Question about square roots on the GMAT, from a DS problem

[capnbenzo]

Hey All,

I encountered the problem:

If (sqrt x)/y = n, what is the value of x?

1) yn = 10
2) y=40 and n=1/4

I simplified the stem to x = sqrt (ny)

Both 1 & @ give yn = 10, thus x = sqrt(10)

I thought this made the answer positive or negative (ie. sqrt (4) is either -2 or 2), so 1 & 2 each gave two answers, thus I thought E was correct.

OA is D

How come I don't consider the negative sqrt of 10 in this problem?

Thanks!

[ssmiles08]

Hey All,

I encountered the problem:

If (sqrt x)/y = n, what is the value of x?

1) yn = 10
2) y=40 and n=1/4

I simplified the stem to x = sqrt (ny)

Both 1 & @ give yn = 10, thus x = sqrt(10)

I thought this made the answer positive or negative (ie. sqrt (4) is either -2 or 2), so 1 & 2 each gave two answers, thus I thought E was correct.

OA is D

How come I don't consider the negative sqrt of 10 in this problem?

Thanks!

Firstly, you can only take square roots of positive numbers(for gmat purposes anyway) otherwise you get complex numbers.

so sqrt(+ve number) = (+ve number)

CHoice A tells us that yn = 10

from the question stem you can get (sqrt x) = n*y

= (sqrt x) = 10

square both sides; x = +100. x cannot be -100 b/c you cannot squareroot it.


Choice B tells us that y = 40 and n = 1/4: from the question stem again:

(sqrt x) = 40*(1/4)

(sqrt x) = 10; x = 10^2 = +100

so (D)

[capnbenzo]

Gotcha. Thanks for your explanation.