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

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Intern
Joined: 19 Nov 2011
Posts: 9
If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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Updated on: 28 Jan 2012, 04:38
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35% (medium)

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64% (00:58) correct 36% (01:13) wrong based on 494 sessions

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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.

Originally posted by RadhaKrishnan on 28 Jan 2012, 04:12.
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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Joined: 02 Sep 2009
Posts: 47037

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28 Jan 2012, 04:37
2
2
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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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
Math Expert
Joined: 02 Sep 2009
Posts: 47037

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05 Jan 2014, 16:06
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
2
That was nasty. Thanks

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Director
Joined: 23 Jan 2013
Posts: 598
Schools: Cambridge'16
Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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04 Jul 2017, 20:59
1
St.1: 36=2*2*3*3, so all multiples of 36 will be even. INSUFF

St.2: 45=5*3*3, multiple is even, only chance if the multiple ends 0 (divisible by 5). It can be 90,180 etc. SUFF

B
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Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]

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07 Sep 2017, 02:26
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.

It's a very simple question.
Given : 100<n<200
DS : value of n

Statement 1 : Let take odd multiple of 36. They are 36, 108, 180 .... So , 108, 180 lies between 100 and 200
NOT SUFFICIENT

Statement 2 : Let take even multiples of 45. They are 90, 180, ....... So only 180 lies between 100 and 200
SUFFICIENT

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Re: If n is an integer and 100 < n <200, what is the value of n?   [#permalink] 07 Sep 2017, 02:26
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# If n is an integer and 100 < n <200, what is the value of n?

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