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ds - factor2 difficult

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Tue Apr 05, 2011 6:17 pm

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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Source: Beat The GMAT — Data Sufficiency | Tue Apr 05, 2011 6:17 pm

MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

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,

"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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.

Anurag Mairal, Ph.D., MBA
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Mike G: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Mon Apr 04, 2011 6:33 pm

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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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

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.

Regards,

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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