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, 13:21
Question Stats:
78% (01:11) correct 22% (02:58) wrong based on 196 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: 49303

Re: Algebra
[#permalink]
Show Tags
19 Jan 2012, 13:29



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, 13:34
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: 1834
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, 21:33
\(\frac{1}{x} + \frac{1}{y} = 1\) 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: 294
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
22 Jul 2015, 00:05
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: 300

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, 04:06
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, 04:02.
Last edited by iliavko on 14 Mar 2016, 04:06, edited 1 time in total.



Current Student
Joined: 20 Mar 2014
Posts: 2638
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, 04:06
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: 300

1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Mar 2016, 04:07
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: 97

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
14 Mar 2016, 04:22
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: 2648

Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
15 Mar 2016, 00:49
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: 36

1/x+1/y=1 xy=6, then what is the value of x^2+y^2?
[#permalink]
Show Tags
25 Apr 2018, 03:45
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.
_________________
Need to get your GMAT score for a 600 minimum to get admitted into RSM or another top uni in the Netherlands? Feel free to PM me for affordable oneonone tutoring or group classes.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3515
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, 15:38
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, 15:38






