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
Exponents - If n and t are positive integers, is n a factor
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are u sure abt the statement 1. it doesnt say anything abt "T"?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
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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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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..
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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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
(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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Excellent explanation ... thanks !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
- kiran.raze
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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
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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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
Thanks,
J