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OG If (x+y)/z > 0 is x < 0?

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Source: — Data Sufficiency |

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by [email protected] » Sat Aug 26, 2017 10:54 am
Hi AbeNeedsAnswers,

We're told that (X+Y)/Z is greater than 0. We're asked if X is less than 0. This is a YES/NO question. We can answer it with a mix of Number Properties and/or TESTing VALUES.

To start, for (X+Y)/Z to be greater than 0, one of two options must occur:
(X+Y) > 0 and Z > 0
(X+Y) < 0 and Z < 0

1) X < Y
IF....
X = 1, Y = 2, Z = 1, then the answer to the question is NO.
X = -2, Y = -1, Z = -1, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) Z < 0
IF...
X = -2, Y = -1, Z = -1, then the answer to the question is YES.
X = 1, Y = -2, Z = -1, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know:
X < Y
Z < 0

Since Z is NEGATIVE, then we know that (X+Y) must ALSO be negative. Since X < Y, we know that either just X or both X and Y must be NEGATIVE. Either way, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

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Rich
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by Brent@GMATPrepNow » Tue Oct 03, 2017 7:17 pm
AbeNeedsAnswers wrote:If (x+y)/z > 0 is x < 0?

(1) x < y
(2) z < 0
Target question: Is x NEGATIVE?

Given: (x+y)/z > 0
What does tell us?
Not much.
It tells us that (x+y)/z is POSITIVE, which means EITHER (x+y) and z are both positive OR (x+y) and z are both negative

Statement 1: x < y
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1 AND the given information. Here are two:
Case a: x = -2, y = -1, and z = -1. In this case x is NEGATIVE
Case b: x = 1, y = 2, and z = 1. In this case x is POSITIVE
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z < 0
There are several values of x, y and z that satisfy statement 2 AND the given information. Here are two:
Case a: x = -2, y = -1, and z = -1. In this case x is NEGATIVE
Case b: x = 1, y = -2, and z = -1. In this case x is POSITIVE
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that z is NEGATIVE
If z is NEGATIVE and (x+y)/z > 0, then it must be the case that (x+y) is also NEGATIVE
In other words, x + y < 0

Statement 1 tells us that x < y
If we subtract y from both sides of the inequality, we get: x - y < 0

So, we now have the following two inequalities:
x + y < 0
x - y < 0

When we ADD the two inequalities, we get: 2x < 0
Divide both sides by 2 to get: x < 0
In other words, x is NEGATIVE
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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Brent
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by Jeff@TargetTestPrep » Thu Jun 21, 2018 3:34 pm
AbeNeedsAnswers wrote:If (x+y)/z > 0 is x < 0?

(1) x < y
(2) z < 0
x < y

Since we don't know anything about z, statement one alone is not sufficient to answer the question.

Statement Two Alone:

z < 0

Since we don't know anything about x and y, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Since (x+y)/z is positive and z is negative, (x + y) must be negative also. Since x < y, the only way (x + y) is negative is if x is also negative.

Answer: C

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