hardik.jadeja wrote:Is 2<x<4?
1. (x^2)-5x+6<0
2. 5(x^2)–25x>0
OA is D but I think its is B.
(1) After reverse FOILing:
(x - 3)(x-2) <0
For this to be true, one bracket must be positive and one must be negative.
So, we could have:
x-3 > 0 and x-2 <0
x>3 and x<2
Well hey, that can't happen, so we can ignore it.
Other possibility:
x-3 < 0 and x-2 > 0
x<3 and x>2
2 < x < 3
If x is between 2 and 3, it's definitely between 2 and 4: sufficient.
(2) 5(x^2)–25x>0
x^2 - 5x > 0
x(x-5) > 0
Positive product, so either both terms are positive or both are negative.
Both positive:
x>0 and x-5>0. Therefore, x>5.
Both negative:
x<0 and x-5<0. Therefore, x<0.
Well, if x<0 Or x>5, then x is definitely NOT between 2 and 4. Sufficient.
HOWEVER,
on the actual GMAT, the two statements never contradict. So, while this question is a good test of factoring skill, it's a 100% bogus GMAT question. What's the source? Always posting your source is good!
