Brent@GMATPrepNow wrote:Here's a practice question I just created. I'd say the difficulty level is in the 600 to 700 range.
Is (y - 3x)/(y - 2x) > 1?
(1) (y - 2x)/x < 0
(2) y - 2x > 0
Answer:
A
Brent original!
It's worth taking a moment to consider the characteristics of a fraction that is greater than 1. Take two simple examples.
Case A: 4/3; In this case the numerator and denominator are both positive and the numerator is larger than the denominator.
Case B: (-4)/(-3); In this case the numerator and denominator are both negative and the numerator is smaller than the denominator.
So when we're asked if a fraction is greater than 1, there are two relevant questions:
are numerator and denominator both + or -? And do we know which is larger?
Statement 2 we can evaluate quickly. It tells us that the denominator of the fraction (y - 2x) is negative, but it tells us nothing about the numerator (y - 3x.) Alone this is not sufficient.
Statement 1, (y - 2x)/x <0, is interesting. If a fraction is negative, either the numerator is positive and the denominator is negative, or vice versa. So let's examine both scenarios.
It could be the case that y - 2x > 0 and x < 0. If we multiply the second inequality by (-1), it will become - x > 0, and we can add them.
y - 2x > 0
-x > 0
y - 3x > 0. Interesting. In this scenario we see that the numerator (y - 3x) and the denominator (y - 2x) are both positive. Moreover, if x is negative, y - 3x will be greater than y - 2x, as we'll be subtracting a negative, the functional equivalent of adding a positive. This gives us the aforementioned Case A, yielding a YES to the question.
Alternatively, it could be the case that y - 2x < 0 and x > 0. If we multiply the second inequality by (-1), it will become - x < 0, and we can add them.
y - 2x < 0
-x < 0
y - 3x < 0. In this scenario we see that the numerator (y - 3x) and the denominator (y - 2x) are both negative. Moreover, if x is positive, y - 3x will be smaller than y - 2x, as we'll be subtracting a positive. This gives us the aforementioned Case B, again yielding a YES to the question.
Because the answer will always be YES, statement 1 alone is sufficient to answer the question. The correct answer is
A
