Reasoning

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Reasoning — Key Facts for CUET Alphabet test: Position of letters (A=1, Z=26); reverse position (A=26, Z=1); word formation from scrambled letters Ranking and ordering: Position from top/bottom, left/right; total = position from top + bottom - 1 Calendar: 28-year cycle for days; leap year rules (divisible by 4, except century not divisible by 400) Clocks: Right angle at 3:00, 9:00, 15:00, 21:00 (but also ~3:33, ~8:27); straight line (0°/180°) at 6:00, 18:00 and ~9:17, ~2:43 Inserting missing number: Find the pattern (row-wise, column-wise, diagonal, or based on operation) ⚡ Exam tip: In ranking problems, always use the formula: Total = Position from one end + Position from other end - 1

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Reasoning — CUET General Test Study Guide

Reasoning in CUET covers non-verbal and verbal reasoning patterns. This section tests your ability to recognise patterns, sequences, and relationships — skills that are language-independent and rely on logical thinking.

Alphabet Test:

Positions: A=1, B=2, …, Z=26. Reverse positions: A=26, B=25, …, Z=1.

Word formation: Given scrambled letters, find if a meaningful word can be formed. Example: From “ENABLE,” words: BEAN, LEAN, NABLE (not common), BALE.

Letter series: Find the next letter or missing letter.

• Pattern types: Skip by constant (A, D, G, J → +3), alternating (A, Z, B, Y, C → first +1, second -1), position-based (A=1, B=2, 1+2=3=C)
• Example: BZD, EYG, HUJ → Next? B(2), Z(26), D(4): 2+26+4=32→6=F; E(5), Y(25), G(7): 5+25+7=37→10=J; H(8), U(21), J(10): 8+21+10=39→12=L → KIL? Actually pattern may be first+3, second+4, third+3…

Ranking and Ordering:

Linear ranking: “Ravi is 5th from the top and 12th from the bottom. How many students are in the class?” Total = 5 + 12 - 1 = 16. (Since Ravi is counted in both)

Overlapping rankings: “In a row, A is 10th from left, B is 9th from right. There are 5 students between A and B. How many students?” Position A = 10, Position B = total - 9 + 1 = total - 8. Gap of 5 between them means |(10) - (total-8)| - 1 = 5. If B > A: (total-8) - 10 - 1 = 5 → total - 19 = 5 → total = 24.

Circular ranking: “In a circle, if A is 5th to the right of B and 3rd to the left of C. How many people minimum?” In circular arrangement, count clockwise and anticlockwise.

Calendar Problems:

Leap Year Rules:

1. Year divisible by 4 → leap year
2. Exception: Year divisible by 100 → not leap year
3. Exception to exception: Year divisible by 400 → leap year

• Examples: 2000 (leap, divisible by 400), 1900 (not leap, divisible by 100 but not 400), 2024 (leap, divisible by 4)

Finding the Day:

• Count days from a reference date
• Odd days = (date + month code + year code) mod 7
• Month codes: Jan=0 (1 for leap year), Feb=3 (1 for leap year), Mar=3, Apr=6, May=1, Jun=4, Jul=6, Aug=2, Sep=5, Oct=0, Nov=3, Dec=5
• Year code: Last two digits + quarter of last two digits (integer division by 4) + century code (1600s: 0, 1700s: 5, 1800s: 3, 1900s: 1, 2000s: 0)

Example: What day was 15 August 1947 (Independence Day)?

• Date: 15
• Month: August → code = 2
• Year: 47 + floor(47/4) = 47 + 11 = 58
• Century code: 1900 → 1
• Total = 15 + 2 + 58 + 1 = 76
• 76 mod 7 = 6
• Reference: 1 Jan 2000 was Saturday (code 0 = Saturday). 6 = Friday. But actually 15 Aug 1947 was a Friday. ✓

Inserting Missing Numbers:

Grid patterns:

• Magic square: Each row, column, and diagonal sums to same number
• Example 3×3: 8 1 6 / 3 5 7 / 4 9 2 → each row/col sums to 15
• Operation-based: Top row numbers operated to give bottom row

Cube and Dice:

Dice rules:

• Opposite faces: In standard dice, 1↔6, 2↔5, 3↔4 (each pair sums to 7)
• If 1 is on top and 2 is in front, the right face is 5
• When two dice are rolled, opposite faces never appear together

Folding a cube: Given a net of a cube with colours/symbols on faces, determine if it can form a valid cube and which faces are opposite.

