selango wrote:If both x and y are nonzero integers what is the value of x/y?

1) x=6

2) x^2=y^2

I'll go with E.

y can be either + or -

Answer is B.

We know neither x nor y is zero right off the bat, and therefore x/y cannot be 0.

1) x=6 is insufficient, because it gives us no information about y. Therefore, we cannot solve for 6/y.
2) x^2 = y^2. Let's play with numbers here. Let's say x is 2 and 2^2 = 4. Then what could y be in order to square with an answer of 4? The only number possible is -2. Remember, a negative number to an even exponent produces a positive answer, while a negative number to an odd exponent produces a negative answer. If you test it with any other positive and negative combo, you get the same result. 3^2 = -3^2, 4^2 = -4^2 and so on.

And no matter what those two numbers are, they will always produce the same answer. A number divided by itself always equals 1, and in this case, a -1.

2/-2 = -1
-3/3 = -1

etc.

Hope that helps!

aleph777 wrote:Answer is B.

We know neither x nor y is zero right off the bat, and therefore x/y cannot be 0.

1) x=6 is insufficient, because it gives us no information about y. Therefore, we cannot solve for 6/y.
2) x^2 = y^2. Let's play with numbers here. Let's say x is 2 and 2^2 = 4. Then what could y be in order to square with an answer of 4? The only number possible is -2. Remember, a negative number to an even exponent produces a positive answer, while a negative number to an odd exponent produces a negative answer. If you test it with any other positive and negative combo, you get the same result. 3^2 = -3^2, 4^2 = -4^2 and so on.

And no matter what those two numbers are, they will always produce the same answer. A number divided by itself always equals 1, and in this case, a -1.

2/-2 = -1
-3/3 = -1

etc.

Hope that helps!

aleph777,

Let's say x is 2 and 2^2 = 4. Then what could y be in order to square with an answer of 4? The only number possible is -2.

y can also be 2 for answer 4.

Why did u pick only negative number?Square of both positive and negative number is positive,.

Aleph, let me know if I'm understanding your logic correctly, but if I am I think it's a point worth making publicly because I've seen this come up quite a bit.

I hear you saying that:

If x were 2, then y^2, in order to equal x^2 = 4, would have to also be 4. And then, by that logic, y would have to be -2 because, and here's where I think you may be going wrong, it cannot be (+) 2, because that value is already assigned to x. Am I right?

Please note that x and y, unless stated otherwise, could be the same. If x is 2, y could also be 2, because there is no statement prohibiting that. But this mistake is pretty common, as people seek order, and like the idea of each variable having its own number.

Unless the GMAT specifically states so, any variable can have any value, and therefore all variables could equal the same value.

For that not to be true, the test would have to stipulate that "x and y are unique integers" or "x does not = y". In this case, x and y must have the same absolute value, but they could go any form of:

-/+
-/-
+/+
+/-

Even when statement 2 is in the mix, we know that x must be positive, but those last two options are still in play, and so we still don't have enough information.

selango wrote:If both x and y are nonzero integers what is the value of x/y?

1) x=6

2) x^2=y^2

individual stmt r not enough
when combined y can have +&- value
hence insuff

E