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

It is currently 07 Dec 2019, 01:36

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 a + b = x and a - b = y , then 3ab =

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

Hide Tags

Find Similar Topics 
Director
Director
avatar
Joined: 29 Nov 2012
Posts: 685
If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 12 Jun 2013, 07:27
1
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:47) correct 17% (02:29) wrong based on 135 sessions

HideShow timer Statistics

If a + b = x and a - b = y , then 3ab =

A. (3x^2 - 3y^2)/4
B. (3y^2 - 3x^2)/4
C. 3x+3y/2
D. 3x - 3y/2
E. 3x^2 - 3y^2/2

can someone explain!
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1010
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 12 Jun 2013, 07:38
1
2
\(a=x-b\)
\(a=y+b\)

\(x-b=y+b\) \(b=\frac{x-y}{2}\)

\(b=x-a\)
\(b=a-y\)

\(x-a=a-y\) \(a=\frac{x+y}{2}\)

\(3ab=3(\frac{x^2-y^2}{4})\)
A
Director
Director
avatar
Joined: 29 Nov 2012
Posts: 685
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 12 Jun 2013, 08:01
Great Explanation! Thanks....
Intern
Intern
User avatar
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 28
Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 12 Jun 2013, 08:16
2
1
Interesting question. Let's try a different approach.

You should recall the following two formulas :

\((a+b)^2 = a^2 + 2ab + b^2\)
\((a-b)^2 = a^2 - 2ab + b^2\)

Using what is given in the question stem, we get :

\(a^2 + 2ab + b^2 = (a+b)^2 = x^2\)
\(a^2 - 2ab + b^2 = (a-b)^2 = y^2\)

Substracting the two equations yields : \(4ab = x^2 - y^2\) meaning that \(ab = \frac{(x^2 - y^2)}{4}\).

Multiply the result by 3 and we get \(3ab = \frac{3(x^2 - y^2)}{4}\)

Which is answer choice A.

Hope that helped :-D
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 12 Jun 2013, 08:50
1
2
Manager
Manager
avatar
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 77
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 14 Jun 2013, 06:47
plugging numbers is quite fast in this case:
Let
a=1
b=2

Then; x= 1+2=> 3 and Y= 1-2=> -1

Question asks 3ab=.........
As our number 3ab= 3*1*2=6

now plug the value of x and y in the answer choices. Option A gives 6 and that is the number we need.

Hence: Ans is A.

Atal Pandit
Manager
Manager
avatar
S
Joined: 06 Jul 2014
Posts: 87
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 660 Q48 V32
GMAT ToolKit User Reviews Badge
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 11 Aug 2017, 12:40
a=x+y/2; b=x-y/2;3ab=3(x^2-y^2/4)= A
Current Student
User avatar
P
Joined: 12 Oct 2015
Posts: 214
Location: Canada
Concentration: Leadership, Accounting
GMAT 1: 700 Q47 V39
GPA: 3
WE: Accounting (Accounting)
Reviews Badge
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 11 Aug 2017, 12:48
Excellent question. saving it in my notebook to try later.
_________________
Winners dont make excuses.

350--> 700

https://gmatclub.com/forum/700-q47-v39-ir-7-awa-246682.html
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3300
Location: India
GPA: 3.12
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

Show Tags

New post 11 Aug 2017, 19:48
Plugging values is another method, you can use to solve this one!
Let a=3, b=2, x = 3+2 = 5
Similarly y = 3-2 = 1

We know that 3ab = 3*2*3 = 18

Of the answer options,
A. (3x^2 - 3y^2)/4 = 3(25) - 3(1)/4 = 75 - 3/4 = 18
B. (3y^2 - 3x^2)/4 = 3(1) - 3(25)/4 = 3 - 75/4 = -18
C. 3x+3y/2 = 3(5) + 3(1)/2 = 9
D. 3x - 3y/2 = 3(5) - 3(1)/2 = 6
E. 3x^2 - 3y^2/2 = 3(25) - 3(1)/2 = 73 - 3/2 = 36

Hence, Option A is the answer.
If you started with evaluating the first choice, it wouldn't take much time to find the answer.
_________________
You've got what it takes, but it will take everything you've got
GMAT Club Bot
Re: If a + b = x and a - b = y , then 3ab =   [#permalink] 11 Aug 2017, 19:48
Display posts from previous: Sort by

If a + b = x and a - b = y , then 3ab =

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





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