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?
Answer & explanation
Answer: (b) P and Q together weigh more than the total weight of A and C.
Adding the last two equations after substituting R = P and S = Q gives 3(P + Q) + B + D = 32, and B + D = 11 from the first two. So P + Q = 7, which is more than A + C = 6.
- From A + B + C + D = 17 and A + C = 6: B + D = 11.
- Put S = Q: P + 2Q + D = 15. Put R = P: 2P + Q + B = 17.
- Add them: 3P + 3Q + B + D = 32, so 3(P + Q) = 32 − 11 = 21 and P + Q = 7.
- (a) B + D = 11 is not less than 7 — false. (b) P + Q = 7 > A + C = 6 — true.
- P and Q individually are not fixed (for example P = 3, Q = 4 or P = 4, Q = 3 with suitable B, D), so (c) and (d) cannot be asserted.
- ✗ (a) B + D = 11 is more than P + Q = 7.
- ✓ (b) P + Q = 7 exceeds A + C = 6.
- ✗ (c) Only P + Q = 7 is fixed; P can be larger or smaller than Q.
- ✗ (d) Same reason: the data do not fix which of P and Q is heavier.
Remember · When single values can't be found, add the equations to get the combined quantity the options ask about.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·