If x 0 ? (1) x/y 0

Question

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

Bunuel · Accepted Answer

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.

Answer: A.

paidlukkha · Answer

keeping in mind - which 2 set of numbers can we try on?
1 is 5-(-3)>0 = 8>0
2 is ?

ENGRTOMBA2018 · Answer

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.

amanvermagmat · Answer

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 .

Hence  A answer

shinrai15 · Answer

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..

Thanks in advance!
Shinrai

Bunuel · Answer

Why y has to be positive? For example, y = -1 and x = -2, y - x = -1 - (-2) = -1 + 2 = 1 > 0.

sahilvijay · Answer

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 A is the answer.

santro789 · Answer

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?

Bunuel · Answer

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.

santro789 · Answer

Thanks Bunuel for the explanation.

Bunuel · Answer

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

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