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N is a positive integer, is 150/n an int?

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N is a positive integer, is 150/n an int?

by jkandas » Thu Feb 11, 2010 4:01 pm
If n is a positive integer, is 150/n an integer? (OG 11 DS 118)

(1) n < 7

(2) n is a prime number

Soln:

(1) -> n could be 1, 2, 3, 4,...6 -> NOT Suff.
(2) -> n is a prime number -> narrows down to 2, 3, 5 -> NOT Suff.

In OG 11, they explain that both statements together narrow n to be 1, 2, 3 and 5...so the answer is C.

I ended up choosing E because the question stem indicates that "n is a positive integer"...so in this case, should we not narrow it down to one number? I couldn't understand OG's explanation as it relates to the question stem.

Any thoughts?
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by Ian Stewart » Thu Feb 11, 2010 4:57 pm
jkandas wrote:If n is a positive integer, is 150/n an integer? (OG 11 DS 118)

(1) n < 7

(2) n is a prime number

Soln:

(1) -> n could be 1, 2, 3, 4,...6 -> NOT Suff.
(2) -> n is a prime number -> narrows down to 2, 3, 5 -> NOT Suff.

In OG 11, they explain that both statements together narrow n to be 1, 2, 3 and 5...so the answer is C.

I ended up choosing E because the question stem indicates that "n is a positive integer"...so in this case, should we not narrow it down to one number? I couldn't understand OG's explanation as it relates to the question stem.

Any thoughts?
The question does not ask for the value of n, and there is no way to find the exact value of n from the two statements. The question only asks if we can be sure that 150/n is an integer. Using both statements, there are three possible values of n: 2, 3 or 5. No matter which of these values is equal to n, 150/n will be an integer, so while we can't find n, we can still answer the question with 100% certainty. The two statements combined are sufficient. Note that Statement 1 alone is almost sufficient; the only reason it is not sufficient is that n might be 4, and 150/4 is not an integer.
jkandas wrote: In OG 11, they explain that both statements together narrow n to be 1, 2, 3 and 5...so the answer is C.
I hope they don't include 1 in that list - there is no way n could be 1 if Statement 2 is true, since 1 is not a prime number.
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by jkandas » Thu Feb 11, 2010 5:12 pm
Thanks! That makes sense...I was too quick to dismiss the choice for C once I saw more than one answer for n.

Yes, I was also wondering how they came up with 1, 2, 3, 5 in the solution...definitely something they need to correct!
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