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If x and y are positive, is √x+y>10?

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Math Expert
Joined: 02 Sep 2009
Posts: 46207
If x and y are positive, is √x+y>10? [#permalink]

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11 May 2017, 03:08
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Difficulty:

75% (hard)

Question Stats:

54% (01:07) correct 46% (01:12) wrong based on 167 sessions

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If x and y are positive, is $$\sqrt{x+y}>10$$?

(1) $$\frac{\sqrt{x}}{2} +\frac{\sqrt{y}}{2}>5$$

(2) $$\sqrt{4x}>20$$

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Re: If x and y are positive, is √x+y>10? [#permalink]

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11 May 2017, 03:28
In Statement one 2 can be taken to the other side.After squaring LHS and RHS it can be seen that the information alone will not provide us with solution.
On squaring statement 2, we get x>100
Since x and y are positive, this statement alone is sufficient
Hence B
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Joined: 14 Dec 2016
Posts: 6
Schools: Booth '18, Stern '18
GMAT 1: 640 Q44 V34
Re: If x and y are positive, is √x+y>10? [#permalink]

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11 May 2017, 06:13
Bunuel wrote:
If x and y are positive, is $$\sqrt{x+y}>10$$?

(1) $$\frac{\sqrt{x}}{2} +\frac{\sqrt{y}}{2}>5$$

(2) $$\sqrt{4x}>20$$

IMO B.

$$\sqrt{x+y}>10$$
square both sides..
so the question becomes : Is |x+y|>100?
Since x & y are both positive x+y will be positive.

statement 1. says : $$\frac{\sqrt{x}}{2} +\frac{\sqrt{y}}{2}>5$$ => $$\sqrt{x}+\sqrt{y}>10$$
This doesn't give any information on values of x and y.

Statement 2 says: $$\sqrt{4x}>20$$ => $$\sqrt{x}>10$$ squaring both sides: x>100 .

Hence this statement itself is sufficient since y is positive x+y has to be greater than 100.

Re: If x and y are positive, is √x+y>10?   [#permalink] 11 May 2017, 06:13
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