If x > 0, is x^2 < x?
(1) 0.1 < x < 0.4
(2) x^3 < x^2
The OA is the option D.
Why is sufficient the second statement? I need a clarification here. Thanks in advance.
If x > 0, is x^2 < x?
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: Is x² < x?M7MBA wrote:If x > 0, is x² < x?
(1) 0.1 < x < 0.4
(2) x³ < x²
Statement 1: 0.1 < x < 0.4
A useful property says: If 0 < x < 1, then x² < x
Since statement 1 basically tells that 0 < x < 1, we can be certain that x² < x
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x³ < x²
Since we're told that x is POSITIVE, we can safely divide both sides of the inequality by x to get: x² < x
Perfect!!!
The answer to the target question is YES, it is true that x² < x
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Here's another approach:M7MBA wrote:If x > 0, is x² < x?
(1) 0.1 < x < 0.4
(2) x^3 < x²
Target question: Is x² < x ?
This is a good candidate for rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?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
Cheers,
Brent