Need help - Data sufficiency

momentary_lapse wrote:Hi,

Please help with the question below:

If m and n are both positive, what is the value of m * sq rt(n)?

1) mn / sq rt (n) = 10
2) ((m^2) * n)/2 = 50

The first option I can understand. If m and n are +ve the only way the expression can be +ve = 10 is if sq rt n is +ve. Therefore 1 is sufficent

For part 2 if sq rt of n is negative, then m^2 * n can still be +ve. ex: if m = 5 and n = 4 then the expression is (25*4)/2 = 50. But by x-multiplying with 2 we get (m^2)*n = 100. So if we take the square root on both sides we get m *sq rt of n which may be + or - 2 . So the answer could be + or - 10.

Please help. This is q 35 from kaplan gmat and the answer is apparently D.

thanks

I guess there's a small difference here

sqrt(n) is always positive, by definition.

But if you have x^2 = n, then x can be +sqrt(n) or -sqrt(n)

how is it always +ve? this is what i dont get? if n is +ve why should the sq rt always +ve?

Valid point.
I also agree that it can be + or - 10.

Okay all.. I have figured it out after significant research. We have missed out an important concept here as well in another post by me under the GMAT Math forum.

The square root in the questions which are written with the square root symbol is actually called a radical. I wasnt able to figure out how to type it which is why i was writing square root.

So when we say √a we actually mean the non negative value of the square root of a. This is totally different from solving an equation where x^2 = 25 and therefore x=+5 or -5

When a is negative √a is = |a| and therefore in the case of the question where we are asked to find the √(-a|a|) it is = √a^2 which is = |a| and since a ia negative the answer is -a.

For more information on the radical symbol check this link:

https://www.jcoffman.com/Algebra2/ch7_1.htm

This is an important concept which i learnt and i feel much more at ease now

Apologies if people knew about this and got confused because of the problem being written as "find the square root" instead of "find √"

thanks