sachindia wrote:Is x2(x square) greater than x?

1)x square greater than 1
2)
x is greater than -1.


the Question has been rephrased as 'Is x a positive proper fraction (a fraction between zero and one)?' in Manhattan book.

I didn't understand how is the question mentioned in the first line equivalent to the one mentioned in single quotes above.

Please help.

X^2 > X
X^2 - X > 0
X( X - 1 ) > 0
ie X > 1 and X < 0
ie on a number line if you plot this equation, X will NEVER be true for any value between 0 and 1.
ie NOT a proper fraction.

Hence reverse of what is asked ie a Proper Fraction.
Both types are conjugates and answer requires a Y/N only.
Hope this helps!

imskpwr wrote:

sachindia wrote:Is x2(x square) greater than x?

1)x square greater than 1
2)
x is greater than -1.


the Question has been rephrased as 'Is x a positive proper fraction (a fraction between zero and one)?' in Manhattan book.

I didn't understand how is the question mentioned in the first line equivalent to the one mentioned in single quotes above.

Please help.

X^2 > X
X^2 - X > 0
X( X - 1 ) > 0
so on a number line if you draw this equation, X will be true for all values between 0 and 1 only.
ie a proper fraction.

Hope this helps!

Thanks but
X(X-1)> 0 for say x=4 as well. How can it be true only for values between 0 and 1 only?

sachindia wrote:Thanks but
X(X-1)> 0 for say x=4 as well. How can it be true only for values between 0 and 1 only?

one correction I have made in above post.

Here's my logic and correct me if i'm wrong:

1) If x^2 is greater than 1, that means that x MUST also be greater than 1 due to the fact that any number between 0 and 1 squared will yield a non- integer number less than 1. So any number squared that is GREATER than 1 would always be greater than its root. SUFFICIENT

2) X could be between 0 and -1 which means that X^2 would be greater than X. If X is 0, then they would both be equal. If X was greater than 1 then X^2 would be greater than X. NOT SUFFICIENT

My answer would be A

I did this in my head so please let me know if I am correct.

Thank you

tisrar02 wrote:Here's my logic and correct me if i'm wrong:

1) If x^2 is greater than 1, that means that x MUST also be greater than 1 due to the fact that any number between 0 and 1 squared will yield a non- integer number less than 1. So any number squared that is GREATER than 1 would always be greater than its root. SUFFICIENT

Your thought process and logic is in the right direction. You did get the right answer, however the logic is slightly flawed. On a different question, it may have lead to the wrong answer.
Let's consider the statements:

x^2 > 1 can mean one of two things.
a. x>1 and also
b. x<-1
You considered only the first case.
Not considering x<-1 in this case worked out because if x<-1, x is negative and x^2 is positive, and hence x^2>x. So A is correct here. Always make sure to consider all possible cases.

tisrar02 wrote: 2) X could be between 0 and -1 which means that X^2 would be less than X. If X is 0, then they would both be equal. If X was greater than 1 then X^2 would be greater than X. NOT SUFFICIENT

Hi tisrar02:
2) Good choice with 0 as an option for x. Again, you knew what you were doing and arrived at the answer. I did, however, notice a slight flaw in logic.

tisrar02 wrote: 2) X could be between 0 and -1 which means that X^2 would be less than X.

In the statement above, if x is between 0 and -1, x is negative, which means x^2 is GREATER than x. You inferred the wrong sign. While some may dismiss these things as "careless errors", these may lead to all the hard-work you did on a question to lead you astray. We all fall prey to such errors, (well at least I certainly do at times), but we should strive for perfect practice. Overall, I am happy with the thought process. With perfect practice, you will only get better!

Thank you Eagle-eye. You made me realize such careless mistakes. I also changed my error so I don't throw anyone off.. Good eye Eagle Eye!

You're AWESOME!