Data sufficiency

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Data sufficiency

by Newaz111 » Thu May 07, 2015 8:10 pm
Is the sum of p2 and q2 greater than 1?
(1)p is greater than 1/2.
(2) q is greater than 1/2.

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by Brent@GMATPrepNow » Thu May 07, 2015 9:23 pm
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.
Target question: Is p² + q² greater than 1?

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
Brent Hanneson - Creator of GMATPrepNow.com
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