If x^2

Question

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

niks18 · Answer

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

HKD1710 · Answer

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.

umadurga · Answer

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

AliciaSierra · Answer

If X^2<x it means x lies between 0 &1. Answer is C i.e. 6/7

warriorguy · Answer

Property: x^2<x ---> 0<x<1

Option C

Nishantg779 · Answer

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

CrackverbalGMAT · Answer

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.

kannu44 · Answer

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

ScottTargetTestPrep · Answer

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

stonecold · Answer

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.

AkshdeepS · Answer

Plug in the answer choices:

Only (C) satisfies the given inequality.

Krunaal · Answer

x^2 < x x^2 - x < 0 x*(x-1) < 0 x cannot be negative since x*(x-1) is negative and negative*negative will be positive. Thus, x > 0 and x-1 < 0 => x < 1 0

JLambert · Answer

Two things to remember when pushing through with logic: 
 
  negative times a negative negates each other  
  fraction times a fraction makes a smaller fraction if it's under 1

That means: 
 A: higher number because it's negative 
 B: higher number because it's negative 
 C: lower number because it's a fraction under 1 
 D: higher number since it's over 1 
 E: higher number since it's over 1

Hope that helps.

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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