Logical reasoning tricks sheet for CUET's General Aptitude Test
The shortcuts for all thirteen Logical and Analytical Reasoning chapters on one page: series, codes, relations, directions, rankings, arrangements, syllogisms, calendars, clocks, Venn diagrams and figures.
This is the page to read the night before the test. Each section is the short version of one chapter; the chapter notes have the worked examples, and every chapter has its own practice questions.
What letter positions should you know by heart?
Almost every letter series, letter analogy and code question runs on the position of a letter in the alphabet. Learn the positions of E, J, O, T and Y and count from the nearest one.
A B C D E F G H I J K L M
1 2 3 4 5 6 7 8 9 10 11 12 13
N O P Q R S T U V W X Y Z
14 15 16 17 18 19 20 21 22 23 24 25 26
EJOTY: E = 5, J = 10, O = 15, T = 20, Y = 25
Opposite letters add to 27: A–Z, B–Y, C–X, D–W, E–V, F–U, G–T, H–S, I–R, J–Q, K–P, L–O, M–N
Position counted from Z = 27 − position from A
How do you find the rule in a number series?
Test in this order, and stop at the first rule that fits every term:
- Differences. Constant: add a fixed number. Growing by a constant: the second differences are equal.
- Ratios. Each term a fixed multiple of the one before, or ×n followed by ±k.
- Squares and cubes. Terms near 1, 4, 9, 16, 25, 36… or 1, 8, 27, 64, 125…, often ±1 or ±n.
- Two series interleaved. Terms 1, 3, 5… follow one rule and terms 2, 4, 6… another.
- Primes, or the sum of the two terms before.
For a wrong term, find the rule from most of the terms, then check which single term breaks it; only one change should repair the whole series.
What are the quickest checks for analogies and odd one out?
Say the first pair's relationship as a sentence ("a carpenter uses a saw"), then find the option that fits the same sentence in the same order. Common relationships: worker and tool, tool and action, part and whole, cause and effect, young one and adult, study and subject (ornithology is to birds), and degree (warm is to hot).
For numbers, check in turn: even or odd, prime, perfect square or cube, divisibility by 3, 4, 5, 7 or 11, and digit sums. The odd one out is the one that breaks a property the other three share, and a good question has only one such property.
How do you crack a letter or number code?
Write the positions of the word and of its code under each other and look at the difference in each place.
| What you see | The code |
|---|---|
| every difference the same | shift by that amount |
| the code reads backwards | reversal, perhaps followed by a shift |
| differences +1, −1, +1… | alternating shift |
| differences 1, 2, 3… | shift growing with position |
| code letters add to 27 with the word's | opposite letters |
| a number for the word | sum or product of positions, or number of letters used |
In sentence codes, compare two sentences: the word common to both has the code common to both.
How do you solve blood relation questions?
Draw the family tree: generations as rows, a vertical line for parent and child, a horizontal line for brothers and sisters, and a double line for husband and wife. Mark + for male and − for female. Start from the person the question is about and read the relation from them.
- "My father's only son" is the speaker himself. "My mother's only daughter" is the speaker herself.
- If someone's gender is never stated, the relation may be "cannot be determined": check whether the answer changes with the gender.
- Maternal means on the mother's side; paternal, on the father's.
How do you track directions and distances?
Use coordinates: north +y, south −y, east +x, west −x. Keep a note of which way the person is facing, because a right turn when facing north means east, but a right turn when facing south means west.
N
NW NE
W E
SW SE
S
Right turn = 90° clockwise, left turn = 90° anticlockwise
- Distance from the start = √(x² + y²). Learn the triples 3-4-5, 6-8-10, 5-12-13 and 8-15-17.
- The direction is measured from the start to the end, not the other way round.
- At sunrise the sun is in the east, so shadows fall to the west. At sunset the shadows fall to the east.
What are the formulas for ranking and positions in a row?
total = position from left + position from right − 1
people between A and B = (difference of their positions from the same end) − 1
- If two people's positions from opposite ends add up to more than the total, their positions overlap, and the number between them is (sum of positions) − total − 2.
- When two people swap places, a person's new position gives a second equation, and the difference in the swapped positions carries over.
- For comparisons (taller, older, heavier), write the chain with the largest first and check whether every clue has been used. If two people cannot be placed, the answer is "cannot be determined".
How do you set up a seating arrangement quickly?
- Place the person with the most definite clue first (someone at an end, or someone whose position is given).
