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:

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?

1. A. B and D together weigh less than the total weight of P and Q.
2. B. P and Q together weigh more than the total weight of A and C. (Correct answer)
3. C. P weighs more than Q.
4. D. Q weighs more than P.

Correct Answer

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

Detailed Solution & Explanation

The correct answer is Option B.

Key Points

• Given P + 2Q + D = 15 (using S = Q) and 2P + Q + B = 17 (using R = P).
• Adding them: 3P + 3Q + (B + D) = 32, and since B + D = 17 − 6 = 11, we get 3(P + Q) = 21, so P + Q = 7.
• Compare with A + C = 6: therefore P + Q (7) > A + C (6).

Additional Information

• Option A fails because B + D = 11 is not less than P + Q = 7. The individual comparison of P and Q cannot be fixed, so the only guaranteed truth is Option B.