missrochelle wrote:If x and y are distinct positive integers, what is the value of x^4 - y^4?

1. (y^2 + x^2)(y + x)(x - y) = 240
2. x^y = y^x and x > y

pretty hard question missrochelle....at least for me....

Alright here we go.

Statement 1 is clearly sufficient and we know the answer is 240.

Since we are looking at statement (2), we can still use the answer from (1) > 240 to help us along. so x^4 - y^4 = 240.

Now you are right that we have to pick numbers for (2). But instead of trying out all possibles numbers, lets get (1) to help us along.

what numbers x,y ^ 4 = 240. Solve this one: x^4 - y^4 = 240?

If you plug in numbers into this one, you will get 4^4 - 2^4=240

so 4,2. And thats our numbers that we can plugin into (2) to solve.

(2) x^y = y^x and x > y

clearly 2,4 fit into all of the rules here.

Therefore its sufficient. So what I did was instead of trying out all possibilities for (2), I used (1) to help me along.

For all DS questions, the two statements are ALWAYS consistent! Therefore you can kind of cheat here! You can use 1 to help you along. But you must be VERY careful not to infer anything from (1).

All I used (1) was to come up with numbers to plugin. Nothing else!

I hope this helps!

I would love to hear how others would approach this question!