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

It is currently 15 Oct 2019, 21:44

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 = 3x^2 – y and x y = x + 2y, which of the following is

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58347
If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 15 Jul 2015, 03:05
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

89% (01:52) correct 11% (02:25) wrong based on 98 sessions

HideShow timer Statistics

CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 15 Jul 2015, 04:20
Bunuel wrote:
If x # y = 3x^2 – y and x @ y = x + 2y, which of the following is equal to 2x # (2x @ y)?

A. 2x^2 + 8xy + 4y^2
B. -x^2 + 8x – 4y
C. 10x^2 – 8 – 4y
D. 8x^2 – 4y^2
E. 12x^2 – 2x – 2y

Kudos for a correct solution.


Given: x # y = 3x^2 – y and x @ y = x + 2y

2x@y = 2x+2y ----> 2x#(2x+2y) ----> 3 (2x)^2- (2x+2y) ---> 12x^2-2x-2y. Thus E is the correct answer.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post Updated on: 15 Jul 2015, 05:37
Bunuel wrote:
If x # y = 3x^2 – y and x @ y = x + 2y, which of the following is equal to 2x # (2x @ y)?

A. 2x^2 + 8xy + 4y^2
B. -x^2 + 8x – 4y
C. 10x^2 – 8 – 4y
D. 8x^2 – 4y^2
E. 12x^2 – 2x – 2y

Kudos for a correct solution.


Given : x # y = 3x^2 – y and x @ y = x + 2y,

Such questions can very well be solved with some substitution of value

Let, @x=1 and y=1
2x @ y = 2 1 = 2 + 2*1 = 4

Question stem has value, 2x # (2x @ y) = 2*1 # (4) = 2 # 4 = 3*2^2 - 4 = 12 - 4 = 8


Options @x=1 and y=1

A. 2x^2 + 8xy + 4y^2 = 2 + 8 + 4 = 14 i.e. not equal to 8 INCORRECT OPTION
B. -x^2 + 8x – 4y = -1 + 8 - 4 = 3 i.e. not equal to 8 INCORRECT OPTION
C. 10x^2 – 8 – 4y = 10 - 8 - 4 = -2 i.e. not equal to 8 INCORRECT OPTION
D. 8x^2 – 4y^2 = 8 - 4 = 4 i.e. not equal to 8 INCORRECT OPTION
E. 12x^2 – 2x – 2y = 12 - 2 - 2 = 8 CORRECT OPTION

Answer: Option E
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 15 Jul 2015, 05:26.
Last edited by GMATinsight on 15 Jul 2015, 05:37, edited 2 times in total.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 15 Jul 2015, 05:33
1
GMATinsight wrote:
Bunuel wrote:
If x # y = 3x^2 – y and x @ y = x + 2y, which of the following is equal to 2x # (2x @ y)?

A. 2x^2 + 8xy + 4y^2
B. -x^2 + 8x – 4y
C. 10x^2 – 8 – 4y
D. 8x^2 – 4y^2
E. 12x^2 – 2x – 2y

Kudos for a correct solution.


Given : x # y = 3x^2 – y and x @ y = x + 2y,

Such questions can very well be solved with some substitution of value

Let, @x=1 and y=1
2x @ y = 2 1 = 2 + 2*1 = 4

Question stem has value, 2x # (2x @ y) = 2*1 # (4) = 2 # 4 = 2*2^2 - 4 = 8 - 4 = 4


Options @x=1 and y=1

A. 2x^2 + 8xy + 4y^2 = 2 + 8 + 4 = 14 i.e. not equal to 4 INCORRECT OPTION
B. -x^2 + 8x – 4y = -1 + 8 - 4 = 3 i.e. not equal to 4 INCORRECT OPTION
C. 10x^2 – 8 – 4y = 10 - 8 - 4 = -2 i.e. not equal to 4 INCORRECT OPTION
D. 8x^2 – 4y^2 = 8 - 4 = 4 CORRECT OPTION
E. 12x^2 – 2x – 2y = 12 - 2 - 2 = 8 i.e. not equal to 4 INCORRECT OPTION

Answer: Option D


Interesting approach.

GMATinsight, I think you have mentioned incorrectly that 2*1 # (4) = 2 # 4 = 2*2^2 - 4 = 8 - 4 = 4 ---> It should be 2*1 # (4) = 2 # 4 = 3*2^2 - 4 = 12 - 4 = 8 with E as the correct answer. Given : x # y = 3x^2 – y and not x # y = 2x^2 – y
Intern
Intern
avatar
Joined: 11 Sep 2013
Posts: 7
GMAT ToolKit User
Re: If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 15 Jul 2015, 22:07
1
2x#(2x@y)
= 3(2x)^2 - (2x@y)
= 12x^2 - (2x+2y)= 12x^2 -2x-2y
Option E
Manager
Manager
avatar
Joined: 20 Jul 2011
Posts: 79
GMAT 1: 660 Q49 V31
GMAT ToolKit User
Re: If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 17 Jul 2015, 23:56
Bunuel wrote:
If x # y = 3x^2 – y and x @ y = x + 2y, which of the following is equal to 2x # (2x @ y)?

A. 2x^2 + 8xy + 4y^2
B. -x^2 + 8x – 4y
C. 10x^2 – 8 – 4y
D. 8x^2 – 4y^2
E. 12x^2 – 2x – 2y

Kudos for a correct solution.


2x @ y = 2x + 2y
2x # (2x @ y) = 2x # (2x + 2y) => 3(2x)^2 - (2x + 2y) => 12x^2 - 2x - 2y.

Option E.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58347
Re: If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 19 Jul 2015, 13:17
Bunuel wrote:
If x # y = 3x^2 – y and x @ y = x + 2y, which of the following is equal to 2x # (2x @ y)?

A. 2x^2 + 8xy + 4y^2
B. -x^2 + 8x – 4y
C. 10x^2 – 8 – 4y
D. 8x^2 – 4y^2
E. 12x^2 – 2x – 2y

Kudos for a correct solution.


800score Official Solution:

Recall from the rules of order of operations (PEMDAS), that we always work with what is in parenthesis first. Essentially, we want to work from the inside out with this problem.

2x # (2x @ y) = 2x # (2x + 2y) = 3(2x)^2 – (2x + 2y) = 12x^2 – 2x – 2y.

The correct answer is E.
_________________
Intern
Intern
avatar
B
Joined: 09 Jul 2018
Posts: 12
Re: If x # y = 3x^2 – y and x y = x + 2y, which of the following is  [#permalink]

Show Tags

New post 22 Sep 2019, 17:32
2x @ y = 2x + 2y
2x # (2x @ y) = 2x # (2x + 2y) =------> 3(2x)^2 - (2x + 2y) =-----> 12x^2 - 2x - 2y

Hence E.
GMAT Club Bot
Re: If x # y = 3x^2 – y and x y = x + 2y, which of the following is   [#permalink] 22 Sep 2019, 17:32
Display posts from previous: Sort by

If x # y = 3x^2 – y and x y = x + 2y, which of the following is

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





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