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# If x+y=a and x-y=b, then 2xy=?

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SVP
Joined: 06 Sep 2013
Posts: 1728
Concentration: Finance
If x+y=a and x-y=b, then 2xy=?  [#permalink]

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06 Oct 2013, 07:43
1
2
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:32) correct 16% (02:11) wrong based on 164 sessions

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If x+y=a and x-y=b, then 2xy=?

a) $$\frac{(a^2 - b^2)}{2}$$
b) $$\frac{(b^2 - a^2)}{2}$$
c) $$\frac{(a - b )}{2}$$
d) $$\frac{(ab)}{2}$$
e) $$\frac{(a^2 + b^2)}{2}$$
Math Expert
Joined: 02 Sep 2009
Posts: 51100
Re: If x+y=a and x-y=b, then 2xy=?  [#permalink]

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06 Oct 2013, 08:11
1
jlgdr wrote:
If x+y=a and x-y=b, then 2xy=?

a) $$\frac{(a^2 - b^2)}{2}$$
b) $$\frac{(b^2 - a^2)}{2}$$
c) $$\frac{(a - b )}{2}$$
d) $$\frac{(ab)}{2}$$
e) $$\frac{(a^2 + b^2)}{2}$$

Sum the equations: 2x = a + b;

Subtract the equations: 2y = a-b;

Multiply: 4xy = a^2 - b^2 --> 2xy = (a^2- b^2)/2.

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SVP
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Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x+y=a and x-y=b, then 2xy=?  [#permalink]

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27 Oct 2014, 23:59
x + y = a

$$x^2 + 2xy + y^2 = a^2$$ ............. (1)

x - y = b

$$x^2 - 2xy + y^2 = b^2$$ ................ (2)

(1) - (2)

$$4xy = a^2 - b^2$$

$$2xy = \frac{a^2-b^2}{2}$$

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Intern
Joined: 25 Jul 2014
Posts: 14
Concentration: Finance, General Management
GPA: 3.54
WE: Asset Management (Venture Capital)
If x+y=a and x-y=b, then 2xy=?  [#permalink]

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28 Dec 2014, 18:35
2
Plug in any number..

Let x=3, y=2, then: 2xy = 2x3x2 = 12
And:
a = 3+2 = 5
b = 3-2 = 1

Now plug a=5, b=1 into the anwers choices:

A. (25-1)/2= 12 (yes!)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If x+y=a and x-y=b, then 2xy=?  [#permalink]

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29 Oct 2017, 06:21
jlgdr wrote:
If x+y=a and x-y=b, then 2xy=?

a) $$\frac{(a^2 - b^2)}{2}$$
b) $$\frac{(b^2 - a^2)}{2}$$
c) $$\frac{(a - b )}{2}$$
d) $$\frac{(ab)}{2}$$
e) $$\frac{(a^2 + b^2)}{2}$$

Squaring the first equation, we have:

x^2 + 2xy + y^2 = a^2

Squaring the second equation, we have:

x^2 - 2xy + y^2 = b^2

Subtracting the second equation from the first, we have:

4xy = a^2 - b^2

2xy = (a^2 - b^2)/2

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Re: If x+y=a and x-y=b, then 2xy=? &nbs [#permalink] 29 Oct 2017, 06:21
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