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Q15·CSAT · Prelims 2026

Logic — Discrete Distribution Routing

ReasoningMatrix PuzzleArithmetic Problem● Medium

Question

Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct? I. No one travels alone. II. Only D travels with F. III. Only C travels with B. Select the answer using the code given below.

Options

a

I and II only

b

I and III only

Answer
c

II and III only

d

All the three

Explanation

Let us systematically distribute the 7 individuals across the three cars X, Y, Z using the clues:

1Car X allocation: Contains exactly 3 people, one of whom is A (A + 2 others).
2Clue 'Only E travels with G': This means E and G travel together as an exclusive pair in one car. Since Car X requires 3 people, the E+G pair must occupy either Car Y or Car Z.
3Clue 'B does not travel by Y' and 'A and B do not share a car': Since A is in Car X, B cannot be in Car X. Since B cannot be in Car Y either, B must be in Car Z.
4Placing the E+G pair: If the exclusive E+G pair were in Car Z, then B would be forced into Car Y, which violates the clues. Therefore, the E+G pair must occupy Car Y.
5Reviewing the distribution so far:
Car X: A + 2 open slots
Car Y: Exactly E and G (Now full based on the 'only' constraint)
Car Z: B + C (since the clue states C travels by Z) + open slots
6Allocating the remaining individuals (D and F): The two remaining people are D and F. They must fill the 2 open slots in Car X to complete its 3-person requirement.
7Final Verified Distribution:
Car X: \{A, D, F\}
Car Y: \{E, G\}
Car Z: \{B, C\}

Let us evaluate the statements based on this final arrangement:

Statement I is correct: Car X has 3 people, Car Y has 2, and Car Z has 2. No one travels alone.
Statement II is incorrect: D and F travel together in Car X along with A, so D does not travel 'only' with F.
Statement III is correct: Car Z contains exactly \{B, C\}, meaning C travels only with B.

Since statements I and III are correct, option (b) is the correct choice.

Solving distribution puzzles requires identifying exclusive pairs and using elimination to assign individuals to fixed groups.

Answer: (b).

Question details

Year

2026

Paper

CSAT

Question

Q15

Section

Analytical Reasoning

Sub-topic

Matrix Puzzle

Type

Arithmetic Problem

Difficulty

Medium

Source hint

Standard puzzles — grouping constraints mapping

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