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# If 5^m = 25^n, what is m?

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Math Expert
Joined: 02 Sep 2009
Posts: 55274
If 5^m = 25^n, what is m?  [#permalink]

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03 Sep 2017, 06:19
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Difficulty:

25% (medium)

Question Stats:

80% (00:52) correct 20% (00:40) wrong based on 63 sessions

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If 5^m = 25^n, what is m?

(1) n = 4
(2) m + n = 12

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Intern
Joined: 16 Apr 2017
Posts: 9
Location: Armenia
GMAT 1: 740 Q51 V39
GPA: 3.97
Re: If 5^m = 25^n, what is m?  [#permalink]

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04 Sep 2017, 13:57
Bunuel wrote:
If 5^m = 25^n, what is m?

(1) n = 4
(2) m + n = 12

Statement 1 provides us with the implication that 5^m = (5^2)^4. From here, m can be derived to equal 8. Thus, Statement 1 is SUFFICIENT.
Statement 2 suggests that m can be expressed in the form of 12-n. After certain simplifications, we arrive at 5^(12-n) = (5^2)^n. The equation can be solved for n, while ignoring the bases and directly operating with exponents:
(12-n) = 2n; n = 4.
Huh, we get the very same piece of information pointed out by Statement A. Without any further due, Statement 2 is confirmed to be SUFFICIENT too.
In conclusion, we end up with answer D - since both statements individually and independently from each other arrive at the exact answer.
Hope this helps
Senior Manager
Joined: 15 Jan 2017
Posts: 351
Re: If 5^m = 25^n, what is m?  [#permalink]

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06 Sep 2017, 13:18
D for me.
5^m =25^n; what is m ?
now based on abv --> 5^m =5^2n --> m = 2n

1) if n = 4; m =8 suff
2) m + n = 12 --> substitute m =2n we get n = 4; which ism = 2*4 = 8 suff

Ans D
Re: If 5^m = 25^n, what is m?   [#permalink] 06 Sep 2017, 13:18
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