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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]

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New post Updated on: 28 Jul 2012, 00:52
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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

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Originally posted by TOUGH GUY on 12 Dec 2005, 05:26.
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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Re: DS- Positive integers and factors - Sounds easy  [#permalink]

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New post 21 Jan 2011, 11:12
6
1
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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New post 12 Dec 2005, 08:54
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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New post 13 Dec 2005, 05:25
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]

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New post 20 Jan 2011, 16:20
1
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]

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New post 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: If n and t are positive integers, is n a factor of t? (1) n  [#permalink]

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New post 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.

please help
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Re: If n and t are positive integers, is n a factor of t? (1) n  [#permalink]

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New post 28 Jul 2012, 01:07
6
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):

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

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]

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New post 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]

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New post 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]

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New post 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.

Answer: C.


----
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]

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New post 24 Jan 2015, 03:26
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.

Answer: C.


----
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.


Have you read the very post you are quoting??? Please re-read!
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Re: If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 26 Jan 2015, 01:22
baadshah wrote:
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]

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New post 08 Jul 2015, 23:12
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t

However this does not help me in any way... Where am i going wrong?
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If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 08 Jul 2015, 23:28
noTh1ng wrote:
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t


However this does not help me in any way... Where am i going wrong?


The highlighted steps are out of Sink

\(a^{(b^c)}\) is NOT equal to \(a^b*a^c\)

Whereas, \((a^b)^c\) = \(a^b*a^c\)

i.e. \(3^{(3^{(n-2)})}\) is NOT same as \(3^{3n} * 1/3^6\)
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Re: If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 08 Jul 2015, 23:34
GMATinsight wrote:
noTh1ng wrote:
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t


However this does not help me in any way... Where am i going wrong?


The highlighted steps are out of Sink

\(a^{(b^c)}\) is NOT equal to \(a^b*a^c\)

Whereas, \((a^b)^c\) = \(a^b*a^c\)

i.e. \(3^{(3^{(n-2)})}\) is NOT same as \(3^{3n} * 1/3^6\)



Thank you, so the only way would be to plug in values for n for \(3^{(3^{(n-2)})}\) ?

Or is there any way to rewrite this?
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Re: If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 08 Jul 2015, 23:42
1
noTh1ng wrote:
GMATinsight wrote:
noTh1ng wrote:
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t


However this does not help me in any way... Where am i going wrong?


The highlighted steps are out of Sink

\(a^{(b^c)}\) is NOT equal to \(a^b*a^c\)

Whereas, \((a^b)^c\) = \(a^b*a^c\)

i.e. \(3^{(3^{(n-2)})}\) is NOT same as \(3^{3n} * 1/3^6\)



Thank you, so the only way would be to plug in values for n for \(3^{(3^{(n-2)})}\) ?

Or is there any way to rewrite this?


There are three ways

1) Plug-in the Values from Options :roll:
2) Take Logarithm on both sides and then solve further :oops:
3) Change the method and follow the methods given in other explanations :lol: :P

Third seems the Best to me :-D

I hope it Helps!
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Re: If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 09 Jul 2015, 00:01
GMATinsight wrote:
There are three ways

1) Plug-in the Values from Options :roll:
2) Take Logarithm on both sides and then solve further :oops:
3) Change the method and follow the methods given in other explanations :lol: :P

Third seems the Best to me :-D

I hope it Helps!



It does ;) Option 3) should indeed be the way to go, however when I first solved the problem I just did not see it ;) happens...
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Re: If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 06 Sep 2016, 22:59
Statement 1: n=3^(n-2). No correlation with 't' is mentioned. Hence, insufficient.

Statement 2: t=3^n. Take n=1, then n is a factor of t. However, n=2 is not a factor of t. Hence, insufficient.

Combined: St:1 can be re-written as, n=3^n.3^-2, with information from statement 2, n=t.3^-2, n=t/9. Given that n&t are positive integers, the information is sufficient.
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Re: If n and t are positive integers, is n a factor of t ?  [#permalink]

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New post 05 Dec 2017, 18:43
TOUGH GUY wrote:
If n and t are positive integers, is n a factor of t ?

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


We need to determine whether t/n = integer

Statement One Alone:

n = 3^(n - 2)

Since we do not have any information regarding t, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

t = 3^n

We can substitute some numbers for n. For example, if n = 1, then t = 3^1 = 3 and 1 is a factor of 3. However, if n = 2, then t = 3^2 = 9 but 2 is not a factor of 9. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we can substitute 3^(n - 2) for n and 3^n for t in our question: t/n = integer ?

(3^n)/3^(n - 2) = integer ?

Since we are dividing similar bases, we can subtract the exponents and keep the base. Then we have:

3^(n - n + 2) = integer ?

3^2 = integer ?

9 = integer ?

Since 9 IS an integer. We have answered “yes” to the question.

Answer: C
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Re: If n and t are positive integers, is n a factor of t ? &nbs [#permalink] 05 Dec 2017, 18:43
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