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Value of X^2 - Y^2?

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by GMATGuruNY » Tue Jun 03, 2014 2:34 pm
bml1105 wrote:What is the value of (x^2 - y^2)?

(1) x + y = 2x
(2) x - y = 0
x² - y² = (x+y)(x-y).
Question stem, rephrased:
What is the value of (x+y)(x-y)?

Statement 1: x+y = 2x
Subtracting x from both sides, we get:
y = x
0 = x-y.
Thus, (x+y)(x-y) = (x+y)(0) = 0.
SUFFICIENT.

Statement 2: x-y = 0
Thus, (x+y)(x-y) = (x+y)(0) = 0.
SUFFICIENT.

The correct answer is D.
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by bml1105 » Tue Jun 03, 2014 7:46 pm
Ughhh so simple and I just blanked. Thanks!
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by carrillo1228 » Mon Aug 11, 2014 7:08 pm
Question on this one...

Since x^2 - y^2 factors into (x+y)(x-y)....

How do you know not to rewrite it as 2x(x-y) where the statement would depend on x and y?
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by [email protected] » Mon Aug 11, 2014 7:18 pm
Hi carrillo1228,

You might not instinctively "know" not to do what you're describing. I can offer some general advice though, when it comes to these types of decisions:

1) When you rewrite a question, your goal should be to make the question "easier" to deal with. It doesn't appear that 2x(x-y) is noticeably easier than (x+y)(x-y). This is a sign that you might be going down the wrong path.

2) When you're given an equation to work with, as you are in Fact 1, it's almost always best to simplify the given equation BEFORE you do anything else with it.

3) Among its other design "elements", DS questions test your thoroughness. You might have to do more work than you initially realize to solve the problem. Thus, your ability to do math in more than one way, or work strategically (TESTing Values, for example), might be required.

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