Source: Revised GRE PDF 2nd Ed. Section 6; #9 (p. 87)

8

# n is an integer greater than 0

n is an integer greater than 0 Quantity A: The number of different prime factors of 9n Quantity B: The number of different prime factors of 8n Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

### 2 Explanations

5

Carolina Seigler

Hi there, I was just wondering why there is no explanation for the previous question, Question #8? Thanks!

Oct 3, 2017 • Comment

Jonathan , Magoosh Tutor

Hi!
Here's the question.

1/(2^(1-k)) < 1/8
and we want to compare k = -2

if 1/(2^(1-k)) < 1/8, then

2^(1-k) > 8 (for example 1/9 or 1/16 would be less than 1/8)

2^(1-k) > 8 when (1 - k) > 3

1 - k > 3
-2 > k
So k is LESS than -2.
Therefore column B (-2) is larger.
Hope I helped :)

Nancy Mai

Could you please explain why the less than sign flipped to point the other way?

Sam Kinsman

Hi Nancy,

First, let's think about what happens if n=1. If that's the case, then QA has 1 prime factor (3). And QB also has 1 prime factor (2).

Now, if n=3, then QA still only has 1 unique prime factor (3). But QB now has two different prime factors (2 and 3). So in this case, QB is greater. So we have QA < QB.

But let's think about what happens if n=2. In this case, QA would have two different prime factors (2 and 3). And QB would still just have one unique prime factor (2). So in this case the QA is greater, so we'd have QA > QB.

So essentially, the signs flip when we plug in different numbers for n.

3

Chris Lele

Sep 27, 2012 • Comment