Is the sum of p2 and q2 greater than 1?
(1)p is greater than 1/2.
(2) q is greater than 1/2.
Data sufficiency
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Target question: Is p² + q² greater than 1?Newaz111 wrote:Is the sum of p² and q² greater than 1?
(1) p is greater than 1/2.
(2) q is greater than 1/2.
Statement 1: p is greater than 1/2
There's no information about q, so this statement is probably not sufficient.
To be certain, let's TEST some values.
Case a: p = 1 and q = 1, in which case p² + q² = 1² + 1² = 2, and 2 IS greater than 1
Case b: p = 2/3 and q = 0, in which case p² + q² = (2/3)² + 0² = 4/9, and 4/9 is NOT greater than 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: q is greater than 1/2
There's no information about p, so this statement is probably not sufficient.
To be certain, let's TEST some values.
Case a: p = 1 and q = 1, in which case p² + q² = 1² + 1² = 2, and 2 IS greater than 1
Case b: p = 0 and q = 2/3, in which case p² + q² = 0² + (2/3)² = 4/9, and 4/9 is NOT greater than 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
The combined statements don't FEEL sufficient, so I'm going to TEST some values.
Case a: p = 1 and q = 1, in which case p² + q² = 1² + 1² = 2, and 2 IS greater than 1
Case b: p = 2/3 and q = 2/3, in which case p² + q² = (2/3)² + (2/3)² = 8/9, and 8/9 is NOT greater than 1
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Cheers,
Brent