Bunuel
Is the sum of p² and q² greater than 1?
(1) p is greater than 1/2.
(2) q is greater than 1/2.
Target question: Is p² + q² > 1?When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the
target question. So, I’m going to head straight to……
Statements 1 and 2 combined There are several values of p and q that satisfy BOTH statements. Here are two:
Case a: p = 1 and q = 1, in which case p² + q² = 1² + 1² = 1 + 1 = 2. So, the answer to the target question is
YES, p² + q² is greater than 1Case b: p = 2/3 and q = 2/3, in which case p² + q² = (2/3)² + (2/3)² = 4/9 + 4/9 = 8/9. So, the answer to the target question is
NO, p² + q² is not greater than 1Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E