Lesson: Negative Exponents

Comment on Negative Exponents

Hi Brent
If x is an integer, is x|x|<2^x?
(1)x<0
(2)x=-10

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
So, we get: (NEGATIVE)(|NEGATIVE|) < 2^NEGATIVE
Evaluate to get: (NEGATIVE)(POSITIVE) < POSITIVE
Simplify: NEGATIVE < POSITIVE
Perfect!

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:

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

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?

Cheers,
Brent

Yulia's picture

Hi Brent,

Could you please show how to solve the question by using just variables?
https://gmatclub.com/forum/x-1-y-1-xy-1-x-y-316172.html

How did you know that x can be 2 and y can be 4?
gmat-admin's picture

Since there are no restrictions on the values of x and y, we can assign any values we wish.
I chose x = 2 and y = 4, because they're easy numbers to work with.
I could have also chosen to use x = 6.215 and y = -0.004213, and the algebraic expression would still evaluate to be -1 (but the calculations would be a lot harder to complete.)

https://gmatclub.com/forum/x-1-y-1-xy-1-x-y-316172.html#p2546544

Hi Brent, Could you solve this question - https://gmatclub.com/forum/m26-184464.html

I'm getting C as the answer, not sure how the OA is D
gmat-admin's picture

https://gmatclub.com/forum/if-x-and-y-are-integers-is-x-y-143771.html

Hi Brent,

I couldn’t find your solution to this question can you help me with that
Thanks
gmat-admin's picture

These 650 questions are killing me I cannot answer any of them, they are solved most crazy way I could never even consider.
gmat-admin's picture

There are several super tricky questions in that list.
Be sure to check the difficulty level rating of questions you find difficult.
If they're rated 75 or greater (for example https://gmatclub.com/forum/if-a-b-c-and-d-are-four-consecutive-integers-...), don't worry about them too much, since they are crazy hard.

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