Bunuel wrote:

If x^3 < x^2, which of the following must be negative?

A. x

B. −x

C. x^5

D. x − 1

E. x^(−1)

Alternatively, we can TEST some values.

We're told that x^3 < x^2

So, one possible value is x =

-1Now let's test the answer choices. We get:

A.

-1, which is negative. KEEP

B. −(

-1) =1, which is positive. ELIMINATE

C. (

-1)^5 = -1, which is negative. KEEP

D. (

-1) − 1 = -2, which is negative. KEEP

E. (

-1)^(−1) = 1/(-1) = -1, which is negative. KEEP

Okay, we're still left with A, C, D and E

We need to test another value.

Another possible value is x =

1/2Test the remaining answer choices...

A.

1/2, which is positive. ELIMINATE

C. (

1/2)^5 = 1/32, which is positive. ELIMINATE

D. (

1/2) − 1 = -1/2, which is negative. KEEP

E. (

1/2)^(−1) = 2/1 = 2, which is positive. ELIMINATE

By the process of elimination, the correct answer is D

Cheers,

Brent

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