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Is 3^n > 2^k ? [#permalink]
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03 Jan 2016, 13:51
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62% (01:12) correct 38% (00:54) wrong based on 125 sessions
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Re: Is 3^n > 2^k ? [#permalink]
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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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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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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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Re: Is 3^n > 2^k ? [#permalink]
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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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09 Oct 2017, 17:36
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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