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# Is x^2 greater than x ?

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Math Expert
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Is x^2 greater than x ?  [#permalink]

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09 Feb 2014, 23:24
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is x^2 greater than x ?

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

Data Sufficiency
Question: 81
Category: Arithmetic; Algebra Exponents; Inequalities
Page: 158
Difficulty: 650

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

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09 Feb 2014, 23:25
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SOLUTION

Is x^2 greater than x ?

Is $$x^2 > x$$? --> is $$x(x-1)>0$$? --> is $$x$$ in the following ranges: $$x<0$$ or $$x>1$$?

(1) x^2 is greater than 1 --> $$x^2>1$$ --> $$x<-1$$ or $$x>1$$. Sufficient.

(2) x is greater than -1 --> $$x>-1$$. Not sufficient.

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

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10 Feb 2014, 12:44
2
(A) alone is sufficient.
Since its given x^2 is greater than 1, so assume x^2 as 1.21/1.44/ 1.69/1.96/2.25 etc. Whether the square root is +/- tive, x^2 will always be greater than x given condition (A).

B alone is insufficient by the same logic as 0.25 is less than 0.5 and greater than -0.5. So no certainty whether X^2 greater than x.

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

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10 Feb 2014, 13:14
2
I'm going with (A) too.

(1) x^2 is greater than 1. Any number greater than 1 will be greater when squared (sign doesn't matter here).
(2) x is greater than - 1. Includes decimals, 0 and 1, so insufficient.
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Re: Is x^2 greater than x ?  [#permalink]

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10 Feb 2014, 15:21
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Is x^2 greater than x ?

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

$$x^2>x$$. So eather $$x>1$$ or $$x<0$$

St(1) Say that $$x^2>1$$ so $$x>1$$. Sufficient.
St(2) Say that $$x>-1$$ So x could be 0 or 2. Not sufficient.

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

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29 Mar 2014, 21:46
Bunuel wrote:
SOLUTION

Is x^2 greater than x ?

Is $$x^2 > x$$? --> is $$x(x-1)>0$$? --> is $$x$$ in the following ranges: $$x<0$$ or $$x>1$$?

(1) x^2 is greater than 1 --> $$x^2>1$$ --> $$x<-1$$ or $$x>1$$. Sufficient.

(2) x is greater than -1 --> $$x>-1$$. Not sufficient.

Hi Bunuel,
If the answer choice satisfy any one of the "Or" inequality does it mean its sufficient?
for eg in 1) x > 1 satisifies ( x >1 or x < 0 ) but x < -1 dosent,
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Re: Is x^2 greater than x ?  [#permalink]

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30 Mar 2014, 10:05
1
abid1986 wrote:
Bunuel wrote:
SOLUTION

Is x^2 greater than x ?

Is $$x^2 > x$$? --> is $$x(x-1)>0$$? --> is $$x$$ in the following ranges: $$x<0$$ or $$x>1$$?

(1) x^2 is greater than 1 --> $$x^2>1$$ --> $$x<-1$$ or $$x>1$$. Sufficient.

(2) x is greater than -1 --> $$x>-1$$. Not sufficient.

Hi Bunuel,
If the answer choice satisfy any one of the "Or" inequality does it mean its sufficient?
for eg in 1) x > 1 satisifies ( x >1 or x < 0 ) but x < -1 dosent,

The question asks whether $$x<0$$ or $$x>1$$:
Attachment:

MSP101751cei440531bcgfbc0000210f0c958eb6ie40.gif [ 997 Bytes | Viewed 5351 times ]
So, whether x is in the blue ranges above.

(1) says that $$x<-1$$ or $$x>1$$. Now, let me ask you a question: is x in the blue ranges???
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Re: Is x^2 greater than x ?  [#permalink]

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16 Mar 2015, 23:10
Bunuel wrote:
$$x^2 > x$$? --> is $$x(x-1)>0$$? --> is $$x$$ in the following ranges: $$x<0$$ or $$x>1$$?

I understand the answer to this questions. Kindly help me understand how we have moved x from the RHS to the LHS here. X could either be +ve or -ve. If it is -ve, then we will have to flip the sign! Am I missing something here?

Thank you!
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Re: Is x^2 greater than x ?  [#permalink]

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17 Mar 2015, 00:04
joseph0alexander wrote:
Bunuel wrote:
$$x^2 > x$$? --> is $$x(x-1)>0$$? --> is $$x$$ in the following ranges: $$x<0$$ or $$x>1$$?

I understand the answer to this questions. Kindly help me understand how we have moved x from the RHS to the LHS here. X could either be +ve or -ve. If it is -ve, then we will have to flip the sign! Am I missing something here?

Thank you!

hi ,
you do not have to change the sign..
say x is a negative number.. then that -ive sign is already there in x...
x=-2.... so wherever x is there you can write -2 and the sign will be there..
but if u change the sign in front of x, it will be mistake...
in this case too.. if u make it -x, this will be equal to -(-2)=+2, which would be wrong...
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Re: Is x^2 greater than x ?  [#permalink]

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20 Mar 2015, 01:55
1
joseph0alexander wrote:
Bunuel wrote:
$$x^2 > x$$? --> is $$x(x-1)>0$$? --> is $$x$$ in the following ranges: $$x<0$$ or $$x>1$$?

I understand the answer to this questions. Kindly help me understand how we have moved x from the RHS to the LHS here. X could either be +ve or -ve. If it is -ve, then we will have to flip the sign! Am I missing something here?

Thank you!

Hi Joseph0alexander!
You can move variables from one side to another without changing signs. You only change signs if you multiply or divide by a negative number. In general if you have a problems with inequalities try the following. Find the numbers that turn inequality into zero. The best way to do it is move all variables to the left or to the right (as you like it) and test intervals on a sign. Here we have x(^2)>x. Hence we can move x to the left and have the following: x(^2)-x>0 ==> x(x-1)>0. Two points that turn this inequality into 0 are 0 and 1. So we have three intervals. If x>1 then inequality is positive, if 0<x<1 then negative and if x<0 again positive. Then start checking statements in the same way. Hope it helps
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Is x^2 greater than x ?  [#permalink]

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01 Jun 2015, 18:00
Hi All,

This DS question is based on a couple of Number Property rules; if you know the rules, then you can answer this question with a more logic-based approach. If you don't know the rules, then you can still discover the patterns involved by TESTing VALUES.

We're asked if X^2 is greater than X. This is a YES/NO question.

By doing a little bit of work up-front, we can make dealing with the two Facts easier. We just have to think about what X COULD be and whether that would make X^2 greater than X (or not).

IF... X = ANY negative value....
Then X^2 = positive and X^2 > X. The answer to the question would be YES.

IF.... X = 0 or X = 1
Then X^2 = X. The answer to the question would be NO.

IF.... X = A positive FRACTION...
Then X^2 < X. The answer to the question would be NO.

IF.... X > 1
Then X^2 > X. The answer to the question would be YES.

Fact 1: X^2 is greater than 1

Here, X COULD be any negative LESS than -1 (eg. -2, -3, -4, -1.5, etc.)....and the answer to the question would be YES.
X COULD also be any positive GREATER than 1 (e.g. 2, 3, 4, 1.5, etc.)...and the answer to the question would also be YES.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

Fact 2: X is greater than -1

X COULD be 0...and the answer to the question would be NO.
X COULD also be any positive GREATER than 1 (e.g. 2, 3, 4, 1.5, etc.)...and the answer to the question would be YES.
Fact 2 is INSUFFICIENT

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

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