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by pradeepkaushal9518 » Sun Jul 04, 2010 4:49 am
Is n an integer?

(1) 2n is an integer.
(2) 3n is an integer.



Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.



Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.



BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.



EACH statement ALONE is sufficient.



Statements (1) and (2) TOGETHER are NOT SUFFICIENT
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by jube » Sun Jul 04, 2010 5:49 am
IMO C.

1) Insuff. since n=2 will result in 2n being an integer & n=1/2 will also result in 2n being an integer
2) Insuff since n=3 will result in 3n being an integer & n=1/3 will also result in 3n being an integer
1) & 2) since LCM of 2 & 3 is 6 and 2/6 & 3/6 is NOT an integer, therefore n has to be an integer - sufficient.

What is the OA?
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by kvcpk » Sun Jul 04, 2010 7:24 am
pradeepkaushal9518 wrote:Is n an integer?
(1) 2n is an integer.
(2) 3n is an integer.
2n is an integer.

take n=1 ->2n=2
n=1/2 -> 2n=1

INSUFFICIENT

3n is an integer.
take n=1 -> 3n=3
take n=1/3 ->3n=1

INSUFFICIENT.

Combined:

Just do 3n-2n =n
Subtraction of two integers is again an integer..SUFFICIENT

pick C
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by mj78ind » Sun Jul 04, 2010 7:29 am
kvcpk wrote:
pradeepkaushal9518 wrote:Is n an integer?
(1) 2n is an integer.
(2) 3n is an integer.
2n is an integer.

take n=1 ->2n=2
n=1/2 -> 2n=1

INSUFFICIENT

3n is an integer.
take n=1 -> 3n=3
take n=1/3 ->3n=1

INSUFFICIENT.

Combined:

Just do 3n-2n =n
Subtraction of two integers is again an integer..SUFFICIENT

pick C
@kvcpk
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by kvcpk » Sun Jul 04, 2010 7:37 am
mj78ind wrote: @kvcpk
ELEGANT My Man Elegant!
Thanks Buddy!! :)
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by pradeepkaushal9518 » Sun Jul 04, 2010 7:45 am
oa is C
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by san2009 » Mon Jul 05, 2010 2:45 am
kvcpk wrote:
pradeepkaushal9518 wrote:Is n an integer?
(1) 2n is an integer.
(2) 3n is an integer.
2n is an integer.

take n=1 ->2n=2
n=1/2 -> 2n=1

INSUFFICIENT

3n is an integer.
take n=1 -> 3n=3
take n=1/3 ->3n=1

INSUFFICIENT.

Combined:

Just do 3n-2n =n
Subtraction of two integers is again an integer..SUFFICIENT

pick C
hey -- what made you think that you should look at the difference between the two integers??
thanks
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by kvcpk » Mon Jul 05, 2010 3:36 am
san2009 wrote:
kvcpk wrote:
pradeepkaushal9518 wrote:Is n an integer?
(1) 2n is an integer.
(2) 3n is an integer.
2n is an integer.

take n=1 ->2n=2
n=1/2 -> 2n=1

INSUFFICIENT

3n is an integer.
take n=1 -> 3n=3
take n=1/3 ->3n=1

INSUFFICIENT.

Combined:

Just do 3n-2n =n
Subtraction of two integers is again an integer..SUFFICIENT

pick C
hey -- what made you think that you should look at the difference between the two integers??
thanks
Thats a difficult question to answer.. though the answer is simple :)
I thought about it this way..
We are given 3n and 2n.
All we need is to get "n" using these two numbers.
First I though of multiplying these two. we will get 6n^2..No use... became sure that I cant proceed like this..So I went back and read the question again. Got reminded that getting "n" will solve the issue.
So used 3n-2n = n.

It will be good to see the fruit.. but under timed conditions, it depends on luck :D
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by Fiver » Mon Jul 05, 2010 6:21 am
Nice work kvcpk.
Here's another approach:
Assume n = 1/x
With both stmts we know that 2 or 3 when divided by x must be an integer.
This means that xa = 2 and xb = 3, when a & b are integers.
For these 2 stmts to be true 'x' has to be a fraction; hence 1/x (i.e. 'n') is an integer.
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