n is an integer greater than 0

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 :)

Oct 30, 2017 • Reply

Nancy Mai

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

Oct 7, 2019 • Reply

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.

Oct 16, 2019 • Reply