Ranking and ordering questions go wrong in two places: counting a person twice or not at all, and assuming an order is fixed when the clues allow more than one. This lesson covers the total from both ends, converting between ends, facing and left and right, people between, crossing positions, 'exactly k between', minimum totals, class ranks, interchanges, and comparison chains, with worked examples and the traps beside them.
A position counts the person themselves: the 12th from the left has 11 people to their left. Every formula in this chapter follows from that, and every classic slip is a person counted twice or not at all.
The other habit is to convert both positions to the same end before comparing them. That one step handles crossing positions, people between, and interchanges without special cases.
If one person's position is known from both ends, the total is the two positions added, minus 1, because that person is counted in both. The same rule works for a queue, front and back, and a class list, top and bottom.
One person, both ends
Exam shortcut
In a queue of 40, the person 13th from the front is th from the back. Without the you get 27, the number of people behind them. And in a row of 30, the person 12th from the left has 11 people to the left and to the right.
Left and right belong to the people in the row, not the ground. Facing north, each person's left hand points west, so the left end is the west end; facing south, the left end is the east end. A row of 20 facing north with Sunita 7th from the left, turned to face south without moving, puts her th from the new left.
Convert both positions to the same end. The number between them is the larger position minus the smaller, minus 1; the plain difference counts one of the two named people.
Example 1 · People between
A row of 45 faces north. Anil is 9th from the left and Beena 16th from the right. How many people stand between them?
Beena from the left: .
Between: .
20
Shortcut when the counts do not cross: total − (left + right) .
They cross when the left-counted person is actually to the right of the right-counted person, which shows at once: the two positions add up to more than the total. Then the people between are the two positions added, minus the total, minus 2.
Watch out
The shortcut total − (left + right) gives here, and dropping the sign gives 5, which is wrong. Converting both to one end never needs a special case: .
Work out both cases, the second person to the right and to the left of the first. Both may be valid, and the question may ask for every possible total or the minimum.
Example 2 · Two cases
In a row facing north, Om is 8th from the left and Rita 10th from the right, with exactly 3 people between them. How many people are in the row?
Rita to Om's right: she is th from the left, so the total is .
Rita to Om's left: she is th from the left, so the total is , and Om, 8th, fits in a row of 13.
13 or 21; the minimum is 13
Place the people as tightly as the clues allow. If two people's order is not fixed, they can cross; if it is fixed, they cannot share a place, and the minimum needs one more.
Example 3 · A queue
In a queue, Ali is 11th from the front, and Neha, who stands somewhere behind Ali, is 6th from the back. What is the least possible number of people?
Neha is behind Ali, so she is at least 12th from the front.
At exactly 12th from the front and 6th from the back, the queue has .
17
would make Ali and Neha the same person.
A class list is a row stood on its end, so class size is rank from the top plus rank from the bottom, minus 1. Watch for ranks given within a subgroup: ranks among those who passed count only those who passed.
Example 4 · Ranks among those who passed
Among the students who passed, Vinay is 9th from the top and 19th from the bottom. Four students failed and one was absent. How many are in the class?
Passed: .
Class: .
32
Exam shortcut
" places below" adds to the rank from the top: 12th from the top, 5 places below, is 17th.
In a swap, each moves into the other's exact place and nobody else moves. After the swap, one place is described twice: by the old position of the person who left it and the new position of the person who arrived. Pair those two numbers.
Example 5 · An interchange
In a row facing north, Sameera is 7th from the left and Pratap 12th from the right. They interchange, and Sameera becomes 18th from the left. Find the total and Pratap's new position from the right.
Sameera's new place is Pratap's old place: 18th from the left and 12th from the right, so the total is .
Pratap moves into Sameera's old place, 7th from the left, which is rd from the right.
29 people; Pratap is 23rd from the right
Watch out
Never add two numbers that describe different places, such as one person's old left position and the other's new right position. The number between the two is the same before and after a swap; after several swaps, write the whole row out each time.
Turn every clue into "bigger > smaller" and join the clues into chains, with the tallest, oldest or highest on the left. "A is shorter than B" becomes B > A; "C is older than D but younger than E" becomes E > C > D.
Example 6 · A height chain
Jaya is taller than Kavi. Lina is shorter than Kavi. Manu is taller than Jaya. Nila is taller than Lina but shorter than Kavi. Who is the second shortest?
Clues: Jaya > Kavi, Kavi > Lina, Manu > Jaya, Kavi > Nila > Lina.
Joined: Manu > Jaya > Kavi > Nila > Lina.
Nila
Only when two or more orders fit every clue and disagree on what is asked. If every possible order agrees on the asked fact, it is fixed even though the full order is not.
Example 7 · Partly fixed
Rohit is heavier than Sara. Sara is heavier than Tarun. Usha is heavier than Tarun. Who is the lightest, and who is the heaviest?
Rohit > Sara > Tarun, and Usha is compared only with Tarun.
Possible orders: Usha, Rohit, Sara, Tarun; Rohit, Usha, Sara, Tarun; Rohit, Sara, Usha, Tarun.
Tarun is last in every order. The first place is Usha in one and Rohit in the others.
