Statement 1: x^2 > xVincen wrote:Is x^2 > 1/x ?
(1) x^2 > x
(2) 1 > 1/x
The OA is D.
Really each statement alone is sufficient? Why?
We can consider three important ranges.
1. If x is negative, then x^2 is always a positive number and x is always a negative number, thus, x^2 is greater than x.
2. If x > 1, then x^2 is always greater than x.
3. If 0 < x < 1, the inequality x^2 > x will not hold true. For example, say x = 1/2, then x^2 = 1/4 < 1/2 (= x). So, this is not a valid case.
From #1 and #2, we get either x < 0 or x > 1.
1. If x < 0, the ineuqality x^2 (= positive) > 1/x (= negative). The asnwer is Yes.
2. If x > 1, say x = 2, then x^2 (= 4) > x (= 1/2). The asnwer is Yes.
Statement 2: 1 > 1/x
Again, we can consider three important ranges.
1. If x is negative, then 1/x is always a negative number, thus, 1 is greater than 1/x.
2. If x > 1, then 1 is always greater than 1/x.
3. If 0 < x < 1, the inequality 1 > 1/x will not hold true. For example, say x = 1/2, then 1 < 1/(1/2) => 1 < 2. So, this is not a valid case.
From #1 and #2, we get either x < 0 or x >1.
This is the same result that we got from Statement 1. Thus, each statement itself is sufficient.
The correct answer: D
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Jakarta | Nanjing | Berlin | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
