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Q6768/80Q69
Q68·CSAT · Prelims 2026

Logic — Simultaneous Equation Weight systems

ReasoningMatrix PuzzleArithmetic Problem● Hard

Question

The weight of X, in kg, is denoted by X. The weights of A, B, C, D, P, Q, R and S are measured. Given: A+B+C+D=17, A+C=6, P+Q+S+D=15, P+Q+R+B=17, P=R and Q=S. Which one of the following statements is correct?

Options

a

B and D together weigh less than the total weight of P and Q.

b

P and Q together weigh more than the total weight of A and C.

Answer
c

P weighs more than Q.

d

Q weighs more than P.

Explanation

Let us evaluate the system of equations step-by-step using the provided variables:

1A + B + C + D = 17
2A + C = 6
3P + Q + S + D = 15
4P + Q + R + B = 17
5P = R and Q = S
Step 1: Substitute equation 2 into equation 1:

(A + C) + B + D = 17 \implies 6 + B + D = 17 \implies B + D = 11

Step 2: Simplify equations 3 and 4 using the equalities P = R and Q = S:
Equation 3 becomes: P + Q + Q + D = 15 \implies P + 2Q + D = 15
Equation 4 becomes: P + Q + P + B = 17 \implies 2P + Q + B = 17
Step 3: Add these two simplified equations together:

(P + 2Q + D) + (2P + Q + B) = 15 + 17 \implies 3P + 3Q + (B + D) = 32

Step 4: Substitute B + D = 11 into this combined equation:

3P + 3Q + 11 = 32 \implies 3(P + Q) = 21 \implies P + Q = 7

Evaluate the Options: We found that P + Q = 7. Comparing this to equation 2 (A + C = 6) shows that P + Q > A + C (7 > 6). This matches option (b) exactly.
Complex simultaneous variable systems can be solved by grouping shared combinations of terms (like B+D or P+Q) to evaluate the options directly.

Answer: (b).

Question details

Year

2026

Paper

CSAT

Question

Q68

Section

Analytical Reasoning

Sub-topic

Matrix Puzzle

Type

Arithmetic Problem

Difficulty

Hard

Source hint

Algebraic puzzles — simultaneous value elimination matrices

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