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DS with exponents

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DS with exponents

by missrochelle » Sat Aug 28, 2010 8:10 am
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

d

I got stuck on stmt 2 when trying to pick numbers. Are there any key "properties of squares" to remember ? Clearly here, knowing that 4 and 2 are the only numbers that worked would save a lot of time. Any other fun "rules" like anyone would like to share would be appreciated.--
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by Gurpinder » Sat Aug 28, 2010 8:36 am
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!
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
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