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GMAT Prep / Number Properties

Expert replies
by Blast » Tue Dec 02, 2008 4:41 pm
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Source: — Data Sufficiency |

by jimmiejaz » Wed Dec 03, 2008 4:54 am
given from stmt 1, n^2 is divisible by 36

or we can write n^2 is divisible by (2^2*3^2)
or n is divisible by 2*3 hence suff.

from 2 we have
144/n^2 is an integer

144= 3^2*4^2
so, 144/4^2 is also an integer
If n =4, n is not divisible by 3 but if n=3, n is divisible
hence insuff.

Ans is A
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by lunarpower » Fri Dec 05, 2008 3:49 am
the above solution is good.

about statement (2), notice that it is a statement to which there is a very circumscribed set of solutions. when you see such statements, you would do well just to make an exhaustive list of their solutions.

if n^2 goes into 144 (that's what it means if the fraction turns out to be an integer), then, since 144 is a perfect square, n must go into √144 = 12.
therefore, the complete list of solutions to statement (2) is 1, 2, 3, 4, 6, 12.

try them one by one until either (a) you've used them all up, or (b) you've established insufficiency (after which you can quit testing, even if you haven't tried them all).

this approach doesn't work for statement (1), of course, as there are an infinity of numbers satisfying that statement.
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