Discussion
P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A is greater than B.
In this context, which of the following statements is correct ?
Answer: D
None of the above can be concluded with certainty.
Subtract:
\[ P - Q = 0.65B - 0.5B - (0.5A - 0.4A) = 0.15B - 0.1A \]
Its sign depends on the actual values. With A = 10, B = 9: \(1.35 - 1 \gt 0\), so P is greater. With A = 10, B = 2: \(0.3 - 1 \lt 0\), so Q is greater. Knowing only that A is greater than B does not fix the sign.
P = Q only when \(0.15B = 0.1A\), that is when A = 1.5B, which is allowed but not required.
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