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

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Senior Manager
Joined: 02 Jan 2017
Posts: 315
If a + b = x, and a – b = y, then ab = [#permalink]

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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
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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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 .
Math Expert
Joined: 02 Sep 2009
Posts: 43792
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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26 Feb 2017, 02:33
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

Please pay attention to formatting when posting a question. Thank you.
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Math Expert
Joined: 02 Sep 2009
Posts: 43792
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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26 Feb 2017, 02:34
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

Similar question to practice: https://gmatclub.com/forum/if-a-b-x-and ... 54248.html
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Manager
Joined: 31 Jan 2017
Posts: 58
Location: India
GMAT 1: 680 Q49 V34
GPA: 4
WE: Project Management (Energy and Utilities)
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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26 Feb 2017, 06:46
Point to Note:

a*b = [(a+b)^2 - (a-b)^2 ] /4
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Senior Manager
Joined: 06 Jan 2015
Posts: 312
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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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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Director
Joined: 07 Dec 2014
Posts: 905
If a + b = x, and a – b = y, then ab = [#permalink]

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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

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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