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

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

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New post 25 Apr 2017, 11:39
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A
B
C
D
E

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  5% (low)

Question Stats:

83% (00:37) correct 17% (00:30) wrong based on 127 sessions

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

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New post 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
number line.jpg [ 21.53 KiB | Viewed 873 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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New post 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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New post 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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New post 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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New post 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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New post 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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New post 25 Apr 2017, 23:39
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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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New post 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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New post 29 Apr 2017, 09:02
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.

Answer: 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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New post 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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