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

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Director
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If a + b = x and a - b = y , then 3ab = [#permalink]

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12 Jun 2013, 07:27
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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!
[Reveal] Spoiler: OA

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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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12 Jun 2013, 07:38
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$$a=x-b$$
$$a=y+b$$

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

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

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

$$3ab=3(\frac{x^2-y^2}{4})$$
A
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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12 Jun 2013, 08:01
Great Explanation! Thanks....
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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12 Jun 2013, 08:16
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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
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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12 Jun 2013, 08:50
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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: $$3ab=\frac{3x^2-3y^2}{4}$$.

Answer: A.
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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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
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Manager
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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11 Aug 2017, 12:40
a=x+y/2; b=x-y/2;3ab=3(x^2-y^2/4)= A
Manager
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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11 Aug 2017, 12:48
Excellent question. saving it in my notebook to try later.
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Re: If a + b = x and a - b = y , then 3ab = [#permalink]

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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.
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Re: If a + b = x and a - b = y , then 3ab =   [#permalink] 11 Aug 2017, 19:48
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