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ds - factor2 difficult

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by MAAJ » Tue Apr 05, 2011 6:38 pm
If n and t are positive integers, is n a factor of t?
t -> n...?

(1) n=3^(n-2)
n = 3^n * 3^(-2)
n = 3^n * 1/9
n = (3^n)/9
Try values and get n = 3
We don't know what "t" is so this is not sufficient

(2) t=3^n
If n=3, then t=27 and 3 is a factor of t
If n=2, then t=9 and 2 is NOT a factor of t
Insufficient

Combining (1) and (2)
n= 3 AND t=3^n
t= 3^3 = 27, THUS n is a factor of t
Sufficient

IMO [spoiler]Correct Answer (C)[/spoiler]
ccassel wrote:Hi,

How would you explain the answer to this question?

If n and t are positive integers, is n a factor of t?

(1) n=3^n-2
(2) t=3^n

Cheers,
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by Anurag@Gurome » Tue Apr 05, 2011 9:33 pm
ccassel wrote:Hi,

How would you explain the answer to this question?

If n and t are positive integers, is n a factor of t?

(1) n=3^n-2
(2) t=3^n

Cheers,
(1)n=3^(n-2) has no relation with the variable 't'. So, definitely, (1) alone is NOT SUFFICIENT.

(2)t=3^n
If n = 1, then t = 3; here n is a factor of t, as 3 = 3 * 1.
If n = 2, then t = 9; here n is not a factor of t, as 9 = 3 * 3.
No unique answer.
So, (2) alone is NOT SUFFICIENT.

Combining (1) and (2), n = 3^(n-2)= 3^n * 3^(-2) = 3^n/3^2 = 3^n/9
So, 9n = 3^n, which is equal to t (using statement 2). So, 9n = t.
Hence, clearly n is a factor of t.

The correct answer is C.
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by Mike G » Thu Apr 07, 2011 7:26 am
Hi Anurag,
can you please explain why you consider n=3^n-2 equivalent to n=3^(n-2)?

I understand n=3^n-2 (original statement) means that n equals (3 to the power of N) MINUS 2. In this case the only possible value for N is 1 ( 1=3^1-2). Every number has 1 as a factor, so the first statement is sufficient to answer the question. Answer A.

If n=3^(n-2) then I completely agree with your line of thought, however n=3^(n-2) is not what's given in the original question ccassel posted.

Mike
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by ccassel » Thu Apr 07, 2011 7:52 am
Mike G,

Statement 1 refers to n=3(power of n-2). Brackets would have eliminated this confusion.

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by Anurag@Gurome » Thu Apr 07, 2011 5:27 pm
Mike G wrote:Hi Anurag,
can you please explain why you consider n=3^n-2 equivalent to n=3^(n-2)?

I understand n=3^n-2 (original statement) means that n equals (3 to the power of N) MINUS 2. In this case the only possible value for N is 1 ( 1=3^1-2). Every number has 1 as a factor, so the first statement is sufficient to answer the question. Answer A.

If n=3^(n-2) then I completely agree with your line of thought, however n=3^(n-2) is not what's given in the original question ccassel posted.

Mike
I understand that parentheses would have eliminated the confusion. I considered it as n=3^(n-2) as there was no spacing before and after the minus sign in the given expression, n=3^n-2, else it would have been written as n=3^n - 2
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