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# If x and y are positive, is √x+y>10?

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

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11 May 2017, 03:08
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75% (hard)

Question Stats:

55% (01:14) correct 45% (01:13) wrong based on 187 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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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? &nbs [#permalink] 11 May 2017, 06:13
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# If x and y are positive, is √x+y>10?

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