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If m and n are Integers, which of the following can be the result of

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If m and n are Integers, which of the following can be the result of [#permalink] New post   27 Oct 2019, 22:54
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If m and n are Integers, which of the following can be the result of \(\frac{mn}{m^2}*\sqrt{\frac{m^2}{n}}\)


A. -\(\sqrt{n}\)

B. \(\frac{nm}{\sqrt{n}}\)

C. \(\frac{m^2}{n}\)

D. All of the above

E. None of the above

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Re: If m and n are Integers, which of the following can be the result of [#permalink] New post   27 Oct 2019, 23:54
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\(\frac{mn}{m^2}\)∗\(\sqrt{\frac{m^2}{n}}\)

= \(\frac{m*n*\sqrt{m^2}}{m*m*\sqrt{n}}\)

= \(\frac{n* |m|}{m* \sqrt{n}}\) {Since |x|= \(\sqrt{x^2}\)}

= \(\sqrt{n}\) or -\(\sqrt{n}\)

(A) Ans
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Re: If m and n are Integers, which of the following can be the result of [#permalink] New post   28 Oct 2019, 23:39
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Video solution is as follows:


gmatbusters wrote:
If m and n are Integers, which of the following can be the result of \(\frac{mn}{m^2}*\sqrt{\frac{m^2}{n}}\)


A. -\(\sqrt{n}\)

B. \(\frac{nm}{\sqrt{n}}\)

C. \(\frac{m^2}{n}\)

D. All of the above

E. None of the above

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Re: If m and n are Integers, which of the following can be the result of [#permalink] New post   29 Oct 2019, 10:28
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gmatbusters wrote:
Video solution is as follows:


gmatbusters wrote:
If m and n are Integers, which of the following can be the result of \(\frac{mn}{m^2}*\sqrt{\frac{m^2}{n}}\)


A. -\(\sqrt{n}\)

B. \(\frac{nm}{\sqrt{n}}\)

C. \(\frac{m^2}{n}\)

D. All of the above

E. None of the above

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My bad. I totally overlooked the 'can be' part in the question stem.
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If m and n are Integers, which of the following can be the result of [#permalink] New post   06 Nov 2021, 07:47
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GMATBusters wrote:
If m and n are Integers, which of the following can be the result of \(\frac{mn}{m^2}*\sqrt{\frac{m^2}{n}}\)


A. -\(\sqrt{n}\)

B. \(\frac{nm}{\sqrt{n}}\)

C. \(\frac{m^2}{n}\)

D. All of the above

E. None of the above

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Solving question stem gives us n/ square root n

Since it says m and n are integers n could be -1 which may be written as -\(\sqrt{n}\) Hence A is possible
\(\frac{nm}{\sqrt{n}}\) if m=1, this is possible - hence B is possible

if both n=m=1, \(\frac{m^2}{n}\) Hence C is possible


HENCE ANSWER IS D ALL THREE POSSIBLE
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If m and n are Integers, which of the following can be the result of [#permalink]
06 Nov 2021, 07:47
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