Logical Reasoning: DILR Notes for CAT (MBA)

Logical Reasoning – Study Notes

(Program: CAT – MBA | Subject: DILR)

Logical Reasoning (LR) tests your ability to analyze information, identify patterns, draw conclusions, and solve problems quickly. It’s a core component of the CAT quantitative section and a key skill in business decision‑making.

1. Simple Explanation

What it is: A set of problems that assess your logical thinking—how well you can deduce, infer, or infer from given data.
Why it matters: Every business decision involves evaluating evidence, spotting inconsistencies, and making reasoned judgments.
Typical formats (CAT 2024‑2026):
- Logical Sequence (series completion)
- Data Sufficiency
- Syllogism & Statement‑Conclusion
- Logical Reasoning Puzzles (e.g., “Which of the following could be true?”)
- Logical Reasoning – Quantitative (e.g., “If X increases, Y decreases”)

2. Key Points & Strategies

Category	What to Look For	Strategy
Logical Sequence	Common patterns: arithmetic progression, geometric progression, alternating sequences, digit manipulation, letter patterns, set‑based patterns (e.g., “3, 5, 8, 13”)	Identify the rule first; eliminate sequences that don’t fit; check all options.
Data Sufficiency (DS)	“Statement 1” & “Statement 2”; answer choices: (A) only statement 1, (B) only statement 2, (C) both, (D) either, (E) neither	1️⃣ Check if data gives a unique answer. 2️⃣ Look for “minimum/maximum” or “range” clues. 3️⃣ Use elimination: if one statement gives a range, it may be enough.
Syllogism / Statement‑Conclusion	Two premises → one conclusion. 4 answer options: (A) true, (B) false, (C) both, (D) none	1️⃣ Translate into “All A are B” or “Some A are B” format. 2️⃣ Check for logical consistency. 3️⃣ Use “counter‑example” to disprove.
Logical Reasoning Puzzles	“Which of the following could be true?”	1️⃣ Draw a diagram (flow‑chart, Venn diagram, table). 2️⃣ Note constraints. 3️⃣ Test each option against constraints.
Logical Reasoning – Quantitative	“If X increases, Y behaves how?”	1️⃣ Write equations/inequalities. 2️⃣ Check monotonicity. 3️⃣ Verify edge cases.

General Tips

Read Carefully – Mis‑reading a single word can flip the answer.
Work Backwards – For “could be true” questions, start with the given answer and see if it violates any constraints.
Mark and Move – If stuck, mark the question and move on; you’ll have time to return.
Time Management – Allocate ~1.5 minutes per question on the LR section.
Practice Pattern Recognition – The more you see the same pattern, the faster you’ll spot it in the test.

3. Worked Example

Question

In a set of numbers, the ratio of the sum of the first two numbers to the sum of the last two numbers is 3:2. If the first number is 4 and the third number is 9, what is the fourth number?

Option	Value
A	6
B	8
C	12
D	15
E	18

Solution

Set up the equation
- Let the numbers be: 4, x, 9, y.
- Ratio: (\frac{4 + x}{9 + y} = \frac{3}{2}).
Cross‑multiply
[ 2(4 + x) = 3(9 + y) \ 8 + 2x = 27 + 3y \ 2x - 3y = 19 ]
Find integer solutions (x and y are whole numbers)
- Test each option for (y):
  - If (y = 6): (2x - 18 = 19 \Rightarrow 2x = 37 \Rightarrow x = 18.5) (not integer).
  - If (y = 8): (2x - 24 = 19 \Rightarrow 2x = 43 \Rightarrow x = 21.5) (not integer).
  - If (y = 12): (2x - 36 = 19 \Rightarrow 2x = 55 \Rightarrow x = 27.5) (not integer).
  - If (y = 15): (2x - 45 = 19 \Rightarrow 2x = 64 \Rightarrow x = 32).
- Check the ratio: (\frac{4+32}{9+15} = \frac{36}{24} = \frac{3}{2}) ✔️
Conclusion
- The fourth number (y = 15).
- Answer: D

Quick Check

Option	4 + x	9 + y	Ratio
A	4 + 18.5	9 + 6	22.5/15 = 1.5 → 3:2 ✔️? No, x not integer
B	…	…	…
C	…	…	…
D	36	24	3:2 ✔️
E	…	…	…

4. Quick Revision Summary

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