February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 May 2012
Posts: 18

If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
Updated on: 04 Jul 2018, 00:01
Question Stats:
72% (01:37) correct 28% (01:55) wrong based on 762 sessions
HideShow timer Statistics
If 0 < x < y, what is the value of \(\frac{(x + y)^2}{(x y)^2}\)? (1) \(x^2 + y^2 = 3xy\) (2) \(xy = 3\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Val1986 on 23 Mar 2013, 20:49.
Last edited by Bunuel on 04 Jul 2018, 00:01, edited 3 times in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
24 Mar 2013, 01:40




Intern
Joined: 10 Mar 2013
Posts: 1
GMAT Date: 03252013

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
23 Mar 2013, 23:29
1) x^2+y^2=3xy => x^2+y^22xy=xy => (xy)^2=xy
So you can replace : (x+y)^2/xy
And then just finish the work : (x+y)^2/xy => (x^2+y^2+2xy)/xy => (3xy+2xy)/xy => 5
1 is enough
2) not enough. (x+y)^2/(xy)^2 => (x^2+y^2+2xy)/(x^2+y^22xy) => (x^2+y^2+6)/(x^2+y^26) => you can't know the value of x^2 or y^2
Hope it helps.




Intern
Joined: 17 May 2014
Posts: 2

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
02 Jun 2014, 23:15
In Second statement: xy=3 and 0<x<y. Is it possible to take x=1 & y=3 and make the second statement sufficient.



Intern
Joined: 17 May 2014
Posts: 2

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
02 Jun 2014, 23:34
kapil20 wrote: In Second statement: xy=3 and 0<x<y. Is it possible to take x=1 & y=3 and make the second statement sufficient. Got it,we also have to take fraction nos.x=0.5 y=6



Current Student
Joined: 23 Feb 2015
Posts: 166

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
26 Nov 2015, 11:35
Can someone explain how to tackle (2)?
I started testing numbers with x=1 and y=3, result is 16. Then I went to x=\(\frac{1}{2}\) and y=6, but I quickly got bogged down in math and I was unable to prove that it is insufficient.
What is the shortcut I am missing to see that xy=3 is insufficient?
Thanks!



CEO
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
26 Nov 2015, 11:54
Dondarrion wrote: Can someone explain how to tackle (2)?
I started testing numbers with x=1 and y=3, result is 16. Then I went to x=\(\frac{1}{2}\) and y=6, but I quickly got bogged down in math and I was unable to prove that it is insufficient.
What is the shortcut I am missing to see that xy=3 is insufficient?
Thanks! You can clearly see that you ar egiven that x<y and that both x,y are >0. Statement 2 tells you that 2 positive number s(integers or not) give you a product of 3. Clearly, you can have different combinations that give you xy=3 but will definitely give you different values of x+y and let alone for (x+)^2/(xy)^2. This makes this statement not sufficient. With x=1 and y=3, the value should be 4 and not 16 (besides the point). As for x=.5 and y =6, you get (x+y)^2 = 6.5^2 and (xy)^2 = 5.5^2 > 6.5^2/5.5^2 = (13/11)^2 = a value close to 1. Thus you get 2 different values for the expression under consideration, making this statement not sufficient. Hope this helps.



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 674
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
05 Apr 2016, 21:28
Attached is a visual that should help.
Attachments
Screen Shot 20160405 at 10.27.13 PM.png [ 151.45 KiB  Viewed 17742 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.)
...or find me on Reddit: http://www.reddit.com/r/GMATpreparation



Manager
Joined: 18 Feb 2015
Posts: 84

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
25 Nov 2016, 15:07
Hi, Im not getting why st2 is not correct. This is how I am solving this. (x+y)^2 x^2+2xy+y^2  =>  => x^2+2xy+y^2 x^2+2xyy^2 => 4xy (xâˆ’y)^2 x^2âˆ’2xy+y^2 So as per the above method, Only st2 is sufficient. What am I doing wrong? Thanks for your help! H. Bunuel wrote: If 0 < x < y, what is the value of (x + y)^2/( x y)^2?
\(\frac{(x + y)^2}{( x y)^2}=\frac{x^2+2xy+y^2}{x^22xy+y^2}\)
(1) x^2 + y^2 = 3xy. Substitute: what is the value of \(\frac{x^2+2xy+y^2}{x^22xy+y^2}=\frac{3xy+2xy}{3xy2xy}=\frac{5xy}{xy}=5\). Sufficient.
(2) xy = 3. Not sufficient.
Answer: A.



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
25 Nov 2016, 22:24



Manager
Joined: 03 Jan 2017
Posts: 147

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
28 Mar 2017, 13:07
let's rewrite the given value: (x^2+2xy+y^2)/(x^22xy+y^2)
1) we see that x^2+y^2=3xy, so if we plug that in, it is 5xy/xy=5 Sufficient 2) alone insufficient
Answer is A



NonHuman User
Joined: 09 Sep 2013
Posts: 9851

Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
Show Tags
12 Apr 2018, 15:22
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If 0 < x < y, what is the value of (x + y)^2/(x y)^2?
[#permalink]
12 Apr 2018, 15:22






