BTGmoderatorDC wrote:If (x+y)/z = -2, is x positive?
(1) z is negative.
(2) y is positive.
First, REPHRASE the question to determine what kind of information we need for sufficiency.
If a fraction is equal to a negative number, then either then numerator is negative and the denominator positive, or vice versa. In order for x to be positive, the entire numerator (x + y) could be positive and z could be negative, or (x + y) could be negative and z positive.
(1) z is negative.
This tells us that our denominator is negative, so the numerator (x + y) must be positive. However, y could be a larger positive and x could be negative, and we'd still have a positive numerator overall. Without information about y, this is insufficient.
(2) y is positive.
This tells us very little. x and y might both be positive and z negative, or z positive and x a negative with a larger absolute value than y. Insufficient.
(1) and (2) together
We know that z is negative, so the numerator (x + y) must be positive. And we're also given that y must be positive. But does x need to be positive? Test some values:
Case 1: x and y both positive, z negative
$$\frac{1+3}{-2}=-2$$
Case 2: x negative, y positive, z positive
$$\frac{-1+5}{-2}=-2$$
Since we can come up with negative and positive values for x that fit the givens, both statements together are insufficient.
The answer is
E.
