GMAT Quant Practice #4:

by on July 25th, 2013

It’s GMAT time for a lot of your right now. I’ve spoken with a number of you who are taking the exam in a few weeks.

There are many more of you who will be taking it for the first (or second, or third) time within the next 1-2 months, depending on which round you are applying to schools in.

GMAT study is probably THE most intense part of this whole journey, and I want to provide at least some small bit of support in the way of additional problems that you can use to test and sharpen your skills with.

Happy GMATing!

Practice Problem 4A

If n is positive, is n an integer?

1) sqrt{n}≠ integer

2) sqrt{n}<1

Solution

Question Stem Analysis:

We know that n is positive. The question is whether n is an integer.

Statement One Alone:

sqrt{n} ≠ integer

We can substitute various values for n to see whether n must be an integer. If sqrt{n} ≠ integer, then n is not a perfect square. But n could be a non-perfect square integer such as 2 since if n=2 then sqrt{2} ≠ integer. The variable n could also be a fraction. For example, if n=1/2 then sqrt{1/2} ≠ integer. Thus statement one is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

sqrt{n}<1

Statement two can be simplified by squaring both sides of the inequality: (sqrt{n})^2< 1^2. That means that n<1.

Since n is less than 1 and n is also positive, it should be clear that n cannot equal an integer. Statement two is sufficient.

Answer: B

Practice Problem 4B

If a^2=5, the expression {{3^(a+b)^2}/{3^b^2}}*9^{-ab} is equal to which of the following?

A) 3
B) 9
C) 27
D) 81
E) 243

Solution:

{{3^(a+b)^2}/{3^b^2}}*9^{-ab}=

{3^(a^2+b^2+2ab)/3^b^2}*3^{-2ab}=

{3^{(a^2+b^2+2ab)-b^2}}*3^{-2ab}=

{3^(a^2+2ab)*{3^-2ab}=

{3^(a^2+2ab+(-2ab))}= 3^{a^2} = 3^5=243 

Note: (a+b)^2=(a+b)(a+b)=a^2+2ab+b^2

Answer: E

Related Stories:

GMAT Quant Practice #3
GMAT Quant Practice #2
GMAT Quant Practice #1

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