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

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If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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28 Jan 2012, 04:12
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Jan 2012, 04:38, edited 1 time in total.
Added the OA and moved to DS subforum.
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28 Jan 2012, 04:37
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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.

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

(1) n/36 is an odd integer --> $$\frac{n}{36}=odd$$ --> $$n=36*odd$$ --> $$n$$ is even multiple of 36 in the range 100-200 --> there are two such numbers possible: $$n=36*odd=36*3=108$$ and $$n=36*odd=36*5=180$$. Two different answers, hence not sufficient.

(2) n/45 is an even integer --> $$\frac{n}{45}=even$$ --> $$n=45*even$$ --> $$n$$ is even multiple of 45 (basically a multiple of 90) in the range 100-200 --> there is only one such number possible: $$n=45*even=45*4=180$$ (as 45*2<100 and 45*6>200). Sufficient.

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11 Feb 2013, 10:12
If n is an integer and 100 < n <200, what is the value of n?
(1) 36n is an odd integer.
(2) 45n 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.

The answer is OA C, however i think the only even multiple of 45 between 100 and 200 is 180 so shuoldn't it be B?plzz explain
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11 Feb 2013, 10:21
Expert's post
4112019 wrote:
If n is an integer and 100 < n <200, what is the value of n?
(1) 36n is an odd integer.
(2) 45n 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.

The answer is OA C, however i think the only even multiple of 45 between 100 and 200 is 180 so shuoldn't it be B?plzz explain

Merging similar topics. Original question is in the first post. OA is B, not C.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic MUST be the first 40 characters (~the first two sentences) of the question.
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Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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10 Oct 2013, 17:37
n/36 is odd. there are only below numbers which are divisible by 36 and between 100 and 200
36*3 = 108
36*5 = 180
so n can be 108 or 180. Hence not sufficient

n/45 is even. There is only 1 choice for n which is between 100 and 200
45*4 = 180
for other mulitples of 45 between 100 and 200, n/45 will be odd (3 or 5). Hence B is sufficient.
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05 Jan 2014, 13:56
Bunuel 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.

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

(1) n/36 is an odd integer --> $$\frac{n}{36}=odd$$ --> $$n=36*odd$$ --> $$n$$ is even multiple of 36 in the range 100-200 --> there are two such numbers possible: $$n=36*odd=36*3=108$$ and $$n=36*odd=36*5=180$$. Two different answers, hence not sufficient.

(2) n/45 is an even integer --> $$\frac{n}{45}=even$$ --> $$n=45*even$$ --> $$n$$ is even multiple of 45 (basically a multiple of 90) in the range 100-200 --> there is only one such number possible: $$n=45*even=45*4=180$$ (as 45*2<100 and 45*6>200). Sufficient.

Why not 90 in statement 2?

Cheers!
J
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05 Jan 2014, 16:06
Expert's post
jlgdr wrote:
Bunuel 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.

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

(1) n/36 is an odd integer --> $$\frac{n}{36}=odd$$ --> $$n=36*odd$$ --> $$n$$ is even multiple of 36 in the range 100-200 --> there are two such numbers possible: $$n=36*odd=36*3=108$$ and $$n=36*odd=36*5=180$$. Two different answers, hence not sufficient.

(2) n/45 is an even integer --> $$\frac{n}{45}=even$$ --> $$n=45*even$$ --> $$n$$ is even multiple of 45 (basically a multiple of 90) in the range 100-200 --> there is only one such number possible: $$n=45*even=45*4=180$$ (as 45*2<100 and 45*6>200). Sufficient.

Why not 90 in statement 2?

Cheers!
J

Because we are told that 100 < n <200, 90 is not in the range.
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Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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05 Jan 2014, 16:25
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Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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27 Jul 2015, 08:27
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Re: If n is an integer and 100 < n <200, what is the value of n?   [#permalink] 27 Jul 2015, 08:27
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