If m and n are both positive, what is the value of

if m^2* n = 100 and both m and n are postive
m* sqrt n will always be equal to positive 10.
there are no square roots of negative numbers on gmat ..( becasue sq rt of negative numbers will lead to imginary numbers and in gmat we deal with real numbers)

I am fully aware of that . what i am asking is : is sqrt(4)=2 ONLY or +/-2. I am NOT squarerooting a negetive number

On the gmat square root of 4 will always be positive 2 .
hope this helps.

but if x^2=4. soution of x = +/-2, right? even in GMAT.

yes even this is right on gmat ...
The following are the rules;
X^2( to the power of even number) = + or -
sqrt (x) = always postive

1) m.n/sqt(n) = 10
means, m.sqrt(n) = 10
Sufficient
We can eliminate B, C, and E.

2) m^2.n/2 = 50
m^2.n = 100
m.sqrt(n) = 10 or -10
m and n are positive (given) so m.sqrt(n) =10
Sufficient

Hence D.

I have the same doubt as Upasana...Will the square root of 100 be 10 or -10 ??

Otherwise the question is very easy...I chose A just because I thought that the root of 100 would 10 or -10.

Although I read that m and n are +ve but forgot about it while solving

I seriously doubt that.. You can never say that conclusively.

If nothing is mentioned about x, then sqrt x is always equal to + or - x. This is, in fact, one of the favorite traps of GMAT..

In this question , since we're given that both m and n are positive, we can conclusively say that the outcome will be positive 10.

For all real numbers x

\sqrt{(x^2)}=|x|=x, if x>=0
=-x if x<0
which means sqrt of 4 will be always 2=>the absolute value
Source: wikipedia https://en.wikipedia.org/wiki/Square_root
edit: One thing I dont understand is why everyone is saying that 'if n is positive, sqrt of n is obviously positive'.....the only thing that can be said if m is positive is that sqrt of n is definitely real, (and also that n is not zero so division is possible.) it is true that sqrt of n will be positive...as explained in the wiki article cited above, but it has got nothing to do with thefact that n is positive.

ok...so m is positive, but sqrt of n could still have been negative....and made the term (m)(sqrt n)= -10
Please , can someone please tell me, am I missing something here?

It is given that mn/sqrt (n)= 10
If you look closely, statement 1 is a disguised form of what is asked in the question.

You can actually re-write statement 1 as following:

m* sqrt (n)* sqrt (n) / sqrt (n)
=> m*sqrt (n) = 10.

(1) m*sqrt(n) = 10 , just simplifying. SUFFICIENT
(2)(m^2)(n)/2=50, m*sqrt(n) = +10 or -10. However it is given that m,n > 0 , so we cannot have m*sqrt(n) = -10. SUFFICIENT
Hence Ans is D.

If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\) --> reduce by \(\sqrt{n}\) --> \(m*\sqrt{n}=10\). Sufficient.

(2) \(\frac{m^2*n}{2}=50\) --> \((m*\sqrt{n})^2=100\) --> \(m*\sqrt{n}=10\) or \(m*\sqrt{n}=-10\). BUT since m and n are both positive (given) \(m*\sqrt{n}\) can not equal to -10. Hence only one solution is valid: \(m*\sqrt{n}=10\). Sufficient.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-and-n-are-both-positive-what-is-the-value-of-m-root-n-78555.html