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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 \(x>1\) --> \(x>1\);

So \(x(x-1)>0\) holds true when \(x<0\) or \(x>1\).

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)

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.
_________________

" \(x(x-1)>0\) 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 \(x>1\) --> \(x>1\);

So \(x(x-1)>0\) holds true when \(x<0\) or \(x>1\).

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 think it can be answered by a bit intuitively as below:-

X^2 will be always greater than equal to 0. ( Square of a number is always positive).

Now taking the two options one by one. x^2 will be greater than 1 only when x>1 ( square of a decimal i.e 0.0~0.9 will increase the decimal place , for 0.2^2 = 0.04). Option 1 looks correct.

Exploring option 2 - For x>-1 we have to be careful that on number line , the closer one gets to zero , the bigger the number is. So extrapolating for say -0.2 ( which is greater than -1) would give value of 0.04 ( square of a negative number is positive) BUT now there is no end range. So even 1.1 is greater than -1. This makes this information insufficient.

Answer is A.

Obviously all this thought process will be done in mind so could be possibly fast compared to quadratic way.

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

can you explain this step please? what confuses me is the "X < 0" part.

This is easy one. We have to find intervals where x(x-1)>0. We have two points where this inequality turns to zero, 0 and 1. If x>1 than this inequality holds. If 0<x<1 then this is not true (negative sign). And if x<0 then inequality is true. You can check this by plugging numbers from different intervals
_________________

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?

jscott319 wrote:

Is x^2 greater than x?

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

This question has more to do with DECIMAL PROPERTIES than actual inequality

(1) x^2 is greater than 1 x^2 is always greater than 1 except for two cases i) x^2 is EQUAL to 0 When x is 0 ii) x^2 is LESS than x when x is a decimal between -1 and 1 example -0.60^2 = 0.36 (0.36 < 1) example 0.40^2 = 0.16 (0.16 < 1) But since here x^2 is greater than 1 we know that x is not a decimal between -1 to 1 Any other value of x (-ve or +ve) will always be smaller than its square ; therefore x^2 > x SUFFICIENT

(2) x is greater than -1 [/quote] x can be 0 and 0^2 is NOT > 0 x can be 4 and 4^2 > 0 INSUFFICIENT

ANSWER IS A
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

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?

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