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If a + b = x, and a – b = y, then ab =

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Senior Manager
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If a + b = x, and a – b = y, then ab = [#permalink]

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New post 25 Feb 2017, 21:58
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Difficulty:

  25% (medium)

Question Stats:

78% (01:07) correct 22% (01:57) wrong based on 51 sessions

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If a + b = x, and a – b = y, then ab =

(A) (x^2 – y^2)/2
(B) (x + y)(x – y)/2
(C) (x^2 – y^2)/4
(D) xy/2
(E) (x^2 + y^2)/4
[Reveal] Spoiler: OA
Senior Manager
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Joined: 19 Apr 2016
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GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
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Re: If a + b = x, and a – b = y, then ab = [#permalink]

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New post 25 Feb 2017, 22:56
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vikasp99 wrote:
If a + b = x, and a – b = y, then ab =

(A) x^2 – y^2/2
(B) (x + y)(x – y)/2
(C) x^2 – y^2/4
(D) xy/2
(E) x^2 + y^2/4


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

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

I - II
\(4ab = x^2 - y^2\)
\(ab = (x^2 - y^2)/4\)

vikasp99 : Could you please add brackets to the numerators of the options as it will make the options more clear ?

Hence option C is correct
Hit Kudos if you liked it 8-).
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Re: If a + b = x, and a – b = y, then ab = [#permalink]

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New post 26 Feb 2017, 02:33
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Re: If a + b = x, and a – b = y, then ab = [#permalink]

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New post 26 Feb 2017, 02:34
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Re: If a + b = x, and a – b = y, then ab = [#permalink]

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New post 26 Feb 2017, 06:46
Point to Note:

a*b = [(a+b)^2 - (a-b)^2 ] /4
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Re: If a + b = x, and a – b = y, then ab = [#permalink]

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New post 26 Feb 2017, 07:18
vikasp99 wrote:
If a + b = x, and a – b = y, then ab =

(A) (x^2 – y^2)/2
(B) (x + y)(x – y)/2
(C) (x^2 – y^2)/4
(D) xy/2
(E) (x^2 + y^2)/4


Hi,

Squaring on both side

\((a + b)^2 = x^2\), and \((a – b)^2 = y^2\)

On simplification

\(x^2-y^2=4ab\)

\(ab=(x^2-y^2)/4\)

Hence C
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If a + b = x, and a – b = y, then ab = [#permalink]

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New post 26 Feb 2017, 09:52
vikasp99 wrote:
If a + b = x, and a – b = y, then ab =

(A) (x^2 – y^2)/2
(B) (x + y)(x – y)/2
(C) (x^2 – y^2)/4
(D) xy/2
(E) (x^2 + y^2)/4


adding, 2a=x+y
subtracting, 2b=x-y
multiplying, 4ab=(x+y)(x-y)
ab=(x^2-y^2)/4
C
If a + b = x, and a – b = y, then ab =   [#permalink] 26 Feb 2017, 09:52
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