BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is x > 0 ?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members

Is x > 0 ?

by VJesus12 » Thu Jun 14, 2018 1:13 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Is x > 0 ?

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

The OA is the option E.

Why is not sufficient any of the statements? Could anyone explain to me how to prove this? I'd be thankful for your help.
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Thu Jun 14, 2018 5:58 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

VJesus12 wrote:Is x > 0 ?

(1) x < x²
(2) x < x³
Target question: Is x > 0 ?
Let's go straight to...

Statements 1 and 2 combined
Statement 1 tells us that x < x²
Statement 2 tells us that x < x³
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 2. Notice that 2 < 2² AND 2 < 2³. In this case, the answer to the target question is YES, x IS greater than 0
Case b: x = -1/2. Notice that (-1/2) < (-1/2)² AND (-1/2) < (-1/2)³. In this case, the answer to the target question is NO, x is NOT greater than 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Jun 14, 2018 6:14 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Hi VJesus12,

We're asked if X is greater than 0. This is a YES/NO question and can be approached in a couple of different ways, including by using Number Properties.

1) X < X^2

For X^2 to be greater than X, there are 2 possibilities:
1) X is ANY negative number... at which point the answer to the question is NO.
2) X is a positive number GREATER than 1... at which point the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) X < X^3

For X^3 to be greater than X, there are 2 possibilities:
1) X is a negative fraction... at which point the answer to the question is NO.
2) X is a positive number GREATER than 1... at which point the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we have some examples that 'fit' BOTH Facts:
1) X is a negative fraction... at which point the answer to the question is NO.
2) X is a positive number GREATER than 1... at which point the answer to the question is YES.
Combined, INSUFFICIENT

Final Answer:E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1