Tarun is the lightest; the heaviest cannot be determined
Key idea
A statement must be true only if it holds in every possible order, and could be true if it holds in at least one. "X is older than exactly two of the others" puts X third from the bottom.
| Situation | Formula |
|---|---|
| One person, both ends | left + right − 1 |
| From the other end | total − position + 1 |
| Between positions and , same end | |
| Opposite ends, not crossing | total − (left + right) |
| Opposite ends, crossing | left + right − total − 2 |
| Two people, between, not crossing | left + + right |
Positions
Between and crossing
Swaps and chains
The same position ideas run through seating arrangement, puzzles and direction sense.
66 questions, grouped by type, easy to hard. Pick an answer and check it. The worked solution opens when you ask for it.
Some girls stand in a row facing north. Ishita is 14th from the left end and 9th from the right end. How many girls are in the row?
AnswerC · 22
Counting from the left, Ishita is the 14th girl; counting from the right, she is the 9th.
Adding counts Ishita twice, so subtract 1.
Total .
Worth noting
23 forgets that Ishita was counted from both ends. 5 is the difference of the two positions, which means nothing here.
Thirty-one people wait in a single queue at a ration shop. Harbhajan is 12th from the front. What is his position from the back of the queue?
AnswerB · 20
Position from the other end total position from this end .
Position from the back .
Worth noting
19 is , which is the number of people BEHIND him, not his position. Add 1 to include Harbhajan himself.
In her class, Nandini ranks 7th from the top and 28th from the bottom. No two students share a rank. How many students are in the class?
AnswerC · 34
Rank from the top and rank from the bottom both count Nandini.
Class strength .
Worth noting
35 counts Nandini twice. 21 is the difference .
Arjun ranks 17th from the top in a class of 45 students, with no ties. How many students rank below Arjun?
AnswerB · 28
Students ranked above Arjun: 16. Arjun himself: 1.
Students below him .
Worth noting
29 is Arjun's rank FROM THE BOTTOM , which includes Arjun. The number of students below him leaves him out.
Fifty children stand in a row facing north. Kavya is 10th from the left end and Rohan is 18th from the right end. How many children stand between Kavya and Rohan?
AnswerB · 22
Rohan's position from the left .
Kavya is at 10 and Rohan at 33, so the children between them are those at 11 to 32.
Between .
Worth noting
23 is the plain difference , which counts Rohan too. Shortcut when the two do not cross: between .
A row has 27 chairs, and Leela sits on the chair exactly in the middle. What is her position counted from either end of the row?
AnswerC · 14
The middle chair has equal numbers of chairs on both sides: each.
Her position from either end .
Worth noting
13 is the number of chairs on EACH SIDE of her, not her position. 13.5 is ; a position must be a whole number.
Thirty-two people stand in a row facing north. Babita is 11th from the left end. How many people stand to her right?
AnswerD · 21
People to her left: 10. Babita: 1.
People to her right .
Worth noting
10 is the number of people to her LEFT. 20 subtracts one person too many.
A line of trees is planted along a road, and a neem tree is 7th from either end of the line. How many trees are in the line?
AnswerB · 13
From either end the neem tree is 7th.
Total .
Worth noting
14 counts the neem tree twice.
Radha ranks 11th from the top in her school's quiz, and exactly 25 participants rank below her. There are no ties. How many participants took part?
AnswerC · 36
Participants from the top down to Radha: 11.
Below her: 25. Total .
Worth noting
35 subtracts 1 as though Radha were counted twice, but '25 below her' does not include her.
In a row of 40 students, Ravi is 12th from the left end and Meera is 15th from the right end. How many students stand between them?
AnswerB · 13
Put both positions on the same scale. Meera is 15th from the right, so from the left she is th.
Ravi is 12th from the left.
The students strictly between positions 12 and 26 are those from 13 to 25, which is students.
Worth noting
Subtracting 1 is what distinguishes "between them" from "from one to the other". The 14 on offer is the count that includes one of the two named students.
In a row of people facing north, Mehul is 11th from the left end and Divya is 16th from the right end. Divya is to the right of Mehul, and exactly 6 people stand between them. How many people are in the row?
AnswerD · 33
Left of and including Mehul: 11 people.
Between them: 6 people. Divya and everyone to her right: 16 people.
Total .
Worth noting
32 subtracts 1 as if someone were counted twice, but no one is: Mehul and Divya are different people and the three groups do not overlap. 26 is , which ignores the 6 in between; 27 is , which also ignores them.
Children stand in a row facing north. Ananya is 8th from the left end. Jyoti is 3rd to the right of Ananya and 15th from the right end. How many children are in the row?
AnswerD · 25
Jyoti is 3 places to the right of Ananya, so from the left she is th.
Jyoti is 11th from the left and 15th from the right.
Total .
Worth noting
22 is , which treats Ananya's position as Jyoti's. '3rd to the right' means 3 places further, not 3 people in between.
Sixteen children stand in a row facing north. Mona is 5th from the left end. Reena is 3rd to the left of the child who is 10th from the right end. How many children stand between Mona and Reena?
AnswerA · 0
The child 10th from the right is th from the left.
Reena is 3 places to the left of that child: th from the left.
Mona is 5th and Reena 4th, so they stand side by side, with 0 children between them.
Worth noting
Convert every position to the same end before comparing. 2 comes from placing Reena 3rd to the RIGHT of the 7th child.
