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Divisibility

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Source: — Data Sufficiency |

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by Rahul@gurome » Thu May 13, 2010 4:23 am
(1) n/36 is an integer implies n should be multiple of 36, which lies between 100 and 200. The possible values are 108, 144, 180. But none of the integers is odd.
So, (1) is NOT SUFFICIENT to answer the question.

(2) n/45 is an integer implies n should be multiple of 45, which lies between 100 and 200. The possible values are 135, 180. But 180 is the only even integer.
So, (2) is SUFFICIENT to answer the question.

The correct answer is (B).
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by [email protected] » Thu May 13, 2010 1:20 pm
Rahul@gurome wrote:(1) n/36 is an integer implies n should be multiple of 36, which lies between 100 and 200. The possible values are 108, 144, 180. But none of the integers is odd.
So, (1) is NOT SUFFICIENT to answer the question.

(2) n/45 is an integer implies n should be multiple of 45, which lies between 100 and 200. The possible values are 135, 180. But 180 is the only even integer.
So, (2) is SUFFICIENT to answer the question.

The correct answer is (B).
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by [email protected] » Thu May 13, 2010 1:28 pm
Rahul@gurome wrote:(1) n/36 is an integer implies n should be multiple of 36, which lies between 100 and 200. The possible values are 108, 144, 180. But none of the integers is odd.
So, (1) is NOT SUFFICIENT to answer the question.

(2) n/45 is an integer implies n should be multiple of 45, which lies between 100 and 200. The possible values are 135, 180. But 180 is the only even integer.
So, (2) is SUFFICIENT to answer the question.

The correct answer is (B).
:roll:

considering both statements, one gets:

n/36 + n/45 = 5n/180 + 4n/180 ... there you go; the answer is the lowest common denominator of the two terms (i.e. 180).

well, 100<'180'<200

finally, to verify this answer, try n = 180 for both statement 1 and 2.

Correct answer (C)
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by Testluv » Fri May 14, 2010 1:29 am
The correct answer is definitely choice B.

We are asked for the value of n.

We know that n is an integer between 100 and 200 exclusive.

(1) n/36 is an odd integer

When n is divided by 36, the result is an odd integer. Or:

n/36 = odd, or:

n = 36*odd

Because n has to be between 100 and 200, n could be:

n = 36*3 = 108 or n = 36*5 = 180

Because n can be either 108 or 180, (1) is insufficient.

(2) n/45 is an even integer

So:

n = 45*Even, and in order to confine n within the restricted range, it has to be: n = 45*4 = 180. Thus, (2) is sufficient.

Choose B.
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by [email protected] » Fri May 14, 2010 3:34 am
Testluv wrote:The correct answer is definitely choice B.

We are asked for the value of n.

We know that n is an integer between 100 and 200 exclusive.

(1) n/36 is an odd integer

When n is divided by 36, the result is an odd integer. Or:

n/36 = odd, or:

n = 36*odd

Because n has to be between 100 and 200, n could be:

n = 36*3 = 108 or n = 36*5 = 180

Because n can be either 108 or 180, (1) is insufficient.

(2) n/45 is an even integer

So:

n = 45*Even, and in order to confine n within the restricted range, it has to be: n = 45*4 = 180. Thus, (2) is sufficient.

Choose B.
:idea:

thanks, i see what you are saying, sorry. how come the book says the answer is C?
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by Testluv » Fri May 14, 2010 3:37 am
thanks, i see what you are saying, sorry. how come the book says the answer is C?
...I don't know. What book is it? Does the book provide an explanation?

@rahul: (1) does not necessitate that n itself is an odd integer. Your interpretation of (1) leads to the conclusion that (1) is impossible to satisfy rather than that (1) is insufficient to answer the question. :)
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