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
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inequalities
Source: Beat The GMAT — Data Sufficiency |
Statement 1:
x not known: INSUFFICIENT
Statement 2:
again , x not known: INSUFFICIENT
Combining also INSUFFICIENT
x not known: INSUFFICIENT
Statement 2:
again , x not known: INSUFFICIENT
Combining also INSUFFICIENT
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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!!!
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!!!
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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)sud21 wrote:Is y>0?
1). (x-y)/x > 0
2). (x^2-y^2)/x^2>0
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
Brent Hanneson - Creator of GMATPrepNow.com
