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N, M integers

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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Dec 26, 2011 3:48 am
karthikpandian19 wrote:If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y?

(1) n=m+1
(2) n=2m
Is x > 2y?

(1) n = m + 1 implies x = 3^(m + 1) and y = 3^m
3^(m + 1) > 2 * 3^m
3 * (3^m) > 2 * 3^m definitely holds true; SUFFICIENT.

(2) n = 2m implies x = 3^(2m) and y = 3^m
3^(2m) > 2 * (3^m)
If m = 1, 9 > 6 holds true
If m = -1, then 1/9 > 2 * 1/3 or 0.11.. > 0.666... does not hold true; NOT sufficient.

The correct answer is A.
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by karthikpandian19 » Tue Dec 27, 2011 9:47 pm
OA is A
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by ArunangsuSahu » Tue Jan 03, 2012 10:17 pm
Statement 1:

n=m+1

Substituting

3^(m+1)>2* 3^m?
3>2?..YES... SUFFICIENT

Statement 2:

m=0

x=3^0=1
y=3^0=1

x>2y


m=-1

x=1/9
y=1/3
x<2y

So INSUFFICINET
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