GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Feb 2019, 13:06

### GMAT Club Daily Prep

#### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

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 7-day 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.

# If 0 < x < y, what is the value of (x + y)^2/(x- y)^2?

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
4
37
00:00

Difficulty:

35% (medium)

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) $$xy = 3$$

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
12
5
If 0 < x < y, what is the value of (x + y)^2/( x- y)^2?

$$\frac{(x + y)^2}{( x- y)^2}=\frac{x^2+2xy+y^2}{x^2-2xy+y^2}$$

(1) x^2 + y^2 = 3xy. Substitute: what is the value of $$\frac{x^2+2xy+y^2}{x^2-2xy+y^2}=\frac{3xy+2xy}{3xy-2xy}=\frac{5xy}{xy}=5$$. Sufficient.

(2) xy = 3. Not sufficient.

_________________
Intern
Joined: 10 Mar 2013
Posts: 1
GMAT Date: 03-25-2013
Re: If 0 < x < y, what is the value of (x + y)^2/(x- y)^2?  [#permalink]

### Show Tags

23 Mar 2013, 23:29
5
1)
x^2+y^2=3xy => x^2+y^2-2xy=xy => (x-y)^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/(x-y)^2 => (x^2+y^2+2xy)/(x^2+y^2-2xy) => (x^2+y^2+6)/(x^2+y^2-6) => you can't know the value of x^2 or y^2

Hope it helps.
##### General Discussion
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
1
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
Schools: Duke '19 (M)
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
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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/(x-y)^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 (x-y)^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
GRE 1: Q168 V169
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
1
Attached is a visual that should help.
Attachments

Screen Shot 2016-04-05 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 test-taker 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 E-Book - 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+2xy-y^2 => 4xy
(x−y)^2 x^2−2xy+y^2

So as per the above method, Only st2 is sufficient. What am I doing wrong?

H.

Bunuel wrote:
If 0 < x < y, what is the value of (x + y)^2/( x- y)^2?

$$\frac{(x + y)^2}{( x- y)^2}=\frac{x^2+2xy+y^2}{x^2-2xy+y^2}$$

(1) x^2 + y^2 = 3xy. Substitute: what is the value of $$\frac{x^2+2xy+y^2}{x^2-2xy+y^2}=\frac{3xy+2xy}{3xy-2xy}=\frac{5xy}{xy}=5$$. Sufficient.

(2) xy = 3. Not sufficient.

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
HarveyKlaus wrote:
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+2xy-y^2 => 4xy
(x−y)^2 x^2−2xy+y^2

So as per the above method, Only st2 is sufficient. What am I doing wrong?

H.

Bunuel wrote:
If 0 < x < y, what is the value of (x + y)^2/( x- y)^2?

$$\frac{(x + y)^2}{( x- y)^2}=\frac{x^2+2xy+y^2}{x^2-2xy+y^2}$$

(1) x^2 + y^2 = 3xy. Substitute: what is the value of $$\frac{x^2+2xy+y^2}{x^2-2xy+y^2}=\frac{3xy+2xy}{3xy-2xy}=\frac{5xy}{xy}=5$$. Sufficient.

(2) xy = 3. Not sufficient.

Next, how is the read part above correct? Does 3/2 equals to 3-2=1???
_________________
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^2-2xy+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

Non-Human 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.
_________________
Re: If 0 < x < y, what is the value of (x + y)^2/(x- y)^2?   [#permalink] 12 Apr 2018, 15:22
Display posts from previous: Sort by