If x 0, is x^2

Question

If x > 0, is x^2 < x ?

(1) 0.1 < x < 0.4
(2) x^3 < x^2

smartyman · Answer

My confusion is on statement 2.

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

Therefore
x< -1 or 0<x<1

So, how can the answer be D?

acegmat123 · Answer

Statement 2:

x^3 < x^2

x^3 - x^2 < 0

x^2(x-1) < 0

x < 1 (since x^2 will always be positive)

From question stem we have to find whether 0<x<1.

Question stem says x>0.

So x lies between 0 and 1.

0<x<1

Sent from my iPhone using  GMAT Club Forum mobile app

BrentGMATPrepNow · Answer

Target question :     Is x² ＜ x ?

This is a great candidate for  rephrasing the target question . 
 Aside: Here’s a video with tips on rephrasing the target question:  https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Given : x ＞ 0  
Since we're told that x is POSITIVE, we can safely take  x² ＜ x  and divide both sides by x to get:  x ＜ 1 
  REPHRASED target question :     Is x ＜ 1 ?

Statement 1 : 0.1 ＜ x ＜ 0.4   
If x is BETWEEN 0.1 and 0.4, then we can be certain that   x ＜ 1 
Since we can answer the  REPHRASED target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : x³ ＜ x²  
If x is POSITIVE, then we know that x² is also POSITIVE
This means we can safely take x³ ＜ x² and divide both sides by x² to get  x ＜ 1 
Aha! This is exactly what our REPHRASED target question is asking! 
Since we can answer the  REPHRASED target question  with certainty, statement 2 is SUFFICIENT

Answer:  D

RELATED VIDEOS
 https://www.youtube.com/watch?v=Od98BOicIq4

https://www.youtube.com/watch?v=MyG1K3ee69w

sobby · Answer

If x ＞ 0, is x^2 ＜ x ?
(1) 0.1 ＜ x ＜ 0.4
(2) x^3 ＜ x^2

lets take x^2-x <0 --We can rewrite it as: x(x-1)<0, if we plot it on number line , we will get a range between {0-1}(0 and 1 not included) that will satisfy x^2-x <0.
so any solution having range 0-1 will satisfy the given equation.

A. Suff.

B.x^2(x-1)<0---if plot in a number line , x can only have value between {0-1}(excluding 0 and 1) and can have x<0 as solution..as in the question stem it is given as x can take only positive value.only possible range is {0-1}.this range satisfy x^2-x <0 also .so suff.

Answer : D

awdxzs · Answer

You did the factorisation wrong.
x^3<x^2
x^3-x^2<0
x^2(x-1)<0
Since x^2 is always >0 so x-1<0 and which leads to x<1
Hope it helps

Posted from my mobile device

malavika1 · Answer

This is strange. The original post says: (2) x^3 > x^2

However, it seems that all the solutions have used (2) x^3 < x^2

What's the actual question?

Bunuel · Answer

Edited. It's (2) x^3 < x^2

malavika1 · Answer

Thanks Bunuel. This is good to know.

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

The question tells us that x is a positive number.

We have to evaluate if \(x^2\) < x.

Using the number line is an effective approach in solving these kind of questions.
On the number line, 4 intervals can be marked and the relationship between different functions can be easily compared.

Attachment:

20th Apr 2022 - Post 1.png [ 1.49 KiB | Viewed 4384 times ]

Of the four intervals, \(x^2\) < x is satisfied only when 0 < x < 1. Therefore, the question can be rephrased as, “ Is 0 < x < 1?”

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: 0.1 < x < 0.4

This information answers the question directly and tells us that 0 < x < 1.

The data in statement 1 is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2: \(x^3\) <\( x^2\)

Picking values from the 4 different intervals on the number line, we see that \(x^3\) < \(x^2\) is satisfied when x lies in the following ranges:

However, it is important to note that the question mentions that x > 0. Therefore, the first range can be ruled out and hence, the only range which satisfies the given inequality is 0 < x < 1.

The data in statement 2 is sufficient to answer the question with a definite YES.
Statement 2 alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

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, is x^2 < x ? (1) 0.1 < x < 0.4 (2) x^3 < x^2

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