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Is x > 0 ?

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

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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.
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Source: — Data Sufficiency |

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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Thu Jun 14, 2018 6:14 pm
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

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Rich
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