Data Sufficiency

riteshpatnaik wrote: Hi, combining st 1 & 2, how did you arrive at X+Y=0. ST1 X>Y

Here's another way to interpret statement (2):

If x^2 = y^2 (assuming that's what the original poster meant), then the two numbers must have the same absolute value. Squaring hides the sign, so we don't know if they're positive or negative, but they must have the same magnitude if they have equal squares. So, |x| = |y|.

If x > y, then we know that the two values are not equal: they can't both be positive or both be negative. The only possibility is that x is positive and y is negative. Since that's the case, the product xy must be negative, and cannot equal 70. Therefore, statements 1&2 are sufficient together.

The answer is C.

If you're still stuck on kvcpk's explanation, here's a breakdown:

x^2 = y^2
Move the y^2 over to the other side, then factor as a difference of squares:
x^2 - y^2 = 0
(x + y)(x - y) = 0
Set each one equal to 0:
x + y = 0 *or* x - y = 0
x = -y *or* x = y
(This, btw, is the same thing that |x| = |y| tells us).

Since statement (1) tells us that x > y, then x = y cannot be true. Therefore, it must be the case that x = -y, or in other words that x + y = 0.

Again, this brings us to the conclusion that x > 0 and y < 0, so we cannot have a positive product.

Does that help?

Hi riteshpatnaik,

Ceilidh's explanation is spot-on, so I won't rehash any of that. Instead, I'm going to add a few examples to help prove the point:

Once we know that:
1) XY is NOT = to 0
2) X > Y
3) X^2 = Y^2

X and Y COULD be...
1 and -1, so XY = -1 and the answer to the question is NO
2 and -2, so XY = -4 and the answer to the question is NO
3 and -3, so XY = -9 and the answer to the question is NO
4 and -4, so XY = -16 and the answer to the question is NO
Etc.

Based on the pattern, XY will ALWAYS be negative, so the answer to the question is ALWAYS NO. Thus, the final answer is C

GMAT assassins aren't born, they're made,
Rich

sumanr84 wrote:If xy NOT= 0, is xy = 70?

(1) x > y

(2) x2 = y2

Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
Either statement by itself is sufficient to answer the question.
Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

[spoiler]source:kaplan, OA later[/spoiler]

Interesting question:

We are given:

1. Neither x nor y is 0
2. From S1: x > y
3. From S2: x^2 = y^2 => |x| = |y| => x and y both can be positive, both can be negative, or anyone one of them can be negative and the other positive.

Combining S1 and S2:

x and y cannot be both positive or both negative since that would mean x = y, but as per S1, x > y, thus x must be positive and y must be negative.

Thus, xy = |x|*(-|y|) = -|x||y| < any positive number, such as 70. The asnwer is NO. A unique answer.

Hope this helps!

-Jay
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