- In a row facing north, each person's left is the west end of the row; in a row facing south, their left is the east end. Always read which way the row faces.
- At a round table with everyone facing the centre, left is clockwise and right is anticlockwise.
- Try the one or two cases a clue allows, draw each one, and drop a case the moment a clue fails.
How do you solve a grid puzzle?
Make a table with people as rows and the attributes (day, colour, city, floor) as columns. Fill in the direct clues first, then use elimination: each value is used exactly once, so a tick in a row rules out that value in every other row. For floors, remember that "above" does not mean "immediately above" unless the question says so.
What follows in a syllogism?
Draw the Venn diagrams, and accept a conclusion only if it is true in every diagram that fits the statements.
| Statements | What definitely follows |
|---|---|
| All A are B, All B are C | All A are C |
| All A are B, No B is C | No A is C |
| Some A are B, All B are C | Some A are C |
| All A are B, Some B are C | nothing definite about A and C |
| Some A are B, No B is C | Some A are not C |
- "No A is B" can be turned round: No B is A. "Some A are B" can be turned round: Some B are A. "All A are B" turns round only to "Some B are A". "Some A are not B" never turns round.
- Either–or is correct only when neither conclusion follows by itself, they are about the same two groups, and between them one must be true: Some/No, or All/Some-not.
- A possibility conclusion follows if it is true in at least one diagram that fits the statements.
How do you judge conclusions, assumptions and courses of action?
- A conclusion follows only if the statement itself makes it true. Do not add what you know from outside.
- An assumption is what the speaker must take for granted for the statement to make sense. Ask: if this were false, would the statement still be reasonable? If not, it is implicit.
- A course of action follows if it is practical, deals with the problem stated and is not extreme. "Ban it completely" and "stop it for ever" are usually too strong.
What are the calendar and clock shortcuts?
Odd days. An ordinary year has 1 odd day and a leap year 2. 100 years have 5 odd days, 200 years 3, 300 years 1 and 400 years 0.
odd days 0 1 2 3 4 5 6
day Sun Mon Tue Wed Thu Fri Sat (counting from a Sunday)
- A year is a leap year if it divides by 4, except century years, which must divide by 400: 2000 was a leap year, 1900 was not.
- A leap year's calendar repeats after 28 years. An ordinary year's repeats after 6 years if it is the year just after a leap year, and after 11 years if it is the second or third year after one. These gaps break when a century year that is not a leap year (2100, 2200) falls in between, so there count the odd days year by year.
Clocks.
angle between the hands at h hours m minutes = |30h − 5.5m| degrees
- The minute hand gains 5.5° a minute on the hour hand, so the hands meet every 65 5⁄11 minutes: 11 times in 12 hours, 22 times in a day.
- They are opposite 11 times in 12 hours and at right angles 22 times in 12 hours.
- Mirror time = 11:60 minus the time shown. For a time between 12:00 and 1:00, subtract from 23:60 instead.
How do you use Venn diagrams for counting?
n(A or B) = n(A) + n(B) − n(A and B)
n(A or B or C) = n(A) + n(B) + n(C) − n(A and B) − n(B and C) − n(A and C) + n(all three)
To choose the right diagram for three groups, decide for each pair whether one is inside the other, they are apart, or they overlap. Men, women and doctors: men and women are apart, and doctors overlap both.
What are the non-verbal shortcuts?
- Mirror image, mirror beside the figure: left and right swap, top and bottom stay. Water image, water below: top and bottom swap, left and right stay. A reflection never turns a figure.
- Paper folding: every fold doubles the holes. Open the folds in reverse order, reflecting each hole across each fold line.
- Figure series: follow one element at a time, such as the arrow, the dot or the number of sides, and check every option against every rule.
- Counting triangles: a triangle with n lines from its top vertex to its base holds (n + 2)(n + 1) ÷ 2 triangles. A square with both diagonals holds 8, and a square with its diagonals and both midlines holds 16. A grid of r rows and c columns holds [(c + 1)c ÷ 2] × [(r + 1)r ÷ 2] rectangles.
Which traps cost the most marks in Logical Reasoning?
- Measuring a direction from the end point instead of the start point.
- Forgetting to subtract 1 when adding positions from both ends.
- Taking "Some A are B" to mean "Some A are not B". It does not; "some" allows "all".
- Reading "above" as "immediately above" in floor puzzles.
- Choosing the rotation in a mirror question.
- Assuming a gender that the question never gave.
- Counting the start day when finding the day of the week after a number of days.