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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: 316
If a + b = x, and a – b = y, then ab = [#permalink]

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25 Feb 2017, 22:58
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Question Stats:

79% (01:10) correct 21% (01:34) wrong based on 89 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
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, 23:56
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KUDOS
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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: 45380
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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26 Feb 2017, 03:33
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: 45380
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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26 Feb 2017, 03:34
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, 07:46
Point to Note:

a*b = [(a+b)^2 - (a-b)^2 ] /4
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Senior Manager
Joined: 06 Jan 2015
Posts: 372
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, 08:18
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: 999
If a + b = x, and a – b = y, then ab = [#permalink]

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26 Feb 2017, 10:52
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
Intern
Joined: 06 Jun 2017
Posts: 6
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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12 Mar 2018, 08:08
Does anybody mind explaining to me why I should automatically think to square "a+b=x" & "a-b=y" upon seeing these clues? What about the given information should indicate to a test taker "Ya know what... lets square those clues in order to solve this problem"?
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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12 Mar 2018, 12:41
1
KUDOS
aaronhew wrote:
Does anybody mind explaining to me why I should automatically think to square "a+b=x" & "a-b=y" upon seeing these clues? What about the given information should indicate to a test taker "Ya know what... lets square those clues in order to solve this problem"?

[(a+b)^2 - (a-b)^2 ] = 4*a*b

[(a+b)^2 + (a-b)^2 ] = a^2 + b^2

These are two of the relevant and standard formula to be at your fingertips. As far as this problem is concerned, asking for the value of a*b is the obvious clue and there is nothing more to research on this problem.
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Manager
Joined: 16 Sep 2016
Posts: 218
WE: Analyst (Health Care)
Re: If a + b = x, and a – b = y, then ab = [#permalink]

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12 Mar 2018, 12:46
$$a+b = x$$
$$a-b = y$$

when we square both .. we will have the squared terms in positive and the product of a& b term with opposite signs in the two equations.

We can subtract to get rid of the quadratic terms

so 1 - 2 leads to

$$4ab = x^2 - y^2$$

SC Moderator
Joined: 22 May 2016
Posts: 1674
If a + b = x, and a – b = y, then ab = [#permalink]

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12 Mar 2018, 14:10
1
KUDOS
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

aaronhew wrote:
Does anybody mind explaining to me why I should automatically think to square "a+b=x" & "a-b=y" upon seeing these clues? What about the given information should indicate to a test taker "Ya know what... lets square those clues in order to solve this problem"?

aaronhew Hilarious. Levity is good.

You may know the algebraic identities but may not have seen the clue.
Bunuel lists them here, Algebraic Identities (scroll down)

If you draw a blank, another way to answer is to assign values.

Let a = 3, b = 2
x = (a + b) = (3 + 2) = 5
y = (a - b) = (3 - 2) = 1

(ab) = (3*2) = 6

Using x = 5 and y = 1, find the answer that yields 6

(A) (x^2 – y^2)/2: $$\frac{(5^2-1^2)}{2}=\frac{24}{2}=12$$. NO

(B) (x + y)(x – y)/2: $$\frac{(5+1)(5-1)}{2}=\frac{24}{2}=12$$. NO

(C) (x^2 – y^2)/4: $$\frac{(5^2-1^2)}{4}=\frac{24}{4}=6$$. MATCH

(D) xy/2: $$\frac{(5*1)}{2}=\frac{5}{2}$$. NO

(E) (x^2 + y^2)/4: $$\frac{(5^2+1^2)}{4}=\frac{26}{4}=\frac{13}{2}$$. NO

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If a + b = x, and a – b = y, then ab =   [#permalink] 12 Mar 2018, 14:10
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