Analytical Reasoning:

Statement-Assumptions:

• Statement given, find which assumption is implicit (necessarily true for the statement to hold)
• Example: Statement: “The government has announced a 10% cut in petrol prices.”
  • Assumption 1: The previous price was higher than it should be → NOT implicit (not necessarily stated)
  • Assumption 2: The cut will affect other fuel prices → NOT implicit (not necessarily true)
  • Assumption 3: The government has the authority to fix fuel prices → IMPLICIT (statement implies government controls prices)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Reasoning — Comprehensive CUET General Test Notes

Non-Verbal Reasoning — Figure Series:

Rotational symmetry: Figure rotates by 90° or multiples. Identify the pattern of change from figure to figure.

Figure matrix: 3×3 or 2×2 matrix with one figure missing. Find the pattern:

• Row-wise: Each row follows same transformation rule
• Column-wise: Each column follows same rule
• Diagonal: Pattern along diagonals
• Global: All figures share a common property

Paper Folding: If a paper is folded and a hole/punch is made, predict the unfolded pattern. Mirror the fold line.

Mirror and Water Images:

• Mirror image: Left-right reversal (along vertical axis)
• Water image: Up-down reversal (along horizontal axis)
• The image flips along the axis of reflection

Counting Figures:

• Count triangles, squares, rectangles, circles in a complex figure
• Systematically label each distinct figure and its sub-figures
• Formula for triangles in a triangle divided by parallels: If a triangle is divided by lines parallel to the base, count all triangles

Embedded Figures: One figure is hidden within another. Identify the part that contains all lines of the embedded figure.

Analogy — Figures: Find the relationship between two figures and apply to a third.

• Rotation: If first figure rotates 90° clockwise to give second figure, the third must also rotate 90° clockwise
• Colour addition: Black becomes white, white becomes black, striped becomes dotted
• Overlay: One figure overlaid on another creates a third

Figure Completion: A part of a figure is missing. Identify which of the options completes it.

Coding of Days: The day before yesterday is Monday. What day is it 3 days after the day after tomorrow?

• Day before yesterday = Monday → Yesterday = Wednesday → Today = Thursday
• Day after tomorrow = Friday
• 3 days after Friday = Monday (Sat, Sun, Mon → Monday)

Inequality-based Reasoning: If A > B, B > C, and C > D, then A > D (transitivity). If A > B and C > D, we cannot compare A and C without more information.

Order of Letters in Alphabet:

• How many letters are between K and P in alphabetical order? K, L, M, N, O, P → 4 letters between them (L, M, N, O)
• If K is 11th from left, and P is 5th from right in a row of 20, P’s position = 20-5+1 = 16. Letters between = 16-11-1 = 4.

Sequence and Series Reasoning:

• ABCD…Z → position of each
• Reverse alphabet: Z=1, Y=2, …
• Jump series: A, E, I, O → vowels (every 4th letter from A)
• Position difference series: A(1), C(3), F(6), J(10) → differences 2, 3, 4…

Word-Based Reasoning: “BOOK” is to “READ” as “PEN” is to ”?” The relationship: “BOOK is used for READING” = instrument for activity. “PEN is used for WRITING.” Answer: WRITE.

Distance and Direction — Complex: A man walks 5 km South, turns right (West) walks 3 km, turns right (North) walks 2 km, turns left (West) walks 1 km. How far is he from starting point?

• Net displacement North-South: 5 - 2 = 3 km South
• Net displacement East-West: 3 - 1 = 2 km East
• Distance = √(3² + 2²) = √13 km

CUET Exam Patterns (2022–2024):

• Alphabet-based reasoning (positions, series) is most frequent
• Calendar problems (day of week for given date) appear every year
• Figure series (non-verbal) are common in the DI/Reasoning section
• Ranking and ordering problems are frequent
• Common mistakes: forgetting to subtract 1 when combining two rankings; miscounting alphabet positions (A=1 to Z=26); confusing mirror and water images

⚡ Key insight: In reasoning, the most reliable approach is to systematically apply the logical rules. Don’t guess or use intuition — follow the algorithm. For alphabet tests, always write out the positions. For calendar problems, memorize the month codes and century codes. For non-verbal reasoning, identify one transformation at a time (rotation, reflection, colour change).

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