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If x and y are positive, is √x+y>10?

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Joined: 02 Sep 2009
Posts: 49366
If x and y are positive, is √x+y>10?  [#permalink]

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New post 11 May 2017, 03:08
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

55% (01:14) correct 45% (01:13) wrong based on 187 sessions

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Senior Manager
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Joined: 02 Mar 2017
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Concentration: Finance, Marketing
Re: If x and y are positive, is √x+y>10?  [#permalink]

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New post 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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New post 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.


Answer: B
GMAT Club Bot
Re: If x and y are positive, is √x+y>10? &nbs [#permalink] 11 May 2017, 06:13
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