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# If x < 0, is y > 0 ?

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Manager
Joined: 02 Dec 2012
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If x < 0, is y > 0 ?  [#permalink]

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26 Dec 2012, 04:50
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5% (low)

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79% (01:01) correct 21% (01:10) wrong based on 1002 sessions

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If x < 0, is y > 0 ?

(1) x/y < 0
(2) y - x > 0
Math Expert
Joined: 02 Sep 2009
Posts: 55801
Re: If x < 0, is y > 0 ?  [#permalink]

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26 Dec 2012, 04:53
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If x < 0, is y > 0 ?

(1) x/y < 0. This implies that x and y have opposite signs and since given that x is negative then y must be positive. Sufficient.

(2) y - x > 0. This implies that y > x. So, y is greater than some negative number. Not sufficient to say whether y is positive. Not sufficient.

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Senior Manager
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Re: If x < 0, is y > 0 ?  [#permalink]

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25 Oct 2015, 08:01
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keeping in mind - which 2 set of numbers can we try on?
1 is 5-(-3)>0 = 8>0
2 is ?
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Re: If x < 0, is y > 0 ?  [#permalink]

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25 Oct 2015, 08:13
paidlukkha wrote:
bumpbot wrote:
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keeping in mind - which 2 set of numbers can we try on?
1 is 5-(-3)>0 = 8>0
2 is ?

For statement 2, you can try :

Case 1: x=-5 and y=-3

Case 2, x=-5 and y=10

The above 2 cases will give you 2 different answers to make statement 2 not sufficient.
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Re: If x < 0, is y > 0 ?  [#permalink]

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30 May 2017, 22:36
Statement 1. If x is negative and x/y is positive, then y MUST be positive. Sufficient.

Statement 2. y-x > 0 means that y>x. y is greater than a negative number, but then it could be negative as well as positive. Insufficient.

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Re: If x < 0, is y > 0 ?  [#permalink]

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12 Sep 2017, 00:00
Hi Bunnel,

My doubt is in statement 2.

y-x > 0 implies y>x, so we cant tell from this if y is positive or negative..agreed.

But when u consider the complete statement y-x > 0 for this to be true y has to be positive right and the statement is sufficient.
whats wrong with this? Please explain..

Shinrai
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Joined: 02 Sep 2009
Posts: 55801
Re: If x < 0, is y > 0 ?  [#permalink]

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12 Sep 2017, 00:03
1
shinrai15 wrote:
Hi Bunnel,

My doubt is in statement 2.

y-x > 0 implies y>x, so we cant tell from this if y is positive or negative..agreed.

But when u consider the complete statement y-x > 0 for this to be true y has to be positive right and the statement is sufficient.
whats wrong with this? Please explain..

Shinrai

Why y has to be positive? For example, y = -1 and x = -2, y - x = -1 - (-2) = -1 + 2 = 1 > 0.
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Re: If x < 0, is y > 0 ?  [#permalink]

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12 Sep 2017, 00:58
If x < 0, is y > 0 ?

(1) x/y < 0
(2) y - x > 0

1) x/y <0 => x<0 and y>0 or x>0 y<0 which is not possible as x<0
so definite yes y>0
A/D

2) y-x>0
y>x
x=-1
y=-0.5

x=-2
y=2

Insufficient

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Re: If x < 0, is y > 0 ?  [#permalink]

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15 Oct 2017, 12:40
I am confused with statement 1)

x/y < 0
Y
x < y Now we know that x is negative and y is greater than x but IMO it does not mean y has to be positive - I mean y can be negative and still greater than x.

Can someone explain where am I going wrong?
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If x < 0, is y > 0 ?  [#permalink]

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15 Oct 2017, 21:14
santro789 wrote:
I am confused with statement 1)

x/y < 0
Y
x < y Now we know that x is negative and y is greater than x but IMO it does not mean y has to be positive - I mean y can be negative and still greater than x.

Can someone explain where am I going wrong?

We cannot multiply x/y < 1 by y and write x < y because we don't know the sign of y. If y is positive, then yes, from x/y < 1, we can get x < y (keep the sign when multiplying by positive value) but if y is negative, then when we multiply by negative value, we should flip the sign and we'll get x > y (recall that we should flip the sign of an inequality if we multiply/divide it by negative value)..

Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its sign.
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Re: If x < 0, is y > 0 ?  [#permalink]

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16 Oct 2017, 02:18
Thanks Bunuel for the explanation.
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Re: If x < 0, is y > 0 ?  [#permalink]

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16 Oct 2017, 02:26
santro789 wrote:
I am confused with statement 1)

x/y < 0
Y
x < y Now we know that x is negative and y is greater than x but IMO it does not mean y has to be positive - I mean y can be negative and still greater than x.

Can someone explain where am I going wrong?

I just noticed that in the post above, I considered x/y < 1, not x/y < 0.

Regarding x/y < 0. This means that x and y have opposite signs and since given that x is negative then y must be positive. Next, you cannot multiply this by y to get x < 0 for the same reason as explained in the post above.
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Re: If x < 0, is y > 0 ?  [#permalink]

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26 Dec 2018, 10:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If x < 0, is y > 0 ?   [#permalink] 26 Dec 2018, 10:00
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