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Senior Manager  Joined: 12 Aug 2015
Posts: 284
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3
WE: Management Consulting (Consulting)
If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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11 00:00

Difficulty:   55% (hard)

Question Stats: 53% (01:30) correct 47% (01:23) wrong based on 180 sessions

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If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

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Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9246
Location: Pune, India
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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8
2
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)
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CEO  S
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If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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5
3
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

Typical inequalities question where a step by step method is a must in order to reach the correct answer.

You are given xy<zy ---> y(x-z)<0 , 2 cases possible here

1. y<0 and x>z
2. y>0 and x<z

The question is asking us whether y >0

Per statement 1, x<z ---> case 2 comes into the picture, providing a definite answer to the question asked. Sufficient.

Per statement 2, x< 0 ---> use the given information that xy<0 --> y must be >0 for xy<0 with x<0. Thus sufficient as well.

Both statements are sufficient ----> D is the correct answer.

Hope this helps.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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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 xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

When you modify the original condition and the question, it becomes (x-z)y<0에서 y>0? --> x-z<0?. x<Z에서 1) is yes, which is sufficient.
For 2), if x<0, y>0 derived from xy<0, which is yes and sufficient. Therefore, the answer is D.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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Can you just divide the original equation by Y?
XY < ZY < 0 --> X< Z < 0?

If not, why not?
CEO  S
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If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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1
glochou wrote:
Can you just divide the original equation by Y?
XY < ZY < 0 --> X< Z < 0?

If not, why not?

Dividing an inequality by a variable whose sign is UNKNOWN is the biggest mistake you can make in inequality questions.

The sign of the inequality changes if you divide or multiply by a negative number. This is the reason why you CAN NOT divide by y.

If xy<zy ---> y*(x-z)<0 --> this means that either

Case 1: y>0 and x-z<0 OR
Case 2: y<0 and x-z>0

When you divide by y WITHOUT reversing the signs, you are inherently assuming that y>0. This is the very question asked.
Intern  G
Joined: 18 Nov 2013
Posts: 41
If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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KarishmaB wrote:
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0;
I agree for option 1 is sufficient on the basis that x<z;
for the second option, since x is -ve
x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve
x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??
Director  P
Joined: 14 Dec 2017
Posts: 522
Location: India
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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harish1986 wrote:
KarishmaB wrote:
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0;
I agree for option 1 is sufficient on the basis that x<z;
for the second option, since x is -ve
x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve
x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??

From Statement 2, we don't get any information for z & we are not bothered about z, all we need to figure out is whether y > 0

We know from question prompt that xy < 0, hence if x < 0, then y > 0

I hope that helps

Thanks,
GyM
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Director  P
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Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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harish1986 wrote:
KarishmaB wrote:
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0;
I agree for option 1 is sufficient on the basis that x<z;
for the second option, since x is -ve
x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve
x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??

The #'s plugged in are not correct x < z, hence x=-5 and z=-10 is not valid
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Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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xy<zy<0
1: x<z, then -x>-z, if we subtract it from above inequality we will get y>0
2: because xy<0 and x<0, therefore y>0
CEO  V
Joined: 12 Sep 2015
Posts: 3729
Location: Canada
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

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1
Top Contributor
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

Target question: Is y positive?

Given: xy < zy < 0,
Let's focus on this part of the inequality: xy < zy
Subtract xy from both sides to get: 0 < zy - xy
Factor out the y to get: 0 < y(z - x) (this will come in handy later)

Statement 1: x < z
Subtract x from both sides to get: 0 < z - x
In other words, (z - x) is POSITIVE
This means we can take our given inequality 0 < y(z - x) and divide both sides by (z - x) to get: 0 < y
So, the answer to the target question is YES, y IS positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is negative
The given information tells us that xy < zy < 0
This means xy < 0
In other words, xy is NEGATIVE
So, if x is negative, then it MUST be the case that y is POSITIVE
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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_________________ Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative   [#permalink] 20 Feb 2019, 09:47
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