Data Sufficiency

Heres a DS quetion

If x and y are integers and x > 0, is y > 0?
(1) 7x – 2y > 0
(2) -y < x


Would appreciate a reply.

OA E

I though it should be A because 7x>2y, x/y>2/7 - so y has to be positive ( since x>0)

1. 7x-2y>0
=> 7x/2>y
or y<7x/2
Since x>0 (given) so y will be in the range from some +ve value to 0 to -ve side of the number line.
In other words y<=0 or y>0 .

Insufficient.

2. -y<x
=> y>-x
As x>0 , y will be greater than some -ve value.
So y can be -ve, zero or positive.

Insufficient.

Combining -x<y<7x/2
In this y is lying in the range from some negative value to some +ve value depending on the value of x.
So again y can have -ve, zero as well as +ve values.

Thus answer should be E.
Do let me know the correct answer.

Thanks.

correct - I see where I went wrong in making x/y>2/7 - i basically assumed that Y is >0 ( since I dint take care of the change in division sign)

Thanks - brilliant explanation