If n and m are integers, and x=3^n, and y=3^m, is the value

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If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

12 Sep 2012, 19:09

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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

[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Sep 2012, 00:36, edited 1 time in total.

Renamed the topic and edited the question.

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Re: Data Sufficiency [#permalink]

12 Sep 2012, 20:58

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saurabhsingh24 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

There will be three cases:
when M is positive: option 1 is sufficient to answer. and option 2 also give answer
When M is negative: Option 1 is sufficient to answer. But option 2 is not sufficient to answer.
When M is Zero: option Option 1 is sufficient to answer But Option 2 is not sufficient to answer.

Try with some nos. for these three cases.
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Re: Data Sufficiency [#permalink]

13 Sep 2012, 00:10

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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

we have to find if x > 2y
i.e. 3^n > 2*3^m

STAT1:
n = m+1
so we have to prove that
3^(m+1) > 2* 3^m
=> 3 * 3^m > 2*3^m
=> 3 * 3^m - 2*3^m > 0
=> 3^m > 0

So ALL integer value of m 3^m will be greater that 0
So, SUFFICIENT

STAT2:
n=2m
so we have to prove that
3^(2m) > 2* 3^m
3^(2m) - 2* 3^m > 0
3^m* (3^m - 2) > 0

for ALL values of m 3^m will be greater than 0
So, 3^m* (3^m - 2) > 0 if (3^m - 2) is > 0

(3^m - 2) > 0 for all positive values of m
(3^m - 2) < 0 for 0 and all negative values of m

So, Answer will be A

Hope it helps!
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Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

13 Sep 2012, 01:32

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saurabhsingh24 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

The question is in fact "is 3^n>2\cdot{3^m}?"

(1) The given inequality becomes 3^{m+1}>2\cdot{3^m}. Dividing through by 3^m, which is for sure a positive number, we obtain 3 > 2, obviously true.
Sufficient.

(2) Now the given inequality becomes 3^{2m}>2\cdot{3^m}. Dividing through again by 3^m, we obtain 3^m>2. This inequality holds only for m>0.
Not sufficient.

Answer A.
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Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink] 13 Sep 2012, 01:32

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If n and m are integers, and x=3^n, and y=3^m, is the value

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If n and m are integers, and x=3^n, and y=3^m, is the value

If n and m are integers, and x=3^n, and y=3^m, is the value

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