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# Is x between 0 and 1? (1) x^5 is positive. (2) x^4 is less than x.

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Intern
Joined: 28 Mar 2017
Posts: 21
Is x between 0 and 1? (1) x^5 is positive. (2) x^4 is less than x.  [#permalink]

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Updated on: 09 Apr 2019, 01:28
1
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:13) correct 32% (00:54) wrong based on 29 sessions

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Is x between 0 and 1?

(1) x^5 is positive.

(2) x^4 is less than x.

Originally posted by rocketmandoman on 30 Mar 2019, 05:37.
Last edited by Bunuel on 09 Apr 2019, 01:28, edited 2 times in total.
Renamed the topic and edited the question.
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Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: Is x between 0 and 1? (1) x^5 is positive. (2) x^4 is less than x.  [#permalink]

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30 Mar 2019, 10:23
1
From S1:

x^5 is positive.
means x is positive. But it is not necessary that x is between 0 and 1.
Hence Insufficient.

From S2:

x^4 is less than x.
Means x is a fraction.
If x is negative fraction then No, x is not between 0 and 1.
If x is a positive fraction such as 1/4, then yes, x is between 0 and 1.
Hence Insufficient.

From combining both, we can say that x is a positive fraction and it is between 0 and 1.
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Re: Is x between 0 and 1? (1) x^5 is positive. (2) x^4 is less than x.  [#permalink]

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30 Mar 2019, 11:20
2
The question seems to have the wrong OA. Statement 1 is not sufficient, since it just means x is positive. For Statement 2, if x^4 < x, then clearly x cannot be negative, because x^4 is always positive (or zero, though not here), and a positive number cannot be less than a negative one. So in Statement 2, we know x > 0, and if x^4 < x, dividing by x on both sides (which we can safely do, since x > 0), we find x^3 < 1, which means x < 1, so 0 < x < 1. So the answer should be B, not C.
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Re: Is x between 0 and 1? (1) x^5 is positive. (2) x^4 is less than x.   [#permalink] 30 Mar 2019, 11:20
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