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If n and t are positive integers, is n a factor of t ? [#permalink]
 12 Dec 2005, 06:26
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Question Stats:
60% (02:10) correct
39% (00:56) wrong based on 4 sessions
If n and t are positive integers, is n a factor of t ? (1) n = 3^(n-2) (2) t = 3^n
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Last edited by Bunuel on 28 Jul 2012, 01:52, edited 1 time in total.
Edited the question and added the OA.
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The answer is E.
The statement I doesnt make sense with "Z" and non mention of T.
And for Statement II, there are both yes and no answers.
like 9 = 3^2 where 2 is not a factor of 9.
also 27 = 3^3 where 3 is a factor of 27.
On combining statements I and II,
n = 3^(n-z)
n=3^n/3^z
n= t/3^z (t= 3^n, from statement II)
For all postive integers of Z (including Zero), n is a factor of T
But for negative integers, we can only say that n is multiple of T, but not the factor.
Hence the answer is E.
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Yes, exp means power of exponents.
A alone makes no sense.
B alone is confusing, if we do pick up numbers, we realise than that
if
n=1; t=3 yes n is a factor of t;
n=2; t=9 no n is not a factor of t;
OA is E
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Re: DS- Positive integers and factors - Sounds easy [#permalink]
20 Jan 2011, 17:20
Sorry for pulling up this old thread, but I googled it because it is a question in the OG12 and I would never come up with an approach like that in the OG12. The initial post states the question incorrectly. Instead of a z, that is subtracted in the exponent, it is actually a 2. You can find the question on p. 310 #66 in the OG12. Well, it makes sense to me that the answer is C, but not by dividing statement (1) by (2)?! I see that each of the statements are not sufficient considered solely, but instead of that weird approach, I would find out that n in the first statement has to be 3, which goes along with statement (2), since 3 is a factor of 27. Isn't it true that the questions in the OG are arranged from easy to tough in the particular sections? Sometimes I need five secs for one of the lower questions and then others like these take, if you can solve it at all, a decent amount of time.
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Re: DS- Positive integers and factors - Sounds easy [#permalink]
21 Jan 2011, 10:13
I think the answer should be C. From (1) we can find it that n will always be multiple of 3, or n can be 1. if put this in (2), it clearly means that n will be a factor of t.
n can be 1,3,9,27 etc... and 3(exp)1,3,9,27 will always be multiple of n and 3.
Is my assumption right?
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Re: DS- Positive integers and factors - Sounds easy [#permalink]
21 Jan 2011, 12:12
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selines wrote: Sorry for pulling up this old thread, but I googled it because it is a question in the OG12 and I would never come up with an approach like that in the OG12. The initial post states the question incorrectly. Instead of a z, that is subtracted in the exponent, it is actually a 2. You can find the question on p. 310 #66 in the OG12. Well, it makes sense to me that the answer is C, but not by dividing statement (1) by (2)?! I see that each of the statements are not sufficient considered solely, but instead of that weird approach, I would find out that n in the first statement has to be 3, which goes along with statement (2), since 3 is a factor of 27. Isn't it true that the questions in the OG are arranged from easy to tough in the particular sections? Sometimes I need five secs for one of the lower questions and then others like these take, if you can solve it at all, a decent amount of time. Yes the question is from OG and it should be: If n and t are positive integers, is n a factor of t ? (1) n = 3^(n-2) --> n=3 (only integer solution for this equation), but we know nothing about t, so this statement is not sufficient. (2) t = 3^n --> if n=1 then the answer will be YES but if n=2 then t=9 and the answer will be NO. Not sufficient. (1)+(2) As n=3 then t=3^n=27 and the answer to the question will be YES as 3 is a factor of 27. Sufficient. Answer: C.
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Re: If n and t are positive integers, is n a factor of t? (1) n [#permalink]
27 Jul 2012, 18:50
hello Bunuel, How'd you figure it out in statement 1 that n=3. i do comprehend that n must be 3 but i cant figure it out by doing algebra. please help
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Re: If n and t are positive integers, is n a factor of t? (1) n [#permalink]
28 Jul 2012, 02:07
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alchemist009 wrote: hello Bunuel, How'd you figure it out in statement 1 that n=3. i do comprehend that n must be 3 but i cant figure it out by doing algebra.
please help You can find that by trial and error: n=1 and n=2 does not satisfy n = 3^(n-2), but n=3 does. Now, if n>3 (4, 5, 6, ...), then RHS is always greater than LHS, so n=3 is the only solution. You can solve this problem without finding the value of n in (1): n = 3^{n-2} --> n=\frac{3^n}{9} --> 9n=3^nFor (1)+(2): since from (2) t = 3^n, then t=9n, hence n is a factor of t. Hope it' helps.
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Re: If n and t are positive integers, is n a factor of t? (1) n
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28 Jul 2012, 02:07
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