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Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]
31 Oct 2010, 16:39

00:00

A

B

C

D

E

Difficulty:

25% (low)

Question Stats:

72% (01:42) correct
27% (00:29) wrong based on 70 sessions

Is x^2 greater than x?

1) x^2 is greater than 1

2) x is greater than -1

I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way: x^2 > x x^2 - x > 0 x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?

I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way: x^2 > x x^2 - x > 0 x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?

Yes it was.

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.

I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way: x^2 > x x^2 - x > 0 x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?

Yes it was.

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.

Answer: A.

Great Thank You!

I am curious though, and maybe I was not fully aware with this in my understanding. How do you conclude to determine the ranges? x<0 or x>1? Should it be x>0 ?

I was doing this question and did not particularly like the explanation that was given. Was my approach of rephrasing this question appropriate?

I rephrased it this way: x^2 > x x^2 - x > 0 x(x-1) > 0

Then from this i deduced that both of those phrases would have to be either positive or both would have to be negative. I felt that statement 1) allowed me to determine that but statement 2) did not. Was my approach correct?

Yes it was.

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.

Answer: A.

Great Thank You!

I am curious though, and maybe I was not fully aware with this in my understanding. How do you conclude to determine the ranges? x<0 or x>1? Should it be x>0 ?

x(x-1)>0 as you noted either both multiples are positive or both are negative: x<0 and x-1<0, or x<1 --> x<0; x>0 and x-1>0, or x>1 --> x>1;

Ah of course, I think I was just mixingup my own thinking and the 'solvinf for x' approach that is also done when solving for a quadratic. Thanks for straightening my thinking and thanks for the link!

Let me see if I can explain this in an easy manner... Statement tells us that x<0 or x>1 - see bunuel's explanation. OR statement also says...x can be a positive integer or a positive fraction greater than 1. Also, x can be a negative integer or a negative fraction (Basically x<0) Statement 1. YES - sufficient. Statement 2. NO - Insuff. This is because x>-1 can be any number such as 0.5 (which does not solve our problem)

Let me see if I can explain this in an easy manner... Statement tells us that x<0 or x>1 - see bunuel's explanation. OR statement also says...x can be a positive integer or a positive fraction greater than 1. Also, x can be a negative integer or a negative fraction (Basically x<0) Statement 1. YES - sufficient. Statement 2. NO - Insuff. This is because x>-1 can be any number such as 0.5 (which does not solve our problem)

Few Tips 1. √x ≥ x for (0 ≤ x ≤ 1) 2. √x ≤ x for (1 ≤ x) 3. x³ ≤ x for (x ≤ -1) and (0 ≤ x ≤ 1) 4. x³ ≥ x for (-1 ≤ x ≤ 0) and (1 ≤ x) 5. x^2 >=x for (1 ≤ x)

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]
14 Aug 2013, 05:13

Hi Bunuel, How would do this sum in your way. The official answer, which is quite confusing is below. I am unable to understand it completely. I did the sum by evaluation the combinations in regions { x<-1 } , { -1<x<0} , { 0<x<1} , {x,1}

Re: Is x^2 greater than x? 1) x^2 is greater than 1 2) x is [#permalink]
14 Aug 2013, 05:16

Expert's post

irda wrote:

Hi Bunuel, How would do this sum in your way. The official answer, which is quite confusing is below. I am unable to understand it completely. I did the sum by evaluation the combinations in regions { x<-1 } , { -1<x<0} , { 0<x<1} , {x,1}