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# If m = 3^(n−1), what is the value of m/n?

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
If m = 3^(n−1), what is the value of m/n?  [#permalink]

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14 May 2017, 10:41
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Difficulty:

35% (medium)

Question Stats:

68% (01:46) correct 32% (01:44) wrong based on 144 sessions

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If $$m = 3^{(n−1)}$$, what is the value of $$\frac{m}{n}$$?

(1) $$3^{(4n−1)} = 27$$

(2) $$m = 3^{(3n-3)}$$

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GMAT 1: 700 Q49 V36
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WE: Engineering (Consumer Products)
Re: If m = 3^(n−1), what is the value of m/n?  [#permalink]

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15 May 2017, 00:41
Statement 1: 3^(4n-1) = 27 so 3^(4n-1) = 3^3; (4n-1)=3; n=1 so m = 1 from main question which gives m/n = 1.
Statement 2: m=3^(3n+1); also m = 3^(n-1); 3^(3n+1) = 3^(n-1); (3n+1)=(n-1); n = -1; m= 1/9; m/n = 1/9.
Please correct if I am wrong.
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Re: If m = 3^(n−1), what is the value of m/n?  [#permalink]

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15 May 2017, 01:20
Statement 1:
Solve to find the value of n
Put this value of n in equation for m to solve for m
So now you the value for both m and m. Hence, you can find the value of m/n

Statement 2:
Equate the values of m from equation provided in stem and statement 2 to solve for n. Put this value of n in equation of m from stem to solve for m. Hence, now you have values for both m and n.

Both the statements are sufficient on their own to find the value of m/n
Hence, D
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Re: If m = 3^(n−1), what is the value of m/n?  [#permalink]

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15 May 2017, 01:43
i am getting n = +1 from statement 1 and n = -1 from statement 2..
i am sure answer is D i dont know where i am doing mistake
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Re: If m = 3^(n−1), what is the value of m/n?  [#permalink]

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15 May 2017, 06:58
The answer must be A because statement 1 tells that n is positive where as the value of m is totally dependent on n (either negative or positive). So we know that n is +1 and we can find the answer of m/n
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Re: If m = 3^(n−1), what is the value of m/n?  [#permalink]

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08 Nov 2017, 12:12
2
Hi Bunuel,

Statement 1: 3^(4n-1) = 27 so 3^(4n-1) = 3^3; (4n-1)=3; n=1 so m = 1 from main question which gives m/n = 1.
Statement 2: m=3^(3n+1); also m = 3^(n-1); 3^(3n+1) = 3^(n-1); (3n+1)=(n-1); n = -1; m= 1/9; m/n = 1/9.

both the statements yielding different values of m/n
Math Expert
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Posts: 50627
Re: If m = 3^(n−1), what is the value of m/n?  [#permalink]

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08 Nov 2017, 20:46
hellosanthosh2k2 wrote:
Hi Bunuel,

Statement 1: 3^(4n-1) = 27 so 3^(4n-1) = 3^3; (4n-1)=3; n=1 so m = 1 from main question which gives m/n = 1.
Statement 2: m=3^(3n+1); also m = 3^(n-1); 3^(3n+1) = 3^(n-1); (3n+1)=(n-1); n = -1; m= 1/9; m/n = 1/9.

both the statements yielding different values of m/n

Yes, you are right. Edited the second statement. Thank you.
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Re: If m = 3^(n−1), what is the value of m/n? &nbs [#permalink] 08 Nov 2017, 20:46
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