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

It is currently 21 Mar 2019, 06:59

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53768
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

Show Tags

New post 13 May 2016, 04:54
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

80% (00:54) correct 20% (01:10) wrong based on 141 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
Joined: 31 Mar 2016
Posts: 383
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
GMAT ToolKit User Premium Member
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

Show Tags

New post Updated on: 13 May 2016, 06:47
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, 06:43.
Last edited by Senthil7 on 13 May 2016, 06:47, edited 1 time in total.
Intern
Intern
avatar
Joined: 07 May 2016
Posts: 26
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

Show Tags

New post Updated on: 13 May 2016, 06:48
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:
\(√5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2\)
\(=>√5 ¤ √5 = (√5+√5)^2\)
\(=>√5 ¤ √5 = (√5)^2 + 2 * √5 * √5 +(√5)^2\)
\(=>√5 ¤ √5 = 5 + 2 * 5 + 5\)
\(=>√5 ¤ √5 = 5+10+5\)
\(=>√5 ¤ √5 = 10+10\)
\(=>√5 ¤ √5 = 20\)

=> answer is E (20)

Originally posted by HungNguyen on 13 May 2016, 06:46.
Last edited by HungNguyen on 13 May 2016, 06:48, edited 1 time in total.
Intern
Intern
avatar
Joined: 10 Dec 2014
Posts: 39
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

New post 13 May 2016, 06:47
(x + y)^2 - (x - y)^2 = 4xy

√5 ¤ √5 = 4*5 = 20

OA : E
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3513
Location: Canada
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

Show Tags

New post 26 Aug 2016, 11:39
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
Image

Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 214
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

Show Tags

New post 26 Jul 2017, 09:35
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 = \((2\sqrt{5})^2 = 20\).

Answer choice E

Aside Moderators: Do you think it will be nice'er' if the stem is made math friendly? :)
_________________

My Best is yet to come!

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10162
Premium Member
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

Show Tags

New post 04 Mar 2019, 07:59
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

GMAT Club Bot
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =   [#permalink] 04 Mar 2019, 07:59
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.