In a class exam, 6 students failed and 2 students were absent. Among the students who passed, Sameer ranks 12th from the top and 30th from the bottom. How many students are in the class, counting the failed and the absent ones?
AnswerD · 49
Sameer's ranks are among the students who PASSED: passed.
Add those who failed and those who were absent: .
Worth noting
41 counts only the students who passed. 47 adds the failed students but forgets the absent ones; they are still in the class. 43 adds only the absent students.
Thirty-five children stand in a row facing north. Deepak is 13th from the left end, and Lalremsiami is 9th to the right of Deepak. What is Lalremsiami's position from the right end?
AnswerB · 14
Lalremsiami from the left .
From the right .
Worth noting
13 forgets the in the conversion. 23 is , Deepak's position from the right.
In a class of 52 students with no ties, Priya ranks 15th from the top. Rahul ranks 8 places below Priya. What is Rahul's rank from the bottom?
AnswerB · 30
Rahul's rank from the top .
From the bottom .
Worth noting
38 is Priya's rank from the bottom ; moving 8 places DOWN the list makes the rank from the bottom smaller, not larger.
In a queue at a railway ticket window, Ravi is 15th from the front. Sita stands somewhere behind Ravi and is 9th from the back. What is the smallest number of people the queue can have?
AnswerC · 24
Sita is behind Ravi, so she is at least 16th from the front.
If she is exactly 16th from the front and 9th from the back, the queue has people.
Any gap between them only adds people, so the minimum is 24.
Worth noting
23 is , which would make Ravi and Sita the same person. Two different people need at least one more place.
Anjali ranks 18th from the top of her class. Bhavesh ranks 9 places below Anjali and is 25th from the bottom. There are no ties. How many students are in the class?
AnswerD · 51
Bhavesh's rank from the top .
Class strength .
Worth noting
42 is , which uses Anjali's rank from the top with Bhavesh's rank from the bottom; 43 also forgets the .
Twenty-five children stand in a row facing north, and Tara is 9th from the left end. The whole row then turns around to face south without anyone changing place. Counting from the children's new left-hand end, what is Tara's position?
AnswerD · 17
Facing north, the left end is the west end, so Tara is 9th from the west.
Facing south, a person's left hand points east, so the new left end is the east end.
Tara from the east end .
Worth noting
9 assumes the left end stays the same after turning. Left and right belong to the direction the people face, not to the ground.
Forty people stand in a row facing north. Irfan is 10th from the left end and Kajal is 13th from the right end. Mira stands exactly midway between Irfan and Kajal. What is Mira's position from the right end?
AnswerA · 22
Kajal from the left .
Midway between positions 10 and 28 is from the left.
From the right .
Worth noting
28 is Kajal's position from the left and 31 is Irfan's position from the right; neither is Mira's. 23 adds 1 twice in the conversion.
Thirty students stand in a row facing north. Tanvi is 20th from the left end and Farhan is 17th from the right end. How many students stand between Tanvi and Farhan?
AnswerA · 5
Farhan's position from the left .
So Farhan (14th) is to the LEFT of Tanvi (20th): the positions cross.
Students between positions 14 and 20 are those at 15 to 19: .
Worth noting
7 comes from the shortcut with the minus sign dropped; that shortcut works only when the two do not cross. Here is more than 30, the sign that they cross, and between .
In a row of students facing north, Pooja is 9th from the left end and Suresh is 7th from the right end. Exactly 3 students stand between Pooja and Suresh. What is the minimum possible number of students in the row?
AnswerA · 11
Case 1, Suresh to the right of Pooja: Suresh is at from the left, so the row has students.
Case 2, Suresh to the left of Pooja: Suresh is at from the left, so the row has students.
Check case 2: Pooja at 9 is inside a row of 11, so it is valid. The minimum is 11.
Worth noting
The stem does not say which of the two is nearer the left end, so both cases are allowed. The minimum, 11, comes from the case where their positions cross (Suresh to the left of Pooja); 19 is the no-crossing case. When a question asks for the minimum, always test the crossing case too.
In a row of girls facing north, Neha is 10th from the left end and Zoya is 12th from the right end. Exactly 4 girls stand between Neha and Zoya. Which of the following could be the number of girls in the row?
AnswerB · 16
Zoya to the right of Neha: Zoya is th from the left, so the row has girls.
Zoya to the left of Neha: Zoya is th from the left, so the row has girls.
The possible totals are 16 and 26. Only 16 is offered.
Worth noting
27 is , an extra person counted. 21 is , treating Neha and Zoya as one person. The crossing case gives the answer.
In a row of people facing north, Rekha is 7th from the left end and Salma is 12th from the right end. Exactly 4 people stand between Rekha and Salma. How many people are in the row?
AnswerC · 13 or 23
Salma to the right of Rekha: Salma is th from the left, so the row has people.
Salma to the left of Rekha: Salma is nd from the left, so the row has people.
Both cases fit every clue, so the row has 13 or 23 people.
Worth noting
23 only is the common answer from forgetting that Salma may stand to Rekha's left. When the stem does not say who is on which side, check both.
In a row of people facing north, Chirag is 13th from the left end and Dolma is 8th from the right end. Chirag and Dolma are different people. What is the least possible number of people in the row?
