GRE Exponents: Practice Question Set

3:17 AM

GRE Exponents: Practice Question Set

Each of the math questions below is directly inspired by a question in the on-line Revised GRE test. I’ve provided an easier version of the question (#1) and a more difficult version of the question (#2).

My recommendation is to try the easier version first. Then, if you answer it correctly, click on the link, and take a stab at the actual Revised GRE question.

If you are able to answer that question correctly, then as prize – you get a fiendishly difficult question (#3). Okay, maybe that’s not a prize – but it is great practice for those aiming for the 90% on quant.

The good news is I have explanations. For the Revised GRE question, I have recorded an explanation video you can watch. Finally, it is a good idea to try the easy question before the medium one, and the medium question before the difficult one.

Good luck!

1. Difficulty: Easy

, where n is a non-negative integer, what is the greatest value of 1/2 ^n

Explanation: Don’t think big – think small. That is the smaller n becomes the greater ½^n becomes. So what is the smallest value? You may be tempted to say 1, which would give us ½. But remember n = 0, because 10^0 = 1

. Therefore ½^0 = 1 Answer: B.

The “hidden zero,” as I like to call it, is a classic GRE math trick. So always keep your eyes open, especially when you see “non-negative integer,” which includes zero.

2. Difficulty: Medium

Section 5, Question 12
http://www.ets.org/s/gre/pdf/practice_book_GRE_pb_revised_general_test.pdf (you’ll have to scroll down a little to page 76).

3. Difficulty: Hard

The equation $n < 1/{(-2)^{-n}} < 135.43$ is true for how many unique integer values of n, where n is a prime number?

7
4
2
1
None of the above

This problem can be difficult, indeed downright inscrutable, unless you take your time and process one piece of information at a time. Once you understand what the problem is saying, you should be able to solve the question relatively quickly.

Explanation:

The most important piece of info is n is a prime number. So do not start by plugging in zero or one. Neither is a prime. The lowest prime is 2. When we plug in ‘2’ we get:

$2 < 1/{(-2)^{-2}} < 135.43$

This is clearly true. Thus we have one instance.

As soon as we plug in other prime numbers a pattern emerges.

$1/{(-2)^{-n}}$ is always a negative number if n is odd. Because all of the primes greater than 2 are odd, the number in the middle will always be negative: