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

 It is currently 28 May 2020, 23:52

### 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

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 29 Nov 2012
Posts: 673
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:

83% (01:46) correct 17% (02:29) wrong based on 136 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!
Director
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 998
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
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
Joined: 29 Nov 2012
Posts: 673
Re: If a + b = x and a - b = y , then 3ab =  [#permalink]

### Show Tags

12 Jun 2013, 07:01
Great Explanation! Thanks....
Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 27
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 $$3ab = \frac{3(x^2 - y^2)}{4}$$

Hope that helped
Math Expert
Joined: 02 Sep 2009
Posts: 64220
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: 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

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
Manager
Joined: 06 Jul 2014
Posts: 85
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 660 Q48 V32
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: 233
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: 3253
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

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 =   [#permalink] 11 Aug 2017, 18:48