AnswerA · 13
The row must hold at least 13 people, because Chirag is 13th from the left.
With exactly 13 people, Dolma 8th from the right is th from the left, a different place from Chirag's. So 13 works.
The least possible number is 13.
Worth noting
20 is , the total if Chirag and Dolma were the same person. When the positions may cross, the minimum is the larger of the two positions, provided they do not land on the same place.
In a row of students facing north, Aarav is 12th from the left end and Meenakshi is 18th from the right end. They interchange places, and Aarav becomes 25th from the left end. How many students are in the row?
AnswerC · 42
After the swap Aarav stands where Meenakshi stood.
That place is 25th from the left (Aarav's new position) and 18th from the right (Meenakshi's old position).
Total .
Worth noting
29 is , which mixes two different places. Always pair the two numbers that describe the SAME place.
Gurpreet and Fatima stand in a row facing north. Gurpreet is 9th from the left end and Fatima is 14th from the right end. When they interchange places, Fatima becomes 21st from the right end. How many people are in the row?
AnswerD · 29
After the swap Fatima stands in Gurpreet's old place.
That place is 9th from the left and 21st from the right.
Total .
Worth noting
22 is : Gurpreet's and Fatima's ORIGINAL positions describe two different places, so they cannot be added.
Thirty people stand in a row facing north. Joseph is 8th from the left end and Tenzin is 11th from the right end. If Joseph and Tenzin interchange places, what will be Joseph's new position from the left end?
AnswerC · 20
Joseph moves into Tenzin's place, which is 11th from the right.
From the left that place is .
Worth noting
11 is Joseph's new position from the RIGHT. 23 is Joseph's old position from the right.
In a row of children, exactly 7 children stand between Dia and Ekam. Dia and Ekam then interchange places. How many children now stand between them?
AnswerA · 7
An interchange moves each of the two into the other's place; nobody else moves.
The same two places are still occupied, so the same 7 children stand between them.
Worth noting
14 doubles the gap as if each had moved past the other's side. The gap between two places does not depend on who stands in them.
Twenty-one people stand in a row facing north. Lata is 6th from the left end and Mohit is 6th from the right end. If they interchange places, how many people will stand to Lata's left?
AnswerC · 15
Mohit's place from the left .
After the swap Lata stands 16th from the left, so 15 people are to her left.
Worth noting
16 is her position, which includes her. 5 is the number to her left BEFORE the swap.
Nine cars are parked side by side in a row, all facing north. The red car is 3rd from the left end and the blue car is 2nd from the right end. If the two cars exchange places, how many cars will be to the left of the red car?
AnswerD · 7
The blue car's place from the left .
The red car moves to 8th from the left, so 7 cars are to its left.
Worth noting
2 is the number of cars to the red car's left BEFORE the exchange. 4 is the number of cars between the two cars.
In a row facing north, Rahul is 10th from the left end. He interchanges places with Neel, after which Rahul is 17th from the left end. Before the swap, Neel was 13th from the right end. How many people stand between Rahul and Neel?
AnswerA · 6
After the swap Rahul is in Neel's old place, so Neel was 17th from the left.
The two places are 10th and 17th from the left.
Between them .
Worth noting
7 is the difference , which counts one of the two. Neel's 13th-from-the-right is not needed for this question; it gives the total, 29.
Twenty-six students stand in a row facing north. Tarun is 7th from the right end, and Veena stands 4 places to Tarun's left. They interchange places. What is Tarun's new position from the left end?
AnswerB · 16
Tarun from the left .
Veena is 4 places to his left: th from the left.
After the swap Tarun takes Veena's place, 16th from the left.
Worth noting
11 is Tarun's new position from the right . 24 moves Veena 4 places to the RIGHT of Tarun instead of the left.
In a row of people facing north, Salim is 15th from the left end and Kriti is 20th from the left end. They interchange places, and Salim is then 12th from the right end. How many people are in the row?
AnswerB · 31
After the swap Salim is in Kriti's old place, 20th from the left.
The same place is 12th from the right.
Total .
Worth noting
26 is , which uses Salim's OLD left position with his NEW right position; those are two different places.
In a row facing north, Mahesh is 14th from the left end and Nikita is 17th from the right end. When they interchange places, Mahesh becomes 20th from the left end. What is Nikita's new position from the right end?
AnswerD · 23
Mahesh's new place is 20th from the left and 17th from the right, so the row has people.
Nikita moves into Mahesh's old place, 14th from the left.
From the right .
Worth noting
17 is Nikita's OLD position from the right. 22 forgets the in the conversion.
In a class of 48 students with no ties, Kamala ranks 9th from the top and Rohit ranks 30th from the bottom. After a re-check of marks, their ranks are exchanged. What is Kamala's new rank from the top?
AnswerB · 19
Kamala now holds Rohit's old rank, 30th from the bottom.
From the top .
Worth noting
30 is her new rank from the BOTTOM, not the top. 40 is her old rank from the bottom .
Ishaan is 11th from the left end of a row facing north. He interchanges places with Uday. After the swap, Ishaan is 18th from the left end and Uday is 22nd from the right end. How many people are in the row?
