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# If x^2 < x, which of the following could be a value of x?

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Math Expert
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If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 11:39
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If x^2 < x, which of the following could be a value of x?

(A) –6
(B) – 2/3
(C) 6/7
(D) 5/4
(E) 25
[Reveal] Spoiler: OA

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If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 12:01
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Bunuel wrote:
If x^2 < x, which of the following could be a value of x?

(A) –6
(B) – 2/3
(C) 6/7
(D) 5/4
(E) 25

x^2<x
this implies: x^2-x<0, or x(x-1)<0
Plotting the inequality on the number line (refer attachment) will give us
0<x<1 (Since the inequality is less than 0, range of x will be in the region with negative sign)
Only option C satisfies this range
Attachments

number line.jpg [ 21.53 KiB | Viewed 1055 times ]

Last edited by niks18 on 25 Apr 2017, 12:13, edited 1 time in total.
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 12:07
Bunuel wrote:
If x^2 < x, which of the following could be a value of x?

(A) –6
(B) – 2/3
(C) 6/7
(D) 5/4
(E) 25

x^2 < x
x^2 - x < 0
x (x-1) < 0

range of x is 0 < x < 1 , so which of the given value fall in this range?

6/7 - Answer should be C.
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 17:01
Upon simplyfying we can have these two options
x<$$\sqrt{x}$$ or X < 1

We know that for numbers between 0 to 1 only , $$\sqrt{x}$$ > x
Hence looking into the options we can have it as 6/7
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 19:33
Bunuel wrote:
If x^2 < x, which of the following could be a value of x?

(A) –6
(B) – 2/3
(C) 6/7
(D) 5/4
(E) 25

If X^2<x it means x lies between 0 &1. Answer is C i.e. 6/7
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 21:50
Property: x^2<x ---> 0<x<1

Option C
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 22:07
x^2<x, will be true for a positive number between 1 and 0 or a proper fraction. Hence only option C fits here. 6/7
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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25 Apr 2017, 23:39
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Top Contributor
Hi All,

Already mathematical approach has been discussed in the above explanations,

So let me show you the plugging in or POE way,

Here plugging in or using POE-Process of Elimination is also actually very easy,

Also note this a could be question, so plugging in is a good option,

In the answer choices, straight away we can eliminate answer choice A and B, because x^2 is always positive for all the values of x (except 0),

So positive cannot be less than negative, so we can eliminate A and B. Answer options A and B both have negative values.

Looking at the other options, E is definitely out, because 25^2 is greater than 25.

Between C and D,

Option D is an improper fraction. So try to substitute the option in the given expression x^2<x,

25/16 > 5/4. So eliminated.

Option C is a proper fraction (numerator less than denominator), this has to be the answer, because all the other options are out.

Remember, for the proper fraction (for positive), x^2 < x always,

So option C, should be the answer.

So the answer has to be C here.

Hope this helps.
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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28 Apr 2017, 02:26
two root 0 and 1

from -infinity to 0 +ive
0 to 1 -ve
1 to infinity +ive
Only C is between 0 to 1
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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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29 Apr 2017, 09:02
1
KUDOS
Expert's post
Bunuel wrote:
If x^2 < x, which of the following could be a value of x?

(A) –6
(B) – 2/3
(C) 6/7
(D) 5/4
(E) 25

In order for x^2 to be less than x, x must be a positive proper fraction. Thus, 6/7 could be a value of x.

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Re: If x^2 < x, which of the following could be a value of x? [#permalink]

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08 Aug 2017, 20:45
As x^2<x

Hence x => (0,1)

The only option that lies in the range is 6/7 which is 0.85something....

Hence C.
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Re: If x^2 < x, which of the following could be a value of x?   [#permalink] 08 Aug 2017, 20:45
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