Does x – y = 0 ? (1) x/y 0 (2) x^2 = y^2

Question

Does x – y = 0 ?

(1) x/y > 0
(2) x^2 = y^2

Kinshook · Answer

Q: is x=y? S1: x/y>0 => (x>0 & y>0) or (x<0 & y<0) => x & y both have same sign (+ve or -ve) x=3 & y=4 => x<>Y x=3 & y=3 => x=y NOT SUFFICIENT S2: x^2 = y^2 |x| = |y| x & y may have different sign (+ve or -ve) NOT SUFFICIENT S1 & S2: S1: x & y both have same sign (+ve or -ve) S2: |x| = |y| => x & y have same magnitude Since x & y have same sign and same magnitude => x & y are same => x =y SUFFICIENT IMO C

RawJoker · Answer

The question is asking whether, X = Y ?

Option 1: x/y > 0

Taking values,
(1) x = 3, y = 2...We get x/y >0. Checking back with main question we get x <> y.
(2) x = 2, y = 2...We still get x/y >0. However, in this case we get x = y.

Hence, Option (1) itself is Not Sufficient.

Option 2: x^2 = y^2

Taking values,
(1) x = -2, y = 2...We get x^2 = y^2. Checking back with main question we get x <> y.
(2) x = 2, y = 2...We still x^2 = y^2. However, in this case we get x = y.

Hence, Option (2) itself is Not Sufficient.

Taking Option (1) and Option (2) together,
x^2 = y^2, will only be possible when the absolute value of x and y are the same, i.e. |x| = |y|

Also, from Option (1), we know x/y > 0, meaning x and y will be of the same sign. If they would be of different signs, then the value would have been negative, which is not the case as per, x/y > 0.

Taking values,
(a) x = 2, y = 2...We get x^2 = y^2 and also x/y > 0. Checking back with main question we get x = y.
(2) x = -2, y = -2...We again get x^2 = y^2 and also x/y > 0. Again, we get x = y.

Therefore, from Option (1) and Option (2) we can clearly say x = y.

Hence, Option (3), both together, is sufficient to solve the question.

subramanya1991 · Answer

I have a question when combining both ethe statements. How did we infer that if x/y > 0 x and y in x^2 and y^ 2 are bothe positive numbers. Anyone help please

Posted from my mobile device

Bunuel · Answer

Does x – y = 0 ?

Notice that the question asks whether x = y.

(1) x/y > 0. This means that x and y have the same sign: either both of them are positive or both of them are negative. Not sufficient.

(2) x^2 = y^2. Take the square root: |x| = |y|. This means that either x = y or x = -y. Not sufficient.

(1)+(2) From (2), x= -y is not possible because this would mean that x and y have different signs (if x is positive, then y is negative and vise-versa), so from (2) we are left with only x = y. Sufficient.

Answer: C.

To elaborate more: after combining we cannot say that x and y are positive, they COULD both be positive but they could both be negative too. The important thing is that we got that x = y.

RawJoker · Answer

subramanya1991 
Post combining, we  did not  infer that both the numbers are +ive.
What we inferred is that the absolute value of both x and y will be same, i.e. |x| = |y|.
And since x/y >0, we inferred that x and y have the same sign.

Putting both these two together, we reach the conclusion that x = y.

For example, when x = 2 and y = 2, both conditions are satisfied. 
The same is the case when x =  - 2 and y =  - 2

Hope it was clear now. Cheers!

Does x – y = 0 ? (1) x/y > 0 (2) x^2 = y^2

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