December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 29 Sep 2011
Posts: 16

1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
19 Jan 2012, 12:21
Question Stats:
79% (01:35) correct 21% (02:27) wrong based on 200 sessions
HideShow timer Statistics
Hi guys, I am struggling with this one, can anyone help pls? 1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2? 1. 12 2. 16 3. 18 4. 20 5. 24 Thanks!
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: Algebra
[#permalink]
Show Tags
19 Jan 2012, 12:29



Intern
Joined: 29 Sep 2011
Posts: 16

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
19 Jan 2012, 12:34
Got it! I forgot that a^2 + b^2 = (a+b)^2  2ab!
Thank you



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Jul 2014, 20:33
\(\frac{1}{x} + \frac{1}{y} = 1\) x+y = xy Squaring both sides \(x^2 + 2(xy) + y^2 = (xy)^2\) \(x^2 + y^2 = (xy)^2  2(xy)\) Placing value of xy = 6 \(x^2 + y^2 = 36  12 = 24\) Answer = 24
_________________
Kindly press "+1 Kudos" to appreciate



Senior Manager
Joined: 28 Jun 2015
Posts: 292
Concentration: Finance
GPA: 3.5

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
21 Jul 2015, 23:05
1/x + 1/y = 1; xy = 6. 1/x + 1/y = 1 x+y/xy = 1 x+y/6 = 1 (since xy = 6) so, x+y = 6. x^2+y^2 = (x+y)^2  2xy = (6)^2  2(6) = 36  12 = 24. Ans (E).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.



Senior Manager
Joined: 08 Dec 2015
Posts: 293

1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
Updated on: 14 Mar 2016, 03:06
Hi everyone!
How come that x^2 + y^2 equals (x+y)^2  2xy ?
Is it like an algebraic identity formula? I haven't seen this one anywhere.
Thanks!
Originally posted by iliavko on 14 Mar 2016, 03:02.
Last edited by iliavko on 14 Mar 2016, 03:06, edited 1 time in total.



CEO
Joined: 20 Mar 2014
Posts: 2631
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Mar 2016, 03:06
iliavko wrote: Hi everyone!
How come that x^2 + y^2 equals (x+y)^2  2xy ?
Is it like a difference of squares formula? I haven't seen this one anywhere.
Thanks! It comes from rearranging terms in the formula: \((a+b)^2 = a^2+2ab+b^2\) > \(a^2+b^2 = (a+b)^22ab\) Hope this helps.



Senior Manager
Joined: 08 Dec 2015
Posts: 293

1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Mar 2016, 03:07
Nice!!.. The stuff you discover at this forum Thanks you so much! One more question, maybe it's silly, but.. What about difference of squares? a^2  b^2 = (a+b)(ab) what is the rationale behind it? Any formula that manipulated leads to it? Thank you!



Manager
Joined: 09 Jun 2015
Posts: 93

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Mar 2016, 03:22
Splendidgirl666 wrote: Hi guys,
I am struggling with this one, can anyone help pls?
1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2?
1. 12 2. 16 3. 18 4. 20 5. 24
Thanks! x*y=6 x+y=6 (x+y)^2=x^2+y^2+2*x*y 36=()+12 Therefore, the answer is 24



Current Student
Joined: 12 Aug 2015
Posts: 2627

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Mar 2016, 23:49
Splendidgirl666 wrote: Hi guys,
I am struggling with this one, can anyone help pls?
1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2?
1. 12 2. 16 3. 18 4. 20 5. 24
Thanks! See here => 1/x+1/y=1 so taking the lcm we get => x+y=xy so (x+y)^2 =36 x^2+y^2=362xy=3612 = 24 hence E
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Intern
Joined: 14 Feb 2016
Posts: 46

1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
25 Apr 2018, 02:45
This is a cheeky little exercise. The concepts that are tested: manipulating algebraic fractions, and square of a sum.
These are the steps I recommend to take, with the tested concepts mentioned in each step. 1/x + 1/y = 1. (we remember that with fractions with a different denominator, we first have to find the least common denominator) y+x / xy =1 y+x = xy y+x = 6 y^2+x^2 = 6^2 y^2+x^2 = 36. (y+x)^2 = 36. (remember that (y+x)^2 → x^2+2xy+y^2 Now we can set up the equation with what we already have:So x^2 + 2xy + y^2 = 36. (Hence we also know that xy = 6. Let’s plug it in. So x^2 + 2(6) + y^2 = 36 → x^2+12+y^2 = 36 → x^2 + y^2 = 3612 = 24. Answer choice E.
_________________
Went from a score from 230 to 600. Still climbing! Onto the top 1%.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4328
Location: United States (CA)

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
26 Apr 2018, 14:38
Quote: 1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2?
1. 12 2. 16 3. 18 4. 20 5. 24
We can multiply the first equation by xy and we have: y + x = xy Since xy = 6 we have: y + x = 6 Squaring both sides we have: x^2 + y^2+ 2xy = 36 x^2 + y^2 + 12 = 36 x^2 + y^2 = 24 Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? &nbs
[#permalink]
26 Apr 2018, 14:38






