Is x^2 greater than x ?
(1) x is less than -1.
If x is less than -1, then x^2 will always be greater than x, because x^2 is positive, and x is negative. SUFFICIENT
(2) x^2 is greater than 1.
The inequality x^2 > 1 can be broken down into the following:
x < -1 or x > 1
We've already determined in Statement (1) that x^2 is greater than x if x < -1. If x > 1, then no matter what value of x you choose, x^2 will always be greater than x. SUFFICIENT
You could also approach this problem by deducing some information from the prompt. The questions asks if x^2 > x. Ask yourself: In what situations is x^2 greater than x?
When faced with questions dealing with inequalities and exponents, consider the four important ranges:
1. x < -1
2. -1 < x < 0
3. 0 < x < 1
4. x > 1
Let's look at each of these ranges and apply them to a comparison between x^2 and x:
1. x < -1 (in this situation, x^2 is greater than x)
2. -1 < x < 0 (in this situation, x^2 is greater than x)
3. 0 < x < 1 (in this situation, x^2 is smaller than x)
4. x > 1 (in this situation, x^2 is greater than x)
Also, in this case, we have to consider that x^2 is equal to x if x is either 0 or 1.
So, the only case in which x^2 is not greater than x is if 0 <= x <= 1 (i.e. if x is 0, 1, or a proper fraction).
So really, the question in the prompt can be rephrased as "Is x anything other than 0, 1, or a proper fraction?". And on a DS question, that's the same thing as asking "Is 0 <= x <= 1?", because answering NO to that question is the exact same thing as answering YES to the actual question. Look how much easier the question becomes when we substitute that rephrasing:
Is 0 <= x <= 1?
(1) x is less than -1.
(2) x^2 is greater than 1.
Be on the lookout for ways to rephrase the prompt if possible! Hope that helps!
Last edited by
Rich@VeritasPrep on Mon Jun 28, 2010 3:26 am, edited 1 time in total.
Rich Zwelling
GMAT Instructor, Veritas Prep
I was solely looking at the statement rather than understanding the same...
