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# If 50^r/m^r = 2^r*r^r, what is r?

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Math Expert
Joined: 02 Sep 2009
Posts: 49430
If 50^r/m^r = 2^r*r^r, what is r?  [#permalink]

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25 Sep 2017, 00:00
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Difficulty:

55% (hard)

Question Stats:

50% (01:41) correct 50% (02:17) wrong based on 37 sessions

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If $$\frac{50^r}{m^r} = 2^r*r^r$$, what is r?

(1) m = 5

(2) 50/m = 2r

_________________
Senior Manager
Joined: 02 Jul 2017
Posts: 294
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: If 50^r/m^r = 2^r*r^r, what is r?  [#permalink]

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25 Sep 2017, 02:11
If $$\frac{50^r}{m^r}=2^r∗r^r$$ , what is r?

(1) m = 5

=> $$\frac{50^r}{m^r}= \frac{5^r * 10^r}{5^r}= 10^r = (2*5) ^r = 2^r * 5^r$$ as this is equal to $$2^r∗r^r$$

=> r = 5
Sufficient

(2) 50/m = 2r
=> $$\frac{50^r}{m^r}= (\frac{50}{m})^r = (2r)^r = = 2^r *r^r$$ This is already given in question stem

Insufficient

Re: If 50^r/m^r = 2^r*r^r, what is r? &nbs [#permalink] 25 Sep 2017, 02:11
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# If 50^r/m^r = 2^r*r^r, what is r?

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