Post subject: Re: Is n an integer (GMAT Prep question)
Posted: Mon Jun 08, 2009 8:31 am
Joined: Mon Apr 06, 2009 5:44 pm Posts: 81
That's actually a great question !
First you want to understand what the definition of integer is. An integer is the set of numbers that includes zero, the positive whole numbers and the negative whole numbers.
Let's look at your data sufficiency question:
(1) Is not sufficient. Let's see why: Suppose I pick some integer k and I set n^2=k. Then, n = +/- sqrt (k). This is fine if k is a perfect square, otherwise it wont work. For example: k^2 = 2 is an integer, but k = +/- sqrt(2) is not an integer. It is an irrational number.
(2) is sufficient. Let's see why: if we square both sides of sqrt(n) = k, where k is an integer, we get n = k^2. And, since k is an integer its square must also be an integer.
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