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

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09 Jul 2012, 04:49
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Difficulty:

55% (hard)

Question Stats:

60% (02:24) correct 40% (01:21) wrong based on 965 sessions

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

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

Diagnostic Test
Question: 41
Page: 26
Difficulty: 650
[Reveal] Spoiler: OA

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Re: If (x+y)/z>0, is x<0? [#permalink]

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10 Jul 2012, 16:28
3
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Bunuel wrote:

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<y ----> x-y<0
Also, based on (2), we know that x+y<0

x -y < 0
x+y <0
--------
2x <0
So,
$$x<0$$

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Re: If (x+y)/z>0, is x<0? [#permalink]

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09 Jul 2012, 04:49
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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): $$x+y+x<y$$ --> $$2x<0$$ --> $$x<0$$. Sufficient.

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Re: If (x+y)/z>0, is x<0? [#permalink]

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10 Jul 2012, 08:52
2
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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
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Re: If (x+y)/z>0, is x<0? [#permalink]

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13 Jul 2012, 03:49
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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): $$x+y+x<y$$ --> $$2x<0$$ --> $$x<0$$. Sufficient.

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Re: If (x+y)/z>0, is x<0? [#permalink]

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09 Jul 2012, 05:38
Bunuel wrote:
If $$\frac{x+y}{z}>0$$, is x<0?

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

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.

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Re: If (x+y)/z>0, is x<0? [#permalink]

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10 Jul 2012, 14:46
For me is E the solution.

I wait for an explanation by Bunuel to understand if something went wrong in my reasoning
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Re: If (x+y)/z>0, is x<0? [#permalink]

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11 Jul 2012, 10:30
if x+y/z > 0, is x<0?

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

Statement 1: if x<y, then necessarily x-y < 0---(1), substitute, x = +ve then always y will have to be a +ve value exceeding x to satisfy the equ.
substitute x = -ve then either y will be a -ve value OR
y will be a +ve value so that |x| > |y|
substitute x = 0, y will always be a +ve value
Statement 2: if z < 0, then necessarily x+y < 0--(2) substitute x = + ve then y will be -ve so that |x| < |y|
substitute x = -ve then y can be +ve if |x| > |y| OR
y wll be -ve
substitute x = 0, y will always be a -ve value

Individually nothing can be concluded but evaluating (1) and (2) together we can see that when x < 0 only then can the given equ. be satisfied,
Hence C.

I have a question can we go ahead and solve two inequalities like
x - y < 0
x + y < 0
------------
2x < 0
x < 0

I tried to substitute some values in equations but it didn't fit..
like if we have 2x + 4y < 0 and 2x - 4y < 0, then we cannot conclusively say anything about the value of x or y

Please comment and provide an explanation
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Re: If (x+y)/z>0, is x<0? [#permalink]

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11 Jul 2012, 11:28
Its C...

statement 1.. if x+y/z>0 that mean numerator or demonitor both have same sign...

x<y..that means x cud be +ve or negative and no any information abt z..so insufficient..

statement 2: .. z<0 .. no any information abt x and y..

state1 and stat 2: .. if x is less than y that means x will be negative and y will be positive or both will be negative.. so both are sufficient ..

ans c..
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Re: If (x+y)/z>0, is x<0? [#permalink]

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21 Nov 2013, 11:19
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Re: If (x+y)/z>0, is x<0? [#permalink]

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04 Jan 2015, 10:59
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Re: If (x+y)/z>0, is x<0? [#permalink]

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23 Jun 2015, 13:14
Here's an approach with algebra
Numerator and denominator of this expression must have same signs to be positive

(x + y) z
+ +
- -
St1
x<y Not sufficient - no info about z

St2
z<0 , ok, this means x+y<0 Not sufficient (let's say x=2, y=-5 NO or x=-, y=2 YES)

St1+St2
SO we have overall this information: z<0, x+y<0, x<y
In order x+y<0 we have 3 Scenarios: a) x and y both negative b) x +,y - and c)y +, x -
We have here scenario c) x<y --> x is definitely negative
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Re: If (x+y)/z>0, is x<0? [#permalink]

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10 Oct 2015, 04:20
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!
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Re: If (x+y)/z>0, is x<0? [#permalink]

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11 Oct 2015, 05:28
Nuktrue wrote:
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!

