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?

To determine the correct statement, we must systematically solve the given system of linear equations.

1. Understand the given equations: We are provided with the following relationships:

1. A + B + C + D = 17
2. A + C = 6
3. P + Q + S + D = 15
4. P + Q + R + B = 17
5. P = R
6. Q = S

2. Simplify the relationships: Substitute equation (2) into equation (1): (A + C) + B + D = 17 6 + B + D = 17 B + D = 11

Next, substitute the equivalencies from equations (5) and (6) into equations (3) and (4): From (3): P + Q + Q + D = 15 => P + 2Q + D = 15 From (4): P + Q + P + B = 17 => 2P + Q + B = 17

3. Find the combined weight of P and Q: Add these two new equations together: (P + 2Q + D) + (2P + Q + B) = 15 + 17 3P + 3Q + B + D = 32

Substitute the known sum (B + D = 11) into this equation: 3(P + Q) + 11 = 32 3(P + Q) = 21 P + Q = 7

4. Evaluate the options:

• Why Option B is correct: We mathematically established that P + Q = 7. We are explicitly given A + C = 6. Therefore, P and Q together (7) weigh more than A and C together (6).
• Why Option A is incorrect: It claims B + D Q or Q > P.

Takeaway: When solving algebraic reasoning questions in CSAT, group known sums together (like A+C and B+D) to systematically eliminate variables and isolate the target expressions.