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

 It is currently 19 Nov 2018, 03:30

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# 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

Director
Joined: 29 Nov 2012
Posts: 765
If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

12 Jun 2013, 06:27
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:43) correct 20% (02:32) wrong based on 184 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!

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1073
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

12 Jun 2013, 06:38
1
1
$$a=x-b$$
$$a=y+b$$

$$x-b=y+b$$ $$b=\frac{x-y}{2}$$

$$b=x-a$$
$$b=a-y$$

$$x-a=a-y$$ $$a=\frac{x+y}{2}$$

$$3ab=3(\frac{x^2-y^2}{4})$$
A
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Director
Joined: 29 Nov 2012
Posts: 765
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

12 Jun 2013, 07:01
Great Explanation! Thanks....
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
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

12 Jun 2013, 07:16
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
Math Expert
Joined: 02 Sep 2009
Posts: 50661
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

12 Jun 2013, 07:50
1
2
fozzzy wrote:
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!

Given: $$a + b = x$$ and $$a - b = y$$.

Sum the equations: $$2a=x+y$$.
Subtract: $$2b=x-y$$.

Multiply: $$4ab=x^2-y^2$$ --> multiply by 3/4: $$3ab=\frac{3x^2-3y^2}{4}$$.

_________________
Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 84
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

14 Jun 2013, 05:47
plugging numbers is quite fast in this case:
Let
a=1
b=2

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

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
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

Manager
Joined: 06 Jul 2014
Posts: 99
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 640 Q48 V30
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

11 Aug 2017, 11:40
a=x+y/2; b=x-y/2;3ab=3(x^2-y^2/4)= A
Manager
Joined: 12 Oct 2015
Posts: 218
GMAT 1: 700 Q47 V39
GPA: 3
WE: Accounting (Accounting)
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

11 Aug 2017, 11:48
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
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

11 Aug 2017, 18:48
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

Re: If a + b = x and a - b = y , then 3ab = &nbs [#permalink] 11 Aug 2017, 18:48
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 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®.