If (x/y)^(1/2)=n, what is the value of x? : GMAT Data Sufficiency (DS)
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# If (x/y)^(1/2)=n, what is the value of x?

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If (x/y)^(1/2)=n, what is the value of x? [#permalink]

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06 Apr 2012, 17:49
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If (x/y)^(1/2)=n, what is the value of x?

(1) (n^2)y = 100
(2) n= 5 and y = 4

[Reveal] Spoiler:
This question is from Total GMAT Math. The statement (1) provides that (n^2)y = 100 which implies that n(y^(1/2)) can be either 10 or -10. However, the solution provided by the book states that the above value is only 10. Hence I chose B, sine the statement (1) can be both 10 or -10. Is my approach incorrect?

[Reveal] Spoiler: OA
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Re: If (x/y)^(1/2)=n, what is the value of x? [#permalink]

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06 Apr 2012, 20:09
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KUDOS
Rearranging/squaring the equation given in the question saves you from the troubles with square roots.

$$\sqrt{\frac{x}{y}}=n$$
$$\frac{x}{y}=n^2$$
$$x=(n^2)y$$

Statement 1: $$(n^2)y=100$$
Hence statement 1 is sufficient.

Also if you were to continue from the equation you've arrived at,
When its 10:
$$n\sqrt{y}=10$$
$$(n^2)y=10^2$$
$$(n^2)y=100=x$$

When its -10:
$$n\sqrt{y}=-10$$
$$(n^2)y=(-10)^2$$
$$(n^2)y=100=x$$

Both lead to $$x=100$$ so statement 1 is still sufficient.
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Re: If (x/y)^(1/2)=n, what is the value of x? [#permalink]

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07 Apr 2012, 01:06
andrewh wrote:
1) (n^2)y = 100
2) n= 5 and y = 4

This question is from Total GMAT Math. The statement (1) provides that (n^2)y = 100 which implies that n(y^(1/2)) can be either 10 or -10. However, the solution provided by the book states that the above value is only 10. Hence I chose B, sine the statement (1) can be both 10 or -10. Is my approach incorrect?

Given that
(x/y)power(1/2) = n
x/y = n square
x = y. n square

now,

1. y.nsquare = 100
sufficient

2. values for Y and N are given, then this is sufficient too...

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Re: If (x/y)^(1/2)=n, what is the value of x? [#permalink]

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07 Apr 2012, 08:01
Thanks so much. I can believe I didn't see that .
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Re: If (x/y)^(1/2)=n, what is the value of x? [#permalink]

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23 May 2013, 05:37
reddevil00 wrote:
If (x/y)^(1/2)=n, what is the value of x?

(1) (n^2)y = 100
(2) n= 5 and y = 4

This question is from Total GMAT Math. The statement (1) provides that (n^2)y = 100 which implies that n(y^(1/2)) can be either 10 or -10. However, the solution provided by the book states that the above value is only 10. Hence I chose B, sine the statement (1) can be both 10 or -10. Is my approach incorrect?

yes, what u have misses is : l x l is +/- and again the same way x^2 is always positive but a root need not be, here we have square only dude.
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Re: If (x/y)^(1/2)=n, what is the value of x? [#permalink]

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24 Dec 2016, 08:34
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Re: If (x/y)^(1/2)=n, what is the value of x?   [#permalink] 24 Dec 2016, 08:34
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