Lesson: Negative Exponents

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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

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