metallicafan wrote:

If \(S = y^2 + 2xy + x^2\), what is the value of \(xy\)?

(1) \(x + y = 1\)

(2) \(S = 1\)

My approach:

(1) \(x + y = 1\)

Scenario A: \(x= 0.6\) and \(y= 0.4\), \(xy=0.24\)

Scenario B: \(x= 0.8\) and \(y= 0.2\), \(xy=0.16\)

INSUFFICIENT

(2) \(S = 1\)

\(1 = y^2 + 2xy + x^2\)

\(1 = (x+y)^2\)

Unsquaring:

\(1 = \sqrt{(x+y)^2}\)

Then:

\(1 = |x+y|\)

So:

\(x+ y = 1\) OR \(x+y = -1\)

It happens the same as in scenarios A and B.

INSUFFICIENT.

(1) and (2) INSUFFICIENT

However, is there a faster way to solve it? This approach is exahusting Source:

http://www.gmathacks.comSolved this in 1 minute and 20 seconds.

Here's my approach:

We know that S = y^2 + 2xy + x^2

The question is asking us, "what is xy?"

The rephrase of the question is S = (x+y)(x+y)

Statement (1) tells us that x + y = 1

So this means that S = (1)(1) = 1

But we don't have the value of xy, so insufficient

Statement (2) tells us that s = 1

So this means that 1 = (x+y)(x+y)

Essentially this is the same data given to us in Statement (1). Check it.

Now, the cardinal rule of the GMAT is that if the two statements are insufficient and are presenting the same thing, it's automatic (E)

How about some kooooodoooowz?

_________________

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