BTGmoderatorDC wrote:If x is a nonzero number, which of the three numbers x, 1/x and x^2 is greatest?

(1) -1 < x < 1
(2) x is negative

OA B

Source: GMAT Prep

Given: x is a nonzero number

Target question: Which of the three numbers x, 1/x and x² is greatest?

Statement 1: -1 < x < 1
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1/2. This means 1/x = 1/(1/2) = 2, and x² = (1/2)² = 1/4. In this case, the answer to the target question is 1/x is the greatest value
Case b: x = -1/2. This means 1/x = 1/(-1/2) = -2, and x² = (-1/2)² = 1/4. In this case, the answer to the target question is x² is the greatest value
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x is negative
This means 1/x = 1/negative = negative, and x² = (negative,)² = positive.
Since x² is positive, and x and 1/x are negative, the answer to the target question is x² is definitely the greatest value
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent