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

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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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28 Jun 2012, 09:03
00:00

Difficulty:

15% (low)

Question Stats:

76% (02:05) correct 24% (00:50) wrong based on 91 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:
[Reveal] Spoiler:
(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
[Reveal] Spoiler: OA

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

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28 Jun 2012, 09:31
2
KUDOS
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)

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Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
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Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 89

Kudos [?]: 783 [0], given: 109

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

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30 Jun 2012, 18:45
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)

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.
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Kudos [?]: 356 [0], given: 23

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

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30 Jun 2012, 22:52
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: 244
Followers: 4

Kudos [?]: 58 [0], given: 47

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

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18 Jul 2013, 15:10
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.
Re: If S = y^2 + 2xy + x^2, what is the value of xy?   [#permalink] 18 Jul 2013, 15:10
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