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# If n is an integer and 100 < n <200, what is the value

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Senior Manager
Joined: 02 Dec 2007
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If n is an integer and 100 < n <200, what is the value [#permalink]  20 Sep 2008, 05:23
If n is an integer and 100 < n <200, what is the value of n?
(1)n/36 is an odd integer.
(2)n/45 is an even integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
SVP
Joined: 21 Jul 2006
Posts: 1553
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Kudos [?]: 336 [0], given: 1

Re: value of n [#permalink]  20 Sep 2008, 05:53
Nihit wrote:
If n is an integer and 100 < n <200, what is the value of n?
(1)n/36 is an odd integer.
(2)n/45 is an even integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

n must be between 100 and 200, so:

(1) n = 36*odd integer, so n is even. Take 36 and multiply it by each integer starting from 1 until you're within 100 and 200:

36*1=36, 36*2=72, 36*3=108, 36*4=144, 36*5=180 ---> stop here cause otherwise you will start to have numbers bigger than 200. We have 108 and 180, both numbers that will yield to an odd integer when divided by 36. Not suff.

(2) n= 45*even integer, so n is also even. Take 45 and multiply it by each integer starting from 1 until you're within 100 and 200:

45*1=45, 45*2=90, 45*3=135, 45*4=180 ---> stop here cause otherwise you will start to have numbers bigger than 200. We have 135 and 180, the only numbers between 100 and 200. Only 180 can be divided by 45 to give us an even integer. So Suff!

Senior Manager
Joined: 02 Dec 2007
Posts: 462
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Re: value of n [#permalink]  20 Sep 2008, 05:56
Thanks Tarek, I think the OA is wrong . C wasn't making any sense !
SVP
Joined: 21 Jul 2006
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Kudos [?]: 336 [0], given: 1

Re: value of n [#permalink]  20 Sep 2008, 06:07
Nihit wrote:
Thanks Tarek, I think the OA is wrong . C wasn't making any sense !

Your OA is C??? It can't be according to what I've just explained. What's the source of this question? It's impossible that C is correct.
SVP
Joined: 05 Jul 2006
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Re: value of n [#permalink]  20 Sep 2008, 09:12
[quote="Nihit"]If n is an integer and 100 < n <200, what is the value of n?
(1)n/36 is an odd integer.
(2)n/45 is an even integer.

from 1

n = 4*3^2*x given the limitation 100 < n <200 thus x can be (3,4,5) another limitation is n/36 is odd intiger thus x can be 3 or 5 and thus n can be either = (108,180)...insuff

from2

n = 5*3^2 *y given the limitation 100 < n <200 thus y can be = (3 or 4) thus x has to be 4

and thus N= 180.......suff

Re: value of n   [#permalink] 20 Sep 2008, 09:12
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