Does x = y? (1) |x| = |y| (2) x^2 = y^2

St (1) For x = 2 and y = -2 also , | x | = | y | Hence it is not sufficient.

St (2) Similar to St (1) , St (2) holds true for x = 2 and y = -2 as well as x = 2 and y = 2... Hence not sufficient.

St (1) + St (2) combined gives no additional information.

Hence Option (E) is our choice.

Best,
Gladi
_________________

For those of you who get confused with the theoretical way of solving this question, plugging in simple values is the best way to solve this question.
Let’s take two cases:
Case 1: x = 2 and y = 2. IS x = y? YES
Case 2: x = 2 and y = -2, IS x = y? NO.

From statement I alone, |x| = |y|.

Do the values in case 1 satisfy the equation above? Yes, they do.
Do the values in case 2 satisfy the equation above? Yes, they do.

This means that using statement I alone, we obtain a YES and a NO. Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone,\( x^2\) = \(y^2\).

Do the values in case 1 satisfy the equation above? Yes, they do.
Do the values in case 2 satisfy the equation above? Yes, they do.

This means that using statement II alone, we obtain a YES and a NO. Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Even when we combine the two statements, both cases 1 and 2 will satisfy both equations but won’t give us a YES or a NO.

The combination of statements is insufficient. Answer option C can be eliminated.
The correct answer option is E.

Hope that helps!
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________