Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47092

Is 3^n > 2^k ? [#permalink]
Show Tags
03 Jan 2016, 13:51
Question Stats:
63% (01:11) correct 37% (00:54) wrong based on 127 sessions
HideShow timer Statistics



Director
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: Is 3^n > 2^k ? [#permalink]
Show Tags
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
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Current Student
Joined: 30 Dec 2015
Posts: 188
Location: United States
Concentration: Strategy, Organizational Behavior
GPA: 3.88
WE: Business Development (Hospitality and Tourism)

Re: Is 3^n > 2^k ? [#permalink]
Show Tags
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



Math Expert
Joined: 02 Aug 2009
Posts: 6240

Re: Is 3^n > 2^k ? [#permalink]
Show Tags
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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior Manager
Joined: 15 Jan 2017
Posts: 362

Re: Is 3^n > 2^k ? [#permalink]
Show Tags
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



Math Expert
Joined: 02 Aug 2009
Posts: 6240

Is 3^n > 2^k ? [#permalink]
Show Tags
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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor










