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Is 3^n > 2^k ?

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Is 3^n > 2^k ? [#permalink]

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New post 03 Jan 2016, 13:51
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  35% (medium)

Question Stats:

64% (01:10) correct 36% (01:01) wrong based on 108 sessions

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Re: Is 3^n > 2^k ? [#permalink]

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New post 03 Jan 2016, 16:39
Bunuel wrote:
Is 3^n > 2^k ?

(1) k = n + 1
(2) n is a positive integer.


(1) k=n+1, k=2 and n=1 NO, k=3 and n=2 Yes, NOT SUFFICIENT
(2) n > 0, no info about k, which could be 1 or 100, NOT SUFFICIENT
(1)+(2) Still not sufficient considering the cases from (1)
Asnwer E
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Re: Is 3^n > 2^k ? [#permalink]

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New post 17 Jan 2016, 06:59
BrainLab wrote:
Bunuel wrote:
Is 3^n > 2^k ?

(1) k = n + 1
(2) n is a positive integer.


(1) k=n+1, k=2 and n=1 NO, k=3 and n=2 Yes, NOT SUFFICIENT
(2) n > 0, no info about k, which could be 1 or 100, NOT SUFFICIENT
(1)+(2) Still not sufficient considering the cases from (1)
Asnwer E



Hi! Can you elaborate on your answer?

I get 3 cases for statement 1

1. n=2 , k=3 9>8 - yes
2. n =3, k=4 27>16 - yes
3. n=-1, k=0 1/3 > 1 ? - no

So statement 2 tells us n is positive -- so why not c?

Thanks

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Re: Is 3^n > 2^k ? [#permalink]

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New post 17 Jan 2016, 07:20
lpetroski wrote:
BrainLab wrote:
Bunuel wrote:
Is 3^n > 2^k ?

(1) k = n + 1
(2) n is a positive integer.


(1) k=n+1, k=2 and n=1 NO, k=3 and n=2 Yes, NOT SUFFICIENT
(2) n > 0, no info about k, which could be 1 or 100, NOT SUFFICIENT
(1)+(2) Still not sufficient considering the cases from (1)
Asnwer E



Hi! Can you elaborate on your answer?

I get 3 cases for statement 1

1. n=2 , k=3 9>8 - yes
2. n =3, k=4 27>16 - yes
3. n=-1, k=0 1/3 > 1 ? - no

So statement 2 tells us n is positive -- so why not c?

Thanks


hi,
another option when n is positive and answer is NO..
n=1, k=2..3>4... no
so dont miss out few values
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Is 3^n > 2^k ? [#permalink]

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New post 09 Oct 2017, 11:35
Hi! Can you elaborate on your answer?

I get 3 cases for statement 1

1. n=2 , k=3 9>8 - yes
2. n =3, k=4 27>16 - yes
3. n=-1, k=0 1/3 > 1 ? - no

So statement 2 tells us n is positive -- so why not c?

Thanks[/quote]

hi,
another option when n is positive and answer is NO..
n=1, k=2..3>4... no
so dont miss out few values[/quote]


Hi, I thought the same case too. Here is my reasoning.

St 1: k = n + 1. Clearly insufficient, cause we don't have any case (positive and negative would have different outcomes)

St 2: n is positive integer. Means more than zero and positive ; hence cannot be 0 but is greater than one.

So one plus two statement means: k = n +1 and n is positive integer.
3^n > 2^n+1 (replacing k).
We get 3 to power 1 NOT GREATER than 2 to power 2. Then if n = 2; k = n +1 => k =2. So 3 to power is always less than 2 to power n +1.

Thus it is sufficient.
Request experts to help out on why E is correct, and point out the issue

Thank you

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Is 3^n > 2^k ? [#permalink]

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New post 09 Oct 2017, 17:36
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Expert's post
Madhavi1990 wrote:
Hi! Can you elaborate on your answer?

I get 3 cases for statement 1

1. n=2 , k=3 9>8 - yes
2. n =3, k=4 27>16 - yes
3. n=-1, k=0 1/3 > 1 ? - no

So statement 2 tells us n is positive -- so why not c?

Thanks

hi,
another option when n is positive and answer is NO..
n=1, k=2..3>4... no
so dont miss out few values


Hi, I thought the same case too. Here is my reasoning.

St 1: k = n + 1. Clearly insufficient, cause we don't have any case (positive and negative would have different outcomes)

St 2: n is positive integer. Means more than zero and positive ; hence cannot be 0 but is greater than one.

So one plus two statement means: k = n +1 and n is positive integer.
3^n > 2^n+1 (replacing k).
We get 3 to power 1 NOT GREATER than 2 to power 2. Then if n = 2; k = n +1 => k =2. So 3 to power is always less than 2 to power n +1.

Thus it is sufficient.
Request experts to help out on why E is correct, and point out the issue

Thank you



Hi...
You are wrong at one point above..
When n=1, k =1+1=2.....3^1>2^2....NO
But when n=2 k=2+1=3...3^2>2^3... YES
Rather for all values of n above 2, Ans will be YES..

So ans is E as different answers possible
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5868 [1], given: 118

Is 3^n > 2^k ?   [#permalink] 09 Oct 2017, 17:36
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