inequalities

[sud21]

Is y>0?
1). (x-y)/x > 0
2). (x^2-y^2)/x^2>0

[avik.ch]

tough one !! like to give it a try

1. (x-y)/x > 0 :

- (x-y) > 0 so X>Y and X > 0 -- > X>0 and X>y then Y can be both nagative and positive
- (x-y) < 0 so x<y and X < 0 -- > X<0 and x<y then Y can be both nagative and positive.

Hence insufficient.

2. (x^2-y^2)/x^2 > 0 : x^2 and Y^2 are always poitive, so we can rewrite the equation as
X^2 - Y^2 > 0 : so x^2 > Y^2
X and Y can take both positive and nagative values as we are comparing the absolute values.

hence insufficient

combining both : we still cannot infer Whether Y is positive or nagative.

IMO: E

[ArunangsuSahu]

Statement 1:
x not known: INSUFFICIENT

Statement 2:
again , x not known: INSUFFICIENT

Combining also INSUFFICIENT

[[email protected]]

Statement 1: [(x-y) > 0 and y > 0] OR [(x-y) < 0 and y < 0]


Statement 2: [x^2 - y^2]/x^2 > 0

here x^2 will always be greater than 0 as it is square of number.

Hence the numerator [x^2 - y^2] is also positive.

Next, solve the numerator as: (x-y) (x+y) > 0

Even in case of the numerator there are two possibilities:

Either both (x+y) and (x-y) are negative or both are positive to make the overall

value greater than 0. Hence insufficient.



Combining both: still insufficient as write the equations again and see. it is not sufficient to decide.


Hence E

Hope this helps!!!

[Brent@GMATPrepNow]

Is y>0?
1). (x-y)/x > 0
2). (x^2-y^2)/x^2>0

If we suspect that a certain statement might be insufficient, we can try the table method (covered in free video #7 at https://www.gmatprepnow.com/module/gmat-data-sufficiency)

Statement 1:
There are many possible values for x and y that satisfy the condition that (x-y)/x > 0.
case a: x=2, y=1 --> y is greater than 0
case b: x=-2, y=-1 --> y is not greater than 0
INSUFFICIENT

Statement 2:
There are many possible values for x and y that satisfy the condition that (x^2-y^2)/x^2>0.
case a: x=2, y=1 --> y is greater than 0
case b: x=-2, y=-1 --> y is not greater than 0
INSUFFICIENT

Statement 1&2:
Notice that I used the same pairs of values for statements 1 and 2. As such, I know that the two statements combined must be INSUFFICIENT, which means the answer is E

Cheers,
Brent