If x

Question

If x < 0, which of the following must be true? I. x^2 > 0 II. x − 2x > 0 III. x^3 + x^2 < 0 A) I only B) I & II C) II & III D) All of the above E) None of the above Source: Chili Hot GMAT

intheend14 · Answer

We're told that x is negative and that is all. Let's evaluate.

Since x is negative, x^2 is always positive (>0). True.
Since x is negative then x-2x>0. True as we're essentially adding a negative number to a larger (effectively positive number). For example, if x=-.5, then -0.5 + 1>0 or if x = -1, then -1+2>0.
However, the third doesn't have to be true. If x is a negative fraction, then x^2 is positive and larger than x^3. If x=-1/2, then x^3+x^2 = -1/8 + 1/4>0. However, if x=-1, then -1+1=0. Insufficient, not always true.

Choice B

amitshri15 · Answer

I. x^2 > 0 -TRUE- Irrespective of x sign, it will always be positive because of even power and since x is less than 0 x^2 can't be 0.
II. x − 2x > 0 -TRUE- Since x<0 , -x will be positive
III. x^3 + x^2 < 0 -Can not say-
x^2(x+1)<0 , since x^2 will always be positive => x+1 < 0 => x < -1. But we know that x<0, so x could be -1/2 etc.

Answer is B.

KarishmaB · Answer

Given: x is negative. Which of the following must be true? I. x^2 > 0 This is always true for real numbers except if x is 0. Since x is negative, this must be true. II. x - 2x > 0 -x > 0 x < 0 (multiplied both sides by -1). This is given so it must be true. III. x^3 + x^2 < 0 x^2*(x + 1) < 0 x^2 is positive so for x^2 * (x+1) to be negative, x+1 should be negative i.e. x < -1. We know that x < 0 but it could very well lie between 0 and -1 and hence this needn't be true. It may or may not be. So only (I) and (II) must be true. Answer (B)

PareshGmat · Answer

Answer = B) I & II

I. x^2 > 0

Square of any number is always positive. Always true

II. x - 2x > 0

-x > 0
x < 0 (This is the given condition in the problem, which has to be obviously true)

III. x^3 + x^2 < 0

\(For x = \frac{-1}{2}\)

\(\frac{1}{4} - \frac{1}{8} > 0\) (Not necessarily true)

Answer = B

JJo · Answer

Given: x < 0,

I. x^2 > 0 --> squaring is never negative --> so always true
II. x − 2x > 0 --> -x>0, since x is given as -ve no. so -ve of -ve no. is always +ve --> so always true
III. x^3 + x^2 < 0 -->x^2(x+1)<0 and given is x<0 so it can be -1, in that case (-1)^2(-1+1)<0 = 0<0 --> so not always true

Ans. B) I & II

TheUltimateWinner · Answer

We can invalid III by putting the fraction value of x. So, the correct choice is B.

GMATinsight · Answer

Given: x<0 I. x^2 > 0 Since x is Non-Zero so x^2 is bound to be Positive hence CORRECT II. x − 2x > 0 i.e. -x > 0 i.e. x <0 hence CORRECT III. x^3 + x^2 < 0 i.e. x^2(x+1) < 0 x^2 is always positive but (x+1) may or may not be negative for values of x less than or greater than -1 hence this is not always True Answer: Option B

manjot123 · Answer

x^2> 0 always x-2x>0 take x = -2 -2+4>0 take x = -1/2 -1/2 + 1>0 so second statement is true x^3 + x^2<0 x = -2 -8 + 4<0 true x = -1/2 -1/8 + 1/4<0 false is my approach correct?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x < 0, which of the following must be true?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions