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OG 12th ed DS #66

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by HPengineer » Sun Aug 08, 2010 8:32 pm
If N and T are positive integers, is N a factor of T?

S1: N = 3^(N-2)

S2: T = 3^(N)

I don't really like the books explanation here... its dependent on manipulating the first statement using algebra. Does anyone have another approach they could kindly share?
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Source: — Data Sufficiency |
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by santoostar » Sun Aug 08, 2010 9:01 pm
The statement 1 is not sufficient for it doesnt show any relation between N and T

Statement 2 is not sufficient for it gives you both possibilities.

When N= 3=> T is 27 which shows that N is a factor of T

When N=2 => T is 9 but N which is 2 is not a factor of T

Combining 1 and 2

There is a relation between T and N and then statement 1 gives you a definite value for N which when used in statement 2 gives you a definite answer.

N=3^(N-2) is possible only when N=3

When you have N=3 from statement 2 we get T=27. Therefore, N is a factor of T ( definite answer) so my choice is C.

C
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by kvcpk » Sun Aug 08, 2010 9:40 pm
HPengineer wrote:If N and T are positive integers, is N a factor of T?

S1: N = 3^(N-2)

S2: T = 3^(N)

I don't really like the books explanation here... its dependent on manipulating the first statement using algebra. Does anyone have another approach they could kindly share?
S1: N = 3^(N-2)
No Info about T. INSUFF

S2: T = 3^(N)
When N=1, T=3 -> 1 is a factor of 3
when N=2, T=9 -> 2 is not a factor of 9
Conflicting answers. Hence INSUFF

Combining:
S1: N = 3^(N-2)
N = 3^N/3^2
N = 3^N/9
9N = 3^N

S2: T = 3^(N)
T = 3^N
Hence T = 9N
Given N and T are positive Integers.
Hence N is a factor of T
SUFF

pick C

Hope this helps!!
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by Ian Stewart » Sun Aug 08, 2010 11:30 pm
HPengineer wrote:If N and T are positive integers, is N a factor of T?

S1: N = 3^(N-2)

S2: T = 3^(N)

I don't really like the books explanation here... its dependent on manipulating the first statement using algebra. Does anyone have another approach they could kindly share?
Neither Statement is sufficient alone, as I think has been pointed out above.

Taking both statements together, using the equations from each Statement, the question 'is N a factor of T?' becomes 'is 3^(N-2) a factor of 3^N ?' Well yes, it is, since 3^N = (3^(N-2))*(3^2). So you don't need to find N here, and the answer is C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by HPengineer » Mon Aug 09, 2010 9:25 am
Thanks all now i see several ways to approach this problem. Ian your approach is exactly what i was looking for Thank you kindly sir..
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by dinesh19aug » Mon Aug 09, 2010 2:13 pm
The answer is C
Given n,t >1 and they are integers

Stmt 1: Not Suff, as no infor abt T is given

Stmt 2: not suff, T = 3^n, if n =3, T =27, Yes BUT if n =2, T =9 NO.

Both Statement:
stmt 1 can be writtern as ==> N = 3^n / 9 ===> 9N = 3^n

Substitute Stmt 2 => 9N = T ....

Hence the answer is C
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