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

Question

If m and n are both positive, what is the value of m*\sqrt{n} ? (1) \frac{m*n}{\sqrt{n}}=10 (2) \frac{m^2*n}{2}=50 OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-and-n-are-both-positive-what-is-the-value-of-m-root-n-78555.html

sudhir18n · Answer

St1: mn/sqrt n = 10 .
 squaring on both sides
m^2*n^2/n = 100
m^2*n = 100
square root on both sides 
m*sqrt n = 10.................................... sufficient

st2: m^2*n /2= 50
 m^2*n = 100
 square root on both sides
 m* sqrt n = 10 ...................... sufficient 
Hence D

Dreaming · Answer

if m^2*n = 100, isnt m*sqrtn = + or - 10???
say m=5 and n=4.....then sqrt(n)=+ or -2.....m*sqrt(n)=+ or -10? 
its only said that n is positive....but sqrt of n could still be negative right?

sudhir18n · Answer

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)

Dreaming · Answer

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

sudhir18n · Answer

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

Dreaming · Answer

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

sudhir18n · Answer

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

gautammalik · Answer

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.

samramandy · Answer

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.

samramandy · Answer

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

gmatpapa · Answer

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.

Dreaming · Answer

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?

gmatpapa · Answer

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.

reatsaint · Answer

(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.

Bunuel · Answer

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

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards