Lesson: Negative Exponents

Comment on Negative Exponents

Hi Brent
If x is an integer, is x|x|<2^x?

Pls explain i couldn't understand how to substitute values for |x| should i take -ve or + ve
gmat-admin's picture

In both statements you are told that x is negative. So, if you're going to plug in (test) values of x, you must use negative values.

The key thing to recognize here is that 2^x IS POSITIVE for ALL values of x (positive or negative)

For example, if x = 5, then 2^x = 2^5 = 32
And if x = -3, then 2^x = 2^(-3) = 1/8

(1) If x < 0, then x is NEGATIVE

2) Same process here as for statement 1.

Answer: D

Here's a thread discussing this question at greater length: https://gmatclub.com/forum/if-x-is-an-integer-is-x-x-2-x-144342.html

Hi Brent. Can you walk through the steps with your answer to this question:


And why/how can you flip each fraction?

Your answer to the question:

Given: 5n/(4n - x) = (0.788)^(-1)
Rewrite as: 5n/(4n - x) = 1/0.788
Flip each fraction: (4n-x)/5n = 0.788
Apply above property: 4n/5n - x/5n = 0.788
Simplify: 4/5 - x/5n = 0.788
Simplify: 0.8 - x/5n = 0.788
So: x/5n = 0.012
Multiply both sides by 5 to get: x/n = 0.06
Rewrite as fraction: x/n = 6/100 = 3/50

gmat-admin's picture

Question link: https://gmatclub.com/forum/if-5n-4n-x-0-788-then-x-n-259657.html

The main property here is as follows:
If wxyz ≠ 0 and w/x = y/z, then it must also be true that: x/w = z/y

For example, since 4/8 = 1/2, it must also be true that 8/4 = 2/1
Likewise, since 9/6 = 3/2, it must also be true that 6/9 = 2/3

So, when I got to this point: 5n/(4n - x) = 1/0.788...
...I could see that flipping both sides was going to make it much easier to solve the equation.

Does that help?


Add a comment

Tweet about the course!

If you're enjoying my video course, help spread the word on Twitter.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!