AnswerA · 32
After the swap Uday stands in Ishaan's old place, which is 11th from the left.
The same place is 22nd from the right (Uday's new position).
Total .
Worth noting
39 is : Ishaan's 18th-from-the-left and Uday's 22nd-from-the-right describe two different places.
Farah and Gopal stand in a row facing north, and Gopal is 9th from the left end. When they interchange places, Farah moves 6 places to the right and ends up 11th from the right end. How many people are in the row?
AnswerA · 19
Farah moves into Gopal's place, so her new place is 9th from the left.
That place is 11th from the right.
Total . (Farah was at rd from the left.)
Worth noting
25 adds the 6 places to Gopal's position, as if Farah ended at . She ends where Gopal WAS. 20 forgets to subtract 1.
Twenty people stand in a row facing north. Priya is 3rd from the left end, Qasim is 8th from the left end and Ruchi is 5th from the right end. First Priya and Qasim interchange places, and then Qasim and Ruchi interchange places. What is Priya's final position from the right end?
AnswerC · 13
Ruchi from the left . Start: Priya 3, Qasim 8, Ruchi 16 (from the left).
First swap: Priya 8, Qasim 3.
Second swap (Qasim and Ruchi): Qasim 16, Ruchi 3. Priya does not move and stays 8th from the left.
Priya from the right .
Worth noting
5 assumes Priya takes part in the second swap. 18 is Priya's original position from the right. Track each swap one at a time.
In a row facing north, Asif is 6th from the left end and Bindu is 10th from the right end. They interchange places, and Asif becomes 15th from the left end. How many people now stand to the right of Asif?
AnswerB · 9
Asif's new place is Bindu's old place: 15th from the left and 10th from the right.
So the row has people.
People to the right of Asif (he is 10th from the right, so 9 stand beyond him).
Worth noting
10 is Asif's position from the right, which counts Asif. 18 is the number who were to his right BEFORE the swap .
Seven friends stand in a row facing north. From the left end they are Asha, Bilal, Chetan, Devika, Esha, Firoz and Gauri. First Asha and Esha interchange places. Then Bilal interchanges places with whoever is at the right end. Finally, whoever is exactly in the middle of the row interchanges places with whoever is 2nd from the left. Who is now exactly in the middle of the row?
AnswerA · Gauri
After Asha and Esha swap: Esha, Bilal, Chetan, Devika, Asha, Firoz, Gauri.
Bilal swaps with the right end, Gauri: Esha, Gauri, Chetan, Devika, Asha, Firoz, Bilal.
The middle (4th) is Devika and 2nd from the left is Gauri; they swap: Esha, Devika, Chetan, Gauri, Asha, Firoz, Bilal.
The 4th place now holds Gauri.
Worth noting
Devika is the answer if the last swap is skipped. Write the whole row after every swap; the people at 'the right end' and 'the middle' change as you go.
Anu is taller than Bela. Chitra is shorter than Bela. Dolly is taller than Anu. Who is the shortest of the four?
AnswerD · Chitra
Anu > Bela, and Bela > Chitra, so Anu > Bela > Chitra.
Dolly > Anu puts Dolly on top: Dolly > Anu > Bela > Chitra.
The shortest is Chitra.
Worth noting
Dolly is the tallest, not the shortest. Write the chain with '>' meaning taller, and read the last name.
Harsh is older than Isha but younger than Jatin. Kunal is older than Jatin. Who is the second oldest among Harsh, Isha, Jatin and Kunal?
AnswerC · Jatin
'Older than Isha but younger than Jatin' gives Jatin > Harsh > Isha (oldest first).
Kunal > Jatin, so Kunal > Jatin > Harsh > Isha.
The second oldest is Jatin.
Worth noting
Kunal is the oldest. 'But younger than' reverses the direction; turn every clue into the same '>' form before joining them.
In a quiz, Meera scored more than Nitin, and Omkar scored less than Nitin. Pallavi scored more than Meera. Qadir scored less than Meera but more than Nitin. No two scores are equal. Whose score is exactly in the middle of the five?
AnswerD · Qadir
Meera > Nitin > Omkar, and Pallavi > Meera: Pallavi > Meera > Nitin > Omkar.
Qadir fits between Meera and Nitin: Pallavi > Meera > Qadir > Nitin > Omkar.
The 3rd of five is the middle: Qadir.
Worth noting
Nitin is the middle only if Qadir is left out. Place every person before reading a position.
Rani is shorter than Sita. Tina is shorter than Uma. Uma is shorter than Rani. Which of the following lists the four girls from tallest to shortest?
AnswerA · Sita, Rani, Uma, Tina
'Rani is shorter than Sita' means Sita > Rani.
'Uma is shorter than Rani' gives Rani > Uma, and 'Tina is shorter than Uma' gives Uma > Tina.
Joined: Sita > Rani > Uma > Tina.
Worth noting
Every clue here is written with 'shorter', so the second name is the taller one. Rewrite each clue as 'taller > shorter' before joining.
Six friends in a hostel, Uma, Varun, Wasim, Yamini, Zubin and Tina, compared their heights. No two of them are equally tall.
Varun is taller than Uma but shorter than Wasim.
Yamini is shorter than Uma.
Zubin is taller than Wasim.
Tina is taller than Yamini but shorter than Varun.
