GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 01:36

### 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

# If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61252
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

13 May 2016, 03:54
2
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:55) correct 25% (01:09) wrong based on 184 sessions

### HideShow timer Statistics

If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =

A. 0
B. 5
C. 10
D. 15
E. 20

_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

26 Aug 2016, 10:39
1
Top Contributor
Bunuel wrote:
If x ¤ y = (x + y)² - (x - y)². Then √5 ¤ √5 =

A. 0
B. 5
C. 10
D. 15
E. 20

This is a great questions that typifies what I love about most GMAT math questions: they can almost always be solved in more than 1 way.

One option is to plug the values into the "recipe" and get...
√5 ¤ √5 = (√5 + √5)² - (√5 - √5)²
= (2√5)² - (0)²
= (2√5)(2√5)
= 4√25
= 20
= D

Another option is to simplify the recipe before plugging in the values
x ¤ y = (x + y)² - (x - y)²
= (x² + 2xy + y²) - (x² - 2xy + y²)
= 4xy
So, x ¤ y = 4xy
NOW plug in the values to get....
√5 ¤ √5 = 4(√5)(√5)
= 4√25
= 20
= D

RELATED VIDEOS

_________________
Test confidently with gmatprepnow.com
Senior Manager
Joined: 31 Mar 2016
Posts: 372
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

Updated on: 13 May 2016, 05:47
X = √5 and Y also =√5
Applying the function (√5+√5)^2 - (√5-√5)^2 = (2√5)^2 - 0 = 4 x 5 = 20. Answer is E.

Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√5 and y = √5 you get the answer 20.

Originally posted by Senthil7 on 13 May 2016, 05:43.
Last edited by Senthil7 on 13 May 2016, 05:47, edited 1 time in total.
Intern
Joined: 07 May 2016
Posts: 25
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

Updated on: 13 May 2016, 05:48
Bunuel wrote:
If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =

A. 0
B. 5
C. 10
D. 15
E. 20

Hi
if x ¤ y = (x + y)^2 - (x - y)^2 then √5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2
let solve the equation:
$$√5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2$$
$$=>√5 ¤ √5 = (√5+√5)^2$$
$$=>√5 ¤ √5 = (√5)^2 + 2 * √5 * √5 +(√5)^2$$
$$=>√5 ¤ √5 = 5 + 2 * 5 + 5$$
$$=>√5 ¤ √5 = 5+10+5$$
$$=>√5 ¤ √5 = 10+10$$
$$=>√5 ¤ √5 = 20$$

Originally posted by HungNguyen on 13 May 2016, 05:46.
Last edited by HungNguyen on 13 May 2016, 05:48, edited 1 time in total.
Intern
Joined: 10 Dec 2014
Posts: 38
Location: India
Concentration: Entrepreneurship, Operations
Schools: ISB '17
GPA: 4
WE: Operations (Consulting)
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

13 May 2016, 05:47
(x + y)^2 - (x - y)^2 = 4xy

√5 ¤ √5 = 4*5 = 20

OA : E
Manager
Joined: 12 Jun 2016
Posts: 202
Location: India
WE: Sales (Telecommunications)
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

26 Jul 2017, 08:35
More than anything - Here it pays to first understand what the function actually does.

x ¤ y simply means - $$(Sum\ of\ x \ and \ y)^2 - (difference \ of \ x \ and \ y)^2$$

Given $$x=y=\sqrt{5}$$.

Therefore (Sum of x and y) = $$2\sqrt{2}$$. (Difference of x and y) = 0

WIth Minimum calculation required answer = $$(2\sqrt{5})^2 = 20$$.

Aside Moderators: Do you think it will be nice'er' if the stem is made math friendly?
_________________
My Best is yet to come!
Manager
Joined: 15 Jan 2018
Posts: 66
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

### Show Tags

11 Apr 2019, 04:26
$$If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =$$

Another way to simplify is to realize that this is a difference of squares pattern. Really, it's a difference of two terms pattern if I can call it that.

x^2-y^2=(x+y)(x-y)

So, you can spell it out but if you realize, the first terms are positive when factoring, and the second set of terms has just one negative. You'll really end up with $$(2*\sqrt{5})$$ $$(2*\sqrt{5})$$
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =   [#permalink] 11 Apr 2019, 04:26
Display posts from previous: Sort by