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Retired Moderator Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
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If S = y^2 + 2xy + x^2, what is the value of xy?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:23) correct 25% (01:22) wrong based on 132 sessions

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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.com

_________________
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Re: If S = y^2 + 2xy + x^2, what is the value of xy?  [#permalink]

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2
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.com

Solved 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? _________________
Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt
Retired Moderator Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1001
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: If S = y^2 + 2xy + x^2, what is the value of xy?  [#permalink]

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gmatsaga wrote:
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.com

Solved 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? Actually, I am not so convinced about your approach.
I think you inmediately assume that you cannot know the value of xy without knowing the possible values of x and y. It is after analyzing them that you can know that there could be diverse combinations of x and y.
That's why asked whether there is a faster approach.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

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GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: If S = y^2 + 2xy + x^2, what is the value of xy?  [#permalink]

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1
Hi,

At the first look at this question, I would say option (1) & (2) state the same thing.
Since, $$S = (x+y)^2$$
so, from either of the statement we will have; $$S = (x+y)^2=1$$
and x & y can have many value satisfying the given condition.

Thus, we can't find xy.

Regards,
Manager  Joined: 12 Jan 2013
Posts: 142
Re: If S = y^2 + 2xy + x^2, what is the value of xy?  [#permalink]

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1
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.com

Regarding your approach to statment 2:

This q can be solved much quicker if you immediately aknowledge that "two unknowns and one known cannot solve for both unknowns". In order to know xy, you must either know that x and/or y is 0, or you must know the value of both if neither is 0.

Since s(2) tells us S = 1, either x or y COULD be 0, and then the other has to be 1, and thus you've solved for xy. But you dont know this for sure because there could be other combinations of x and y on the right side that could lead to 1. The point is that two unknowns and one known is not enough, EVEN when either COULD be zero (because they dont HAVE TO be zero for S = 1). Thus, we have 2 unknowns (x and y), and one known (S = 1), and this is INSUFFICENT.

This approach saves you at least 20 seconds. However, you have to be careful in that C might be correct answer, but given my above asssesment and given the info in s(1), C cannot be OA; s(1) also gives you two unknowns and one known.
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Re: If S = y^2 + 2xy + x^2, what is the value of xy?  [#permalink]

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_________________ Re: If S = y^2 + 2xy + x^2, what is the value of xy?   [#permalink] 03 Mar 2018, 11:34
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