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Is x < 1?

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Manager
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D
Joined: 17 May 2015
Posts: 249
Is x < 1?  [#permalink]

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New post 06 May 2017, 04:09
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:24) correct 30% (01:09) wrong based on 66 sessions

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Is \(x < 1\)?

(1) \(x^{2}\) is greater than \(x\).

(2) \(x^{3}\) is positive.


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Joined: 12 Aug 2015
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Schools: Boston U '20 (M)
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Re: Is x < 1?  [#permalink]

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New post 06 May 2017, 04:21
We need to see if x<1 or not.

Statement 1 ->
x^2>x

x<0
or
x>1

Not sufficient

Statement 2 =>

x>0

Not sufficient

Combing the two statements => x>1

Hence we have a definite NO for x<1

Thus x is never less than 1

Sufficient

SMASH THAT C

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Re: Is x < 1?  [#permalink]

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New post 06 May 2017, 04:23
Need to figure out if x-1<0
(1) x^2-x>0
x(x-1)>0
It happens only when x and x-1 have the same signs. As long as we have two cases x can be more or less than 1.
Insufficient
(2) x^3>0, hence x is positive by itself however from this statement we cannot deduce whether x<1
Insufficient
(1)+(2) We can cross out negative case from statement (1) and we are left with x(x-1)>0, which means that x>1 and the answer to the main question will be NO

C
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Re: Is x < 1?  [#permalink]

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New post 06 May 2017, 04:52
Is x < 1?

1) \(x^2\) > x
2) \(x^3\) > 0

Considering Statement 1 alone:
\(x^2\) > x
This is true for x > 1 and also for x < 0........INSUFFICIENT
AD out, BCE stays.

Considering statement 2 alone:
\(x^3\) > 0
=> x > 0, so can be < 1 and > 1............INSUFFICIENT

Considering both the statements together:
Both statements hold true only when x > 1.
SUFFICIENT.

The answer is C.
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Re: Is x < 1? &nbs [#permalink] 06 May 2017, 04:52
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