Which of the six hostel friends is the tallest?
AnswerB · Zubin
Zubin > Wasim > Varun > Uma > Yamini (tallest first).
Tina is below Varun and above Yamini, so she is either just above or just below Uma.
In both possible orders Zubin is at the top.
Worth noting
Wasim is taller than Varun but shorter than Zubin.
Six friends in a hostel, Uma, Varun, Wasim, Yamini, Zubin and Tina, compared their heights. No two of them are equally tall.
Varun is taller than Uma but shorter than Wasim.
Yamini is shorter than Uma.
Zubin is taller than Wasim.
Tina is taller than Yamini but shorter than Varun.
Which friend in the hostel group is the shortest?
AnswerB · Yamini
Zubin > Wasim > Varun > Uma > Yamini (tallest first).
Tina is below Varun and above Yamini, so she is either just above or just below Uma.
Yamini is shorter than both Uma and Tina, so she is the shortest in both orders.
Worth noting
The order of Uma and Tina is open, but both are above Yamini, so the bottom place is fixed.
Five colleagues, Harini, Irfan, Jasleen, Kunal and Manoj, compared their ages. No two of them are the same age.
Kunal is older than exactly two of the others.
Harini is older than Kunal.
Irfan is older than Jasleen.
Manoj is older than Irfan but younger than Harini.
Which of the five colleagues is the oldest?
AnswerA · Harini
Kunal is older than exactly two people, so he is 3rd oldest, with two above him and two below.
Manoj > Irfan > Jasleen is a chain of three; it cannot fit entirely below Kunal (only two places), so Manoj is above Kunal and Irfan, Jasleen are below.
Harini > Manoj, so the order is Harini > Manoj > Kunal > Irfan > Jasleen.
Worth noting
Manoj is older than Irfan but younger than Harini, so he is second.
Six students, Naveen, Oindrila, Prakash, Rukhsar, Sanjay and Tejas, got different marks in a mathematics test.
Tejas scored the lowest marks.
Exactly two students scored more than Prakash.
Oindrila scored less than Rukhsar but more than Sanjay.
Naveen scored more than Oindrila.
Rukhsar did not get the highest marks.
Who got the highest marks in the mathematics test?
AnswerD · Naveen
Tejas is 6th and Prakash is 3rd, leaving places 1, 2, 4 and 5.
Oindrila is below Rukhsar and Naveen but above Sanjay, so Oindrila and Sanjay take 4th and 5th, and Rukhsar and Naveen take 1st and 2nd.
Rukhsar is not first, so the order is Naveen, Rukhsar, Prakash, Oindrila, Sanjay, Tejas (highest first).
Worth noting
Rukhsar scored more than Oindrila, but the last clue rules her out of first place.
Ravi is heavier than both Sunil and Tara. Uday is lighter than Tara. Vikas is heavier than Ravi. Who is the heaviest of the five?
AnswerA · Vikas
Vikas > Ravi, and Ravi is heavier than Sunil, Tara and (through Tara) Uday.
So Vikas is heavier than Ravi and, through Ravi, heavier than everyone else.
Sunil's place below Ravi is not fixed, but that does not affect the top: the heaviest is Vikas.
Worth noting
The full order is not known (Sunil can sit anywhere below Ravi), but the question asks only for the heaviest, which is the same in every possible order. Do not answer 'Cannot be determined' just because the whole order is open.
Lata is taller than Mohan, and Mohan is taller than Nisha. Omar is taller than Nisha. Preeti is taller than Lata. Who is the second shortest?
AnswerD · Cannot be determined
Preeti > Lata > Mohan > Nisha, and Omar > Nisha.
Nisha is shorter than everyone, so she is the shortest. Omar is compared only with Nisha.
Order 1: Preeti > Lata > Mohan > Omar > Nisha, second shortest Omar. Order 2: Omar > Preeti > Lata > Mohan > Nisha, second shortest Mohan.
Both orders fit every clue, so the second shortest cannot be determined.
Worth noting
Mohan is the tempting answer because he sits just above Nisha in the long chain, but Omar can slip in between them.
Arvind is older than Bhanu. Charu is younger than Bhanu but older than Elina. Daksh is older than Charu. Which of the following must be true?
AnswerC · Elina is the youngest.
Arvind > Bhanu > Charu > Elina (oldest first), and Daksh > Charu.
Daksh can be above Arvind, between Arvind and Bhanu, or between Bhanu and Charu: three possible orders.
In all three, Elina is below Charu and Daksh, so Elina is always the youngest.
Arvind is the oldest, Daksh is older than Bhanu and Bhanu is the second oldest are each true in some orders but not all.
Worth noting
'Must be true' means true in EVERY order that fits the clues. A statement that is true in one possible order is only 'could be true'.
Six students, Arun, Bani, Charles, Dev, Ekta and Faiz, stand in a row facing north, arranged by height with the shortest at the left end and the tallest at the right end. Charles is the shortest. Arun is taller than Bani, and Bani is taller than Charles. Dev is taller than Arun but shorter than Ekta. Faiz is taller than Ekta. What is Arun's position from the right end?
AnswerC · 4
Tallest first: Faiz > Ekta > Dev > Arun > Bani > Charles.
