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Exponents - If n and t are positive integers, is n a factor

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II Master | Next Rank: 500 Posts
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Exponents - If n and t are positive integers, is n a factor

Post Sun Aug 17, 2008 12:10 am
Hi, Interested in seeing the various approachs people have in answering this question ... please illustrate your logic/thinking when answering this. Thanks.

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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sudhir3127 Legendary Member Default Avatar
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Post Sun Aug 17, 2008 12:14 am
II wrote:
Hi, Interested in seeing the various approachs people have in answering this question ... please illustrate your logic/thinking when answering this. Thanks.

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

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

(2) t = 3^n
are u sure abt the statement 1. it doesnt say anything abt "T"?

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sudhir3127 Legendary Member Default Avatar
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Post Sun Aug 17, 2008 12:22 am
II wrote:
Hi, Interested in seeing the various approachs people have in answering this question ... please illustrate your logic/thinking when answering this. Thanks.

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

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

(2) t = 3^n
are u this is not the question.. because i have seen such a question on some forum..

If n and t are positive integers, is n a factor of t?
(1) n = 3^(n-z)
(2) t = 3^n

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II Master | Next Rank: 500 Posts
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Post Sun Aug 17, 2008 12:39 am
Hi Sudhir,
I have posted the question correctly. Everything you see there is correct.
Also see attachment, which is screen shot of the question.
Attachments

This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.

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sudhir3127 Legendary Member Default Avatar
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Post Sun Aug 17, 2008 1:28 am
i go with C.

here the explanation.

Statement 1. it doesnt say anything abt t .. hence in suffcient.

statement 2.

assume if n= 1 then t= 3 , n is a factor of t but if n= 2 t=9 but if n= 2 then t = 9 .. then n is not a factor of t. hence insufficient..

when we take both together..

statement 1 :
n has to greater than or equal to 2 to be an interger.. thus the possible values of n are 1,3,9,27.....

and statement 2. the t can be 3, 27......

thus we are clear that every for all the values of n and t... n is a factor of t.

Hope it helps..

do let me know if u have any doubts..

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pepeprepa Legendary Member Default Avatar
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Post Sun Aug 17, 2008 1:37 am
If n and t are positive integers, is n a factor of t ?

(1) n = 3^(n-2)
Alone, this has no sens, the logic is just that there is no "t" in the equation so it is useless.

(2) t = 3^n
If n=2 then t=9, n is not a a factor of t
But if n=1 and t=3, n is a factor of t (3=3*1)
So it is insufficient, given we have example and counter-example.

(1) & (2)
n = 3^(n-2) can be written like that: n=(3^n)/(3^2)
Then, 9*n=3^n

Thanks to the 2) we have,
t=9*n

So it is clear n is a factor of t given they are both integers.
My answer is C

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Post Sun Aug 17, 2008 1:42 am
pepeprepa wrote:
If n and t are positive integers, is n a factor of t ?

(1) n = 3^(n-2)
Alone, this has no sens, the logic is just that there is no "t" in the equation so it is useless.

(2) t = 3^n
If n=2 then t=9, n is not a a factor of t
But if n=1 and t=3, n is a factor of t (3=3*1)
So it is insufficient, given we have example and counter-example.

(1) & (2)
n = 3^(n-2) can be written like that: n=(3^n)/(3^2)
Then, 9*n=3^n

Thanks to the 2) we have,
t=9*n

So it is clear n is a factor of t given they are both integers.
My answer is C
Excellent explanation ... thanks !

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Post Sun Aug 17, 2008 4:16 am
did anyone else have other approaches to this one ?

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sharad Newbie | Next Rank: 10 Posts Default Avatar
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Post Mon Aug 18, 2008 8:02 am
IMO a

this gives n as 1

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

1 is factor for all the numbers...

B is insufficient

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pepeprepa Legendary Member Default Avatar
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Post Mon Aug 18, 2008 8:37 am
yep sharad you seem to be right the only solution for n=3^(n-2) is 1 ...
Need to check more the proposals and not skip them so fast

II can you give OA

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kiran.raze Senior | Next Rank: 100 Posts
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Post Mon Aug 18, 2008 9:30 am
Hi Pepeprepa,

The solution to n=3^(n-2) is not 1 but n=3, when we have 3=3;

which only means n=3 and so we cannot be sure whether it can be a factor of
t,

and option 2 alone is not sufficient i.e t=3^n because t/n = 3^n/n , which for n=1 is divisible and n=2 is not divisible , therefore insufficient.

Together, of course we have t/n= 3^(n-2)/3^n which equals 9

therefore sufficient ...

Thanks,
Kiran

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pepeprepa Legendary Member Default Avatar
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Post Mon Aug 18, 2008 9:36 am
Thanks for claryfing this post man, I don't know why I bugged between 1 and 3.
Kind of small things which make you doubt, I was right indeed Very Happy

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Post Mon Aug 18, 2008 1:34 pm
yes ... official answer is C.

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arorag Master | Next Rank: 500 Posts Default Avatar
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Post Mon Aug 18, 2008 6:56 pm
There is no need to put the values.

key point:
Is t/n= integer

Combining

3^n/3^(n-2)= 9

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drabblejhu MBA Student
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Post Wed Sep 16, 2009 9:20 pm
Yes, combining by dividing expressions for t and n is great. Don't you need to be careful to test B with numbers, though? To see that you can get yes and no with varying n values?

Thanks,
J

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