If x is less than zero, which of the following must be greater than zero?

I. $x^2$

II. $(-2) x$

III. $1/x$

Answer Choices

Correct answer marked below

I only

I and II only

Correct

I and III only

II and III only

I, II, and III

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Explanation

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Official Explanation

Official

Let x be a negative number.

I. The expression

x^2

will always yield a positive result since squaring any number results in a positive value.

II. The expression (-2) x equals -2 times a negative number, which results in a positive value.…

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Comments

ANUBHAOct 2, 2024

got this wrong on my practice

NikhilAug 8, 2024

Great question!

What this question tests

What it tests

Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.

Common trap

Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.

If x is less than zero, which of the following must be greater than zero? I. x2x^2x2 II. (−2)x(-2) x(−2)x III. 1/x1/x1/x