshop and the pottery workshop.

4. Dance is held on the day immediately after pottery.

5. Photography is held on some day after dance, and coding on some day before pottery.

6. The yoga workshop is held before the coding workshop.

Which one of the clues could be left out and the whole schedule would still be fixed?

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AnswerB · Exactly two days lie between the yoga workshop and the pottery workshop.

  1. The solving above never used the clue about two days between yoga and pottery; it simply holds in the result (Monday and Thursday, with Tuesday and Wednesday between).

  2. Without the free-day clue, coding and the free day could swap (free Tuesday, coding Wednesday).

  3. Without the dance clue, dance could move to Monday with yoga, coding, the free day, pottery and photography after it. Without the yoga clue, yoga could move to Saturday with coding on Monday.

  4. So only the yoga and pottery clue can be removed.

Worth noting

Before you answer, write the solution path and note which clues it used. An unused clue is the candidate; test the others by finding a second arrangement.

The area names are NTA's. The chapters inside them are EduFarming's own division, not NTA's.