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

It is currently 25 Jan 2020, 14:16

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

An operation Ф is defined by the equation x Ф y = x²/4

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

Hide Tags

Find Similar Topics 
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4226
Location: Canada
An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 02 Aug 2017, 11:17
2
Top Contributor
7
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (02:12) correct 30% (02:35) wrong based on 223 sessions

HideShow timer Statistics

An operation Ф is defined by the equation \(x Ф y = \frac{x^2}{4} - xy + y^2\) for all numbers x and y. What is the value of 186 Ф 91?

A) 1
B) 4
C) 8
D) 16
E) 24

*kudos for all correct solutions

_________________
Test confidently with gmatprepnow.com
Image
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 313
Re: An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 02 Aug 2017, 11:32
4
xФy=\(\frac{x^2}{4}−xy+y^2\) , can be simplified to \((\frac{x}{2} - y)^ 2\)

So, 186 Ф 91 = \((\frac{186}{2} - 91)^ 2\) = \((93 - 91)^2\) = \(2^2\) = 4

Answer is B
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1156
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 02 Aug 2017, 11:32
1
GMATPrepNow wrote:
An operation Ф is defined by the equation \(x Ф y = \frac{x^2}{4} - xy + y^2\) for all numbers x and y. What is the value of 186 Ф 91?

A) 1
B) 4
C) 8
D) 16
E) 24

*kudos for all correct solutions


The expression can be simplified as \(x Ф y = (\frac{x}{2}-y)^2\)
therefore \(= (\frac{186}{2}-91)^2 = 4\)
Option \(B\)
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 729
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 02 Aug 2017, 11:34
2
1
GMATPrepNow wrote:
An operation Ф is defined by the equation \(x Ф y = \frac{x^2}{4} - xy + y^2\) for all numbers x and y. What is the value of 186 Ф 91?

A) 1
B) 4
C) 8
D) 16
E) 24

*kudos for all correct solutions


\(x\) \(Ф\) \(y = \frac{x^2}{4} - xy + y^2\) \(=> \frac{(x^2 - 4xy + 4y^2)}{4}\)

\(x\) \(Ф\) \(y = \frac{(x - 2y)^2}{4}\)

\(186\) \(Ф\) \(91 = \frac{(186 - 2*91)^2}{4}\)

\(186\) \(Ф\) \(91 = \frac{(186 - 182)^2}{4}\)

\(186\) \(Ф\) \(91 = \frac{4^2}{4}\)

\(186\) \(Ф\) \(91 = 4\)

Answer (B)...

_________________
Please Press "+1 Kudos" to appreciate. :)
Manager
Manager
avatar
S
Joined: 22 May 2017
Posts: 114
An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 02 Aug 2017, 19:31
1
Good question to be done mentally


xФy=(x/2−y)^2=(93−91)^2=4

Posted from my mobile device

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4226
Location: Canada
Re: An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 03 Aug 2017, 07:40
Top Contributor
1
GMATPrepNow wrote:
An operation Ф is defined by the equation \(x Ф y = \frac{x^2}{4} - xy + y^2\) for all numbers x and y. What is the value of 186 Ф 91?

A) 1
B) 4
C) 8
D) 16
E) 24

*kudos for all correct solutions


When we see that the expression x²/4 - xy + y² has two squares (x²/4 = (x/2)² and y² is obviously a square), we should start wondering whether the expression can be factored into the form (something)²

To make this factorization easier to see, let's factor out 1/4 first.
We get: x²/4 - xy + y² = (1/4)(x² - 4xy + 4y²)
= (1/4)(x - 2y)²

Perfect, we can now say that x Ф y = (1/4)(x - 2y)²
So, 186 Ф 91 = (1/4)[186 - 2(91)]²
= (1/4)[186 - 182]²
= (1/4)[4]²
= (1/4)[16]
= 4

Answer:

RELATED VIDEOS



_________________
Test confidently with gmatprepnow.com
Image
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14013
Re: An operation Ф is defined by the equation x Ф y = x²/4  [#permalink]

Show Tags

New post 05 Nov 2018, 02:37
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 Club Bot
Re: An operation Ф is defined by the equation x Ф y = x²/4   [#permalink] 05 Nov 2018, 02:37
Display posts from previous: Sort by

An operation Ф is defined by the equation x Ф y = x²/4

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





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