If (x + y)/z 0, is x

Question

If  \frac{x+y}{z}>0 , is x<0?

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

Bunuel · Accepted Answer

SOLUTION If \frac{x+y}{z}>0 , is x<0? Noticee that: \frac{x+y}{z}>0 means that x+y and z have the same sign: either both are positive or both are negative. (1) x < y. No info about z . Not sufficient. (2) z < 0. This statement implies that x+y must also be negative: x+y<0 . But we cannot say whether x<0 . Not sufficient. (1)+(2) From (1) we have that x < y and from (2) we have that x+y<0 . Sum these two inequalities (remember we can add inequalities with the sign in the same direction): x+y+x 2x<0 --> x<0 . Sufficient. Answer: C.

Injuin · Answer

If (x+y)/z is greater than 0, then it is basically saying that either both z and (x+y) are negative or they are both positive. Question asks if x is negative.

Statement 1 says that x is less than y but does not say anything about z. 3 unknown variables, 2 equations, insufficient data.

Statement 2 says that z is negative. The result is that (x+y) is negative then, but there are a lot of possibilities for x+y to be negative.

If we were to combine the two, then we know that x+y is negative with x being less than y. No matter what combination of numbers we put together, x can never be positive. If y is negative and x < y, x is negative. If y is positive then x must be negative to the point that x + y is still negative.

C.

EDIT: people might not like my explanation since I was taught to simplify or reword questions. Might not be for everyone

cyberjadugar · Answer

Hi,

Difficulty: 650

\frac{x+y}{z}>0

Using (1),
x < y,
Possible values, x= -2, y = -1 & z = -1
or x= 1, y = 2 & z = 1
Both satisfy the given condition, thus Insufficient.

Using (2),
z < 0
or x + y < 0,
Possible values, x = -1, y = -1 or x = 1, y = -2. Insufficient.

Using both the statements,
z < 0 & x < y, we have x + y < 0
if y=2, x < -2 for x+y < 0 to hold true.
or if y=-2, x<-2. Sufficient.

Answer (C)

Regards,

metallicafan · Answer

If \frac{x+y}{z}>0 , then dividend and divisor must be or positive or negative at the same time. Let's analyze the clues: (1) x < y We don't know whether z is positive or negative. We cannot know whether x is positive or negarive. (2) z<0 Then x + y <0. However, with this info we cannot claim that x<0. Combining (1) and (2): (1) x x-y<0 Also, based on (2), we know that x+y<0 Adding the inequalities: x -y < 0 x+y <0 -------- 2x <0 So, x<0 C is the answer.

Nuktrue · Answer

Hi guys! While doing this question I was wondering, if the answer we'd get combining the 2 options gave us x>0, would C still be the correct answer? I'm just trying to understand whether data sufficiency in the gmat is confirming the information in the question or also can be used as a negative answer, yet sufficient to give it.

Hope you understand what I mean and can help me out with this.

Many thanks and good luck with your preparation!

Hope you understand what I mean and can help me out with this.

Many thanks and good luck with your preparation!

Bunuel · Answer

A definite NO answer to the question is still considered to be sufficient.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If x+yz >0 , is x<0? (1) x < y (2) z < 0 There are 3 variables (x,y,z) and 1 equation ((x+y)/z>0) in the original condition, and there are 2 more equations given from the 2 conditions, so there is high chance of (C) becoming the answer. Looking at the conditions together, as z<0, x+y<0, x<-y. But as x

BrentGMATPrepNow · Answer

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 Cheers, Brent

Raj94* · Answer

Sir in the 2nd statement i am having doubt. How we can rewrite Z<0 as X+Y <0. Please Explain

Bunuel · Answer

\frac{x+y}{z}>0 , means that x + y and z have the same sign, either both are positive or both are negative. (2) says that z is positive, so x + y must also be positive.

Hope it's clear.

EMPOWERgmatRichC · Answer

Hi All,

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:

Show Spoiler

C

GMAT assassins aren't born, they're made,
Rich

frosnapper24 · Answer

In statement 2, can't we say z<0, so of course x+y<0, meaning x<-y and so x is < 0? Please someone help me out, what math concept am i getting wrong?

Bunuel · Answer

Yes, from z < 0, in (2) it follows that x + y < 0. However, this does not necessarily mean that x < 0. Think of it this way: x + y < 0 means that the sum of two numbers is negative, so at least one of them must be negative. Can we say which one? No, x, y, or both can be negative. If we go the way you are doing, x < -y does not necessarily mean that x is negative. For instance, consider x = 1 and y = -2.

Hope it's clear.

frosnapper24 · Answer

Thank you so much Bunuel, that makes sense. Do you happen to know where I can find similar questions to practice of the same type?

Bunuel · Answer

Check DS inequalities questions here: https://gmatclub.com/forum/search.php?s ... tag_id=184 or use filters in DS forum: https://gmatclub.com/forum/data-sufficiency-ds-141/ or use our questions bank: https://gmatclub.com/forum/search.php?view=search_tags Hope it helps.

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If (x + y)/z > 0, is x < 0 ? (1) x < y (2) z < 0

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