Is x^3

Question

Is  x^3  < x ?

(1)  x^2  < 1

(2)  x^3  > -1

ga821 · Answer

Please guide if my solution is right

ga821 · Answer

KarishmaB Bunuel

I did it this way, the official video of Expert Global doesn't consider the possibility of taking zero as a substitute, and I wanted to know why :

Statement 1 :
\(x^2\) < 1
Let's take 0.5 and 0, both's square is less than 1, hence it satisfies the equation
With 0.5, you get 0.125 as its cube, which is less than 0.5 - thus proving yes for \(x^3\) < x
With 0, you get that it is not less than 0 - thus proving no for \(x^3\) < x
hence insufficient

Statement 2 :
\(x^3\) > -1
Let's again take 0.5 and 0, both's cube is more than -1, hence it satisfies the equation
With 0.5, you get 0.125 as its cube, which is less than 0.5 - thus proving yes for \(x^3\) < x
With 0, you get that it is not less than 0 - thus proving no for \(x^3\) < x
hence insufficient

Combined :
Both have similar values being substituted, hence insufficient

Answer - E

Expert Global soln - https://www.youtube.com/watch?v=gjHyD4iTpNM (refer to the last question of the video)

Bunuel · Answer

Is x^3 < x ?

Is x^3 < x ?
Is x^3 - x < 0 ?
Is x(x^2 - 1) < 0 ?
Is x(x - 1)(x + 1) < 0 ?

Is x < -1 or 0 < x < 1 ?

(1) x^2 < 1

Take the square root: |x| < 1, so -1 < x < 1.

If x = -1/2, the answer is NO.
If x = 1/2, the answer is YES.

Not sufficient.

(2) x^3 > -1

Take the cube root: x > -1.

If x = -1/2, the answer is NO.
If x = 1/2, the answer is YES.

Not sufficient.

(1)+(2) Combining we get -1 < x < 1.

If x = -1/2, the answer is NO.
If x = 1/2, the answer is YES.

Not sufficient.

Answer: E.

Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems
Work Problems
Distance Problems
Mixture Problems
Percent and Interest Problems
Overlapping Sets Problems
Statistics Problems
Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

ga821 · Answer

Thanks but wanted to know why you didn't consider 0 as a value to substitute in the equation

Is x^3 < x (1) x^2 < 1 (2) x^3 > -1

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