A definite NO answer to the question is still considered to be sufficient.
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Re: If (x+y)/z>0, is x<0? [#permalink]

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06 Dec 2015, 13:28
Or another way to look at 1+2:
St2-->when we know x+y<0 both x and y cant be positive. Possible scenarios:
1) Both are negative: -->Yes
2) x<0 & y>0 ;|x|>|y|-->No
3) x>0 & y<0; |x|<|y|--> Yes
Since st1 tells us that x<y scenario3 is not possible

Ans: C
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Re: If (x+y)/z>0, is x<0? [#permalink]

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09 Dec 2015, 07:14
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<y, if both sides are added together,
x+x<y-y=0, 2x<0, x<0 this answers the question 'yes' and the conditions become sufficient, making the answer become (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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How to approach a DS problem? Confused [#permalink]

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11 Oct 2016, 08:33
Question #41 from OG 2017 Diagnostic test questions , pg 26

If x+y/z >0, is x>0?

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

When approaching a DS question like this where I can use values to test cases, what is it that I'm supposed to be doing first?

1) Starting with stmt 1), Am I trying to prove stmt 1 CORRECT and see if it answers the question of if x>0?

After evaluating stmt 1) it is in fact not answering the question (if x=-3, y=5 , then x<y but x NOT>0 OR if x=1, y=2, z=1, x<y & x>0 and x=y/z >0)

So after i've found that x CAN be less than y BUT it doesn't HAVE to be +ve then does that mean it is NOT SUFF? I am so confused.

Am I trying to prove Stmt 1 CORRECT and then finding if it answers the question or not? but stmt 1) can be correct in many different ways which itself will not answer the question of if x is -ve or not

2) z<0 : if z<0, that means z must be -ve. if Z is -ve then it says nothing about whether x is > or < 0. does that also mean that this is also NOT SUFF?

So now I combine the two stmts together:
I understand that stmt 2) is saying that z must be -ve but
stmt 1) can have x=-ve or +ve to make it x<y so this is where i'm stuck. I dont know how to answer stmt 1) and the entire question.

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Re: If (x+y)/z>0, is x<0? [#permalink]

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11 Oct 2016, 09:06
serena32 wrote:
Question #41 from OG 2017 Diagnostic test questions , pg 26

If x+y/z >0, is x>0?

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

When approaching a DS question like this where I can use values to test cases, what is it that I'm supposed to be doing first?

1) Starting with stmt 1), Am I trying to prove stmt 1 CORRECT and see if it answers the question of if x>0?

After evaluating stmt 1) it is in fact not answering the question (if x=-3, y=5 , then x<y but x NOT>0 OR if x=1, y=2, z=1, x<y & x>0 and x=y/z >0)

So after i've found that x CAN be less than y BUT it doesn't HAVE to be +ve then does that mean it is NOT SUFF? I am so confused.

Am I trying to prove Stmt 1 CORRECT and then finding if it answers the question or not? but stmt 1) can be correct in many different ways which itself will not answer the question of if x is -ve or not

2) z<0 : if z<0, that means z must be -ve. if Z is -ve then it says nothing about whether x is > or < 0. does that also mean that this is also NOT SUFF?

So now I combine the two stmts together:
I understand that stmt 2) is saying that z must be -ve but
stmt 1) can have x=-ve or +ve to make it x<y so this is where i'm stuck. I dont know how to answer stmt 1) and the entire question.

Merging topics. Please refer to the discussion above.
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Re: If (x+y)/z>0, is x<0?   [#permalink] 11 Oct 2016, 09:06
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