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

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If n and t are positive integers, is n a factor of t ? [#permalink]  12 Dec 2005, 05:26
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If n and t are positive integers, is n a factor of t ?

(1) n = 3^(n-2)
(2) t = 3^n
[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Jul 2012, 00:52, edited 1 time in total.
Edited the question and added the OA.
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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.

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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, 16:20
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, 09:13
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, 11:12
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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.

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Re: If n and t are positive integers, is n a factor of t? (1) n [#permalink]  27 Jul 2012, 17:50
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.

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Re: If n and t are positive integers, is n a factor of t? (1) n [#permalink]  28 Jul 2012, 01:07
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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.

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):

$$n = 3^{n-2}$$ --> $$n=\frac{3^n}{9}$$ --> $$9n=3^n$$

For (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 ? [#permalink]  06 Sep 2013, 02:51
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Bumping for review and further discussion.
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Re: If n and t are positive integers, is n a factor of t ? [#permalink]  23 Sep 2014, 04:42
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Re: If n and t are positive integers, is n a factor of t ? [#permalink]  23 Sep 2014, 06:01
is n a factor of t?
is t/n= integer ?

statement 1 : n= 3^(n-2)
nothing is given about t... statement is insufficient

statement 2 : t=3^n
let n=2, then t=9 n is not a factor of t .... false
let n=3, then t=27 n is a factor of t .... true
statement is insufficient

both statements combined
n= 3^(n-2)... given
n=3^n/3^2
n=t/3^2 ..... (replacing 3^n by t as given in statement 2)
t/n= 3^2
t/n= integer
Therefore n is a factor of t.

Ans - C
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Re: If n and t are positive integers, is n a factor of t ? [#permalink]  18 Jan 2015, 23:56
Ya original question has z in place of '2'in the exponent....ans for tat is E

But for the given question
Ans is C

just observe t/n =9...tats enough
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Re: If n and t are positive integers, is n a factor of t ? [#permalink]  24 Jan 2015, 02:07
Bunuel wrote:
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.

----
I think this question is mathematically a wrong question. The equation n=3^(n-2) does not qualified for any existing integer. Can you find any integer that can put this equation for n and get n=3^(n-2)????? This question does not make sense for me.
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Re: If n and t are positive integers, is n a factor of t ? [#permalink]  24 Jan 2015, 03:26
Expert's post
miriampirooz wrote:
Bunuel wrote:
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.

----
I think this question is mathematically a wrong question. The equation n=3^(n-2) does not qualified for any existing integer. Can you find any integer that can put this equation for n and get n=3^(n-2)????? This question does not make sense for me.

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Re: If n and t are positive integers, is n a factor of t ? [#permalink]  26 Jan 2015, 01:22
Ya original question has z in place of '2'in the exponent....ans for tat is E

But for the given question
Ans is C

just observe t/n =9...tats enough

Yes i did this way too. (3^n)/((3^n)/(3^2))=9
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Re: If n and t are positive integers, is n a factor of t ?   [#permalink] 26 Jan 2015, 01:22
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