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If (x+y)/z = -2, is x positive?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Jul 31, 2018 12:14 am
BTGmoderatorDC wrote:If (x+y)/z = -2, is x positive?

(1) z is negative.
(2) y is positive.
Given: (x+y)/z = -2

Question: Is x positive?

Let's take each statement one by one.

(1) z is negative.

We have (x+y)/z = -2 => (x+y) = -2*-|z| => (x+y) = 2|z| => (x+y) = Positive

x can be positive, 0 or negative. Insufficient.

(2) y is positive.

We have (x+y)/z = -2 => x + |y| = -2z => x = -|y| - 2z

Depending on the value of z, x can be negative, 0 or positive. Insufficient.

(1) and (2) together

We have (x+y)/z = -2 =>x + |y| = -2*-|z| => x = -|y| + 2|z|

Depending on the value of y, x can be negative, 0 or positive. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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by ceilidh.erickson » Wed Aug 01, 2018 6:37 am
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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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