The tallest stands at the right end, so counting from the right follows this order.
Arun is 4th in the order, so he is 4th from the right end.
Worth noting
3 is Arun's position from the LEFT end (Charles, Bani, Arun). Decide which end the tallest is at before counting.
Gopi and Ira are both taller than Hina. Hina is taller than both Jai and Kiran. How many of these five people are taller than Hina?
AnswerB · 2
Taller than Hina: Gopi and Ira. Shorter than Hina: Jai and Kiran.
That accounts for all four others, so exactly 2 are taller than Hina, whatever the order within each pair.
Worth noting
The order of Gopi and Ira, and of Jai and Kiran, is unknown, but the count is fixed. 1 counts only one of Gopi and Ira; 4 counts everyone except Hina.
Tenzin is younger than Joseph. Fatima is older than Joseph but younger than Gurpreet. Lalremsiami is younger than Tenzin. How many of the others are younger than Fatima?
AnswerC · 3
Oldest first: Gurpreet > Fatima > Joseph > Tenzin > Lalremsiami.
Below Fatima are Joseph, Tenzin and Lalremsiami: 3 people.
Worth noting
2 misses Lalremsiami, who is younger than Tenzin and therefore younger than Fatima too. 4 counts everyone except Fatima, including Gurpreet, who is older.
Among five cousins, Pavan is older than only Rina. Sonal is older than Qamar, and Qamar is older than Pavan. Tanya is older than Sonal. Who is the second oldest cousin?
AnswerA · Sonal
'Pavan is older than only Rina' means Rina is the youngest and Pavan is just above her: 4th and 5th.
Tanya > Sonal > Qamar fill the top three places, with Qamar above Pavan.
Order: Tanya > Sonal > Qamar > Pavan > Rina. The second oldest is Sonal.
Worth noting
'Older than only Rina' fixes TWO places at once. Qamar is third, not second; Tanya is the oldest.
Six students received their science marks. Bhuvan scored more than Ehsaan, and Aditi scored more than Bhuvan. Ehsaan scored more than Fiza. Chirag scored more than Aditi. Deepa scored less than Aditi but more than Bhuvan. Who ranks 4th from the top?
AnswerD · Bhuvan
Chirag > Aditi > Bhuvan > Ehsaan > Fiza.
Deepa goes between Aditi and Bhuvan: Chirag > Aditi > Deepa > Bhuvan > Ehsaan > Fiza.
4th from the top is Bhuvan.
Worth noting
Deepa is 3rd. Without placing Deepa, Bhuvan looks 3rd and Ehsaan 4th, which is the trap.
Six friends in a hostel, Uma, Varun, Wasim, Yamini, Zubin and Tina, compared their heights. No two of them are equally tall.
Varun is taller than Uma but shorter than Wasim.
Yamini is shorter than Uma.
Zubin is taller than Wasim.
Tina is taller than Yamini but shorter than Varun.
How many of the hostel friends are definitely taller than Varun?
AnswerB · 2
Zubin > Wasim > Varun > Uma > Yamini (tallest first).
Tina is below Varun and above Yamini, so she is either just above or just below Uma.
Above Varun are Wasim and Zubin in every order: 2 friends.
Worth noting
3 comes from counting Varun himself. The open Uma/Tina pair is below Varun and does not matter here.
Five colleagues, Harini, Irfan, Jasleen, Kunal and Manoj, compared their ages. No two of them are the same age.
Kunal is older than exactly two of the others.
Harini is older than Kunal.
Irfan is older than Jasleen.
Manoj is older than Irfan but younger than Harini.
Who is the second youngest of the colleagues?
AnswerC · Irfan
Kunal is older than exactly two people, so he is 3rd oldest, with two above him and two below.
Manoj > Irfan > Jasleen is a chain of three; it cannot fit entirely below Kunal (only two places), so Manoj is above Kunal and Irfan, Jasleen are below.
Harini > Manoj, so the order is Harini > Manoj > Kunal > Irfan > Jasleen.
Second youngest = 4th oldest = Irfan.
Worth noting
Kunal is exactly in the middle (3rd). Count from the young end: Jasleen, then Irfan.
Five colleagues, Harini, Irfan, Jasleen, Kunal and Manoj, compared their ages. No two of them are the same age.
Kunal is older than exactly two of the others.
Harini is older than Kunal.
Irfan is older than Jasleen.
Manoj is older than Irfan but younger than Harini.
How many colleagues are younger than Manoj?
AnswerC · 3
Kunal is older than exactly two people, so he is 3rd oldest, with two above him and two below.
Manoj > Irfan > Jasleen is a chain of three; it cannot fit entirely below Kunal (only two places), so Manoj is above Kunal and Irfan, Jasleen are below.
Harini > Manoj, so the order is Harini > Manoj > Kunal > Irfan > Jasleen.
Below Manoj: Kunal, Irfan and Jasleen, which is 3 people.
Worth noting
2 counts only the chain Manoj > Irfan > Jasleen and forgets that Kunal is also younger than Manoj.
Six students, Naveen, Oindrila, Prakash, Rukhsar, Sanjay and Tejas, got different marks in a mathematics test.
Tejas scored the lowest marks.
Exactly two students scored more than Prakash.
