Last visit was: 21 Jun 2024, 00:59 It is currently 21 Jun 2024, 00:59
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
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93895
Own Kudos [?]: 633520 [2]
Given Kudos: 82410
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30600 [1]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
User avatar
Senior Manager
Senior Manager
Joined: 31 Mar 2016
Posts: 324
Own Kudos [?]: 196 [0]
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
Send PM
avatar
Intern
Intern
Joined: 07 May 2016
Posts: 23
Own Kudos [?]: 19 [0]
Given Kudos: 1
Send PM
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
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.
User avatar
Intern
Intern
Joined: 10 Dec 2014
Posts: 34
Own Kudos [?]: 144 [0]
Given Kudos: 11
Location: India
Concentration: Entrepreneurship, Operations
Schools: ISB '17
GPA: 4
WE:Operations (Consulting)
Send PM
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
(x + y)^2 - (x - y)^2 = 4xy

√5 ¤ √5 = 4*5 = 20

OA : E
Manager
Manager
Joined: 12 Jun 2016
Posts: 145
Own Kudos [?]: 232 [0]
Given Kudos: 151
Location: India
Concentration: Technology, Leadership
WE:Sales (Telecommunications)
Send PM
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
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? :)
Manager
Manager
Joined: 15 Jan 2018
Posts: 54
Own Kudos [?]: 128 [0]
Given Kudos: 30
Send PM
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
\(If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =\)

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 \((2*\sqrt{5})\) \((2*\sqrt{5})\)
GMAT Club Bot
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
Moderator:
Math Expert
93896 posts