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# Is the sum of p^2 and q^2 greater than 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 44650
Is the sum of p^2 and q^2 greater than 1? [#permalink]

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19 Nov 2017, 09:27
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Difficulty:

35% (medium)

Question Stats:

77% (00:46) correct 23% (00:31) wrong based on 30 sessions

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Is the sum of p^2 and q^2 greater than 1?

(1) p is greater than 1/2.

(2) q is greater than 1/2.
[Reveal] Spoiler: OA

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Joined: 25 Feb 2013
Posts: 1060
Location: India
GPA: 3.82
Is the sum of p^2 and q^2 greater than 1? [#permalink]

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19 Nov 2017, 09:43
Bunuel wrote:
Is the sum of p^2 and q^2 greater than 1?

(1) p is greater than 1/2.

(2) q is greater than 1/2.

Is $$p^2+q^2>1$$

Statement 1: $$p>\frac{1}{2}$$

so $$p^2>\frac{1}{4}$$. but nothing mentioned about $$q$$. Hence insufficient

Statement 2: $$q>\frac{1}{2}$$

so $$q^2>\frac{1}{4}$$. but nothing mentioned about $$p$$. Hence insufficient

combining 1 & 2 we get $$p^2+q^2>\frac{1}{4}+\frac{1}{4}$$

hence $$p^2+q^2>0.5$$. So we can have both a Yes & No situation. Hence Insufficient

Option E
Is the sum of p^2 and q^2 greater than 1?   [#permalink] 19 Nov 2017, 09:43
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