Oindrila scored less than Rukhsar but more than Sanjay.
Naveen scored more than Oindrila.
Rukhsar did not get the highest marks.
In the mathematics test, whose marks rank 4th from the top?
AnswerA · Oindrila
Tejas is 6th and Prakash is 3rd, leaving places 1, 2, 4 and 5.
Oindrila is below Rukhsar and Naveen but above Sanjay, so Oindrila and Sanjay take 4th and 5th, and Rukhsar and Naveen take 1st and 2nd.
Rukhsar is not first, so the order is Naveen, Rukhsar, Prakash, Oindrila, Sanjay, Tejas (highest first).
4th from the top is Oindrila.
Worth noting
Prakash is 3rd; 'exactly two scored more than Prakash' puts him 3rd, not 2nd.
Kabir is heavier than Leena, and Leena is heavier than Manav. Nargis is heavier than Manav. Om is heavier than Kabir. If Nargis is also heavier than Kabir, who is the third heaviest?
AnswerB · Kabir
Om > Kabir > Leena > Manav from the first clues.
With Nargis > Kabir, Nargis must sit above Kabir: either Nargis > Om > Kabir or Om > Nargis > Kabir.
In both orders two people (Om and Nargis) are above Kabir, so Kabir is the third heaviest.
The order of Om and Nargis at the top stays unknown, but it does not change the third place.
Worth noting
Without the 'if' clue, the third heaviest could be Leena, Kabir or Nargis. The extra clue fixes the third place even though the top two stay open.
In a test, Lalit scored more than Mansi, and Neeraj also scored more than Mansi. Mansi scored more than Ojas. Parul scored more than Lalit. No two scores are equal. Which one additional fact would fix the complete order of the five scores?
AnswerD · Neeraj scored more than Parul.
Parul > Lalit > Mansi > Ojas, and Neeraj > Mansi, so Neeraj may be 1st, 2nd or 3rd.
'Neeraj scored more than Parul' leaves only Neeraj > Parul > Lalit > Mansi > Ojas: one order.
'Neeraj scored less than Parul' still leaves Neeraj above or below Lalit: two orders.
'Ojas scored the least' and 'Lalit scored more than Ojas' are already known, so three orders remain.
Worth noting
A clue that is already implied adds nothing. Test each extra clue by counting how many orders survive; the right one leaves exactly one.
Leela and Kamal are both heavier than Jugal, and Jugal is heavier than Hari. Gita is heavier than Hari but is not the heaviest. Irene is lighter than Hari. Who is the second lightest of these six?
AnswerA · Hari
Irene is lighter than Hari, and everyone else (Jugal, Leela, Kamal, Gita) is heavier than Hari.
So Irene is the lightest and Hari is directly above her.
The top four can be ordered in six ways (Gita may sit above or below Jugal), but Hari is 5th of 6 in all of them.
Worth noting
Jugal is the tempting answer, but Gita is only known to be heavier than Hari, so she can be lighter than Jugal. Hari's place is fixed; Jugal's is not.
Six friends in a hostel, Uma, Varun, Wasim, Yamini, Zubin and Tina, compared their heights. No two of them are equally tall.
Varun is taller than Uma but shorter than Wasim.
Yamini is shorter than Uma.
Zubin is taller than Wasim.
Tina is taller than Yamini but shorter than Varun.
Among the six friends in the hostel, who is the fourth tallest?
AnswerD · Cannot be determined
Zubin > Wasim > Varun > Uma > Yamini (tallest first).
Tina is below Varun and above Yamini, so she is either just above or just below Uma.
Order 1: Zubin > Wasim > Varun > Uma > Tina > Yamini, fourth tallest Uma.
Order 2: Zubin > Wasim > Varun > Tina > Uma > Yamini, fourth tallest Tina.
Both orders fit every clue, so the fourth tallest cannot be determined.
Worth noting
Uma is the tempting answer because she appears in the main chain, but no clue compares Uma with Tina.
Six students, Naveen, Oindrila, Prakash, Rukhsar, Sanjay and Tejas, got different marks in a mathematics test.
Tejas scored the lowest marks.
Exactly two students scored more than Prakash.
Oindrila scored less than Rukhsar but more than Sanjay.
Naveen scored more than Oindrila.
Rukhsar did not get the highest marks.
The six students from the mathematics test now sit in a row facing north in increasing order of marks from left to right, with the lowest scorer at the left end. How many students sit between Rukhsar and Sanjay?
AnswerB · 2
Tejas is 6th and Prakash is 3rd, leaving places 1, 2, 4 and 5.
Oindrila is below Rukhsar and Naveen but above Sanjay, so Oindrila and Sanjay take 4th and 5th, and Rukhsar and Naveen take 1st and 2nd.
Rukhsar is not first, so the order is Naveen, Rukhsar, Prakash, Oindrila, Sanjay, Tejas (highest first).
From the left (lowest first): Tejas, Sanjay, Oindrila, Prakash, Rukhsar, Naveen.
Sanjay is 2nd and Rukhsar 5th from the left, so Oindrila and Prakash sit between them: 2 students.
Worth noting
3 is the difference of their places , which counts one of them. The order from the left is the marks order reversed.
The area names are NTA's. The chapters inside them are EduFarming's own division, not NTA's.