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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.

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

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.

Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]
10 Oct 2013, 16:37

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. _________________

“Confidence comes not from always being right but from not fearing to be wrong.”

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.

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.

Answer: B.

Why not 90 in statement 2?

Cheers! J

Because we are told that 100 < n <200, 90 is not in the range. _________________

Re: If n is an integer and 100 < n <200, what is the value of n? [#permalink]
27 Jul 2015, 07:27

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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