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# Is x^2 greater than x? 1) x^2 is greater than 1 2) x is

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Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]

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29 Oct 2011, 09:24
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35% (medium)

Question Stats:

74% (01:43) correct 26% (01:17) wrong based on 19 sessions

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Is x^2 greater than x?

1) x^2 is greater than 1
2) x is greater than -1
[Reveal] Spoiler: OA
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
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Re: Is x^2 greater than x? [#permalink]

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29 Oct 2011, 10:14
siddhans wrote:
Is x^2 greater than x?

1) x^2 is greater than 1
2) x is greater than -1

Is x^2>x
OR
Is x(x-1)>0
OR
Is x<0 or x>1?

1) x^2 > 1
Means;
x>1 OR x<-1; Either way it will be less than 0 or more than 1.
Sufficient.

2)x>-1
Now; x can be 2, which is greater than 1.
OR
x can be from 0 to 1.
Not Sufficient.

Ans: "A"
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Re: Is x^2 greater than x? [#permalink]

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29 Oct 2011, 16:32
fluke wrote:
siddhans wrote:
Is x^2 greater than x?

1) x^2 is greater than 1
2) x is greater than -1

Is x^2>x
OR
Is x(x-1)>0
OR
Is x<0 or x>1?

1) x^2 > 1
Means;
x>1 OR x<-1; Either way it will be less than 0 or more than 1.
Sufficient.

2)x>-1
Now; x can be 2, which is greater than 1.
OR
x can be from 0 to 1.
Not Sufficient.

Ans: "A"

Where highlighted in red, I think you mean x>0...or am I missing a property here?

Thx.
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Re: Is x^2 greater than x? [#permalink]

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29 Oct 2011, 17:50
martie11 wrote:
fluke wrote:
siddhans wrote:
Is x^2 greater than x?

1) x^2 is greater than 1
2) x is greater than -1

Is x^2>x
OR
Is x(x-1)>0
OR
Is x<0 or x>1?

1) x^2 > 1
Means;
x>1 OR x<-1; Either way it will be less than 0 or more than 1.
Sufficient.

2)x>-1
Now; x can be 2, which is greater than 1.
OR
x can be from 0 to 1.
Not Sufficient.

Ans: "A"

Where highlighted in red, I think you mean x>0...or am I missing a property here?

Thx.

Fluke,

You mentioned : from st1 x>1 OR x<-1; Either way it will be less than 0 or more than 1.

So, how can we prove x^2 > x ?

does that mean x(x-1)>0
=> either both positive or both negative ?
thus x > 0 and x> 1 OR x< 0 and x <-1

Thus we have to prove x>1 or x <1?? which is what statement 1 says? hence it is A? Is this the right way ?

Also, why is 2 insufficient then? St 2 says x>-1
Is it because we cant prove x> 1 or x <1 using this statement ?
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Re: Is x^2 greater than x? [#permalink]

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29 Oct 2011, 21:50
martie11 wrote:
fluke wrote:
siddhans wrote:
Is x^2 greater than x?

1) x^2 is greater than 1
2) x is greater than -1

Is x^2>x
OR
Is x(x-1)>0
OR
Is x<0 or x>1?

1) x^2 > 1
Means;
x>1 OR x<-1; Either way it will be less than 0 or more than 1.
Sufficient.

2)x>-1
Now; x can be 2, which is greater than 1.
OR
x can be from 0 to 1.
Not Sufficient.

Ans: "A"

Where highlighted in red, I think you mean x>0...or am I missing a property here?

Thx.

Q: Is x^2>x;
Now, what values of x will satisfy this condition?

Any x that is less than 0 or more than 1 will satisfy the condition.
Say, x=-0.1; x^2=+0.01; x^2>x
x=1.1; x^2=1.21; x^2>x

But, if x is any value from 0 to 1, the expression will not hold true.
x=0; x^2=x
x=1; x^2=x
x=0.5; x^2<x

1) x^2 > 1
This tells us that x is NOT between 0 and 1.
Thus, x is number either >1 OR <0.
So, x^2>x will always be true.
Sufficient.
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Re: Is x^2 greater than x? [#permalink]

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29 Oct 2011, 22:04
Solving by number line

X^2 > x => requires that x < 0 AND x > 1 - call this set Z
(1) x^2 > 1 => true for all x such that x < -1 AND x > 1 => this is a subset of Z, hence sufficient
(2) x > -1 => this covers even the set (0, 1) which is not part of Z, hence insufficient
Re: Is x^2 greater than x?   [#permalink] 29 Oct 2011, 22:04
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# Is x^2 greater than x? 1) x^2 is greater than 1 2) x is

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