Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(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

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

Show Tags

28 Jun 2012, 08:31

2

This post received 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

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

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

Show Tags

30 Jun 2012, 17:45

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

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

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

Show Tags

30 Jun 2012, 21:52

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.

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

Show Tags

18 Jul 2013, 14:10

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

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.

gmatclubot

Re: If S = y^2 + 2xy + x^2, what is the value of xy?
[#permalink]
18 Jul 2013, 14:10

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...