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Senior Manager  V
Joined: 02 Jan 2017
Posts: 293
If a + b = x, and a – b = y, then ab =  [#permalink]

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2 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:27) correct 24% (01:45) wrong based on 115 sessions

### HideShow timer Statistics 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  G
Joined: 19 Apr 2016
Posts: 271
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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1
2
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 V
Joined: 02 Sep 2009
Posts: 56304
Re: If a + b = x, and a – b = y, then ab =  [#permalink]

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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

Please pay attention to formatting when posting a question. Thank you.
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Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: If a + b = x, and a – b = y, then ab =  [#permalink]

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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

Similar question to practice: https://gmatclub.com/forum/if-a-b-x-and ... 54248.html
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Manager  G
Joined: 31 Jan 2017
Posts: 56
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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Point to Note:

a*b = [(a+b)^2 - (a-b)^2 ] /4
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Kindly press "+1 Kudos" if the post helped Director  V
Joined: 06 Jan 2015
Posts: 681
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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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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Resource: GMATPrep RCs With Solution
VP  P
Joined: 07 Dec 2014
Posts: 1209
If a + b = x, and a – b = y, then ab =  [#permalink]

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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

subtracting, 2b=x-y
multiplying, 4ab=(x+y)(x-y)
ab=(x^2-y^2)/4
C
Intern  B
Joined: 06 Jun 2017
Posts: 10
Re: If a + b = x, and a – b = y, then ab =  [#permalink]

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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  G
Joined: 31 Jan 2017
Posts: 56
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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1
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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Kindly press "+1 Kudos" if the post helped Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If a + b = x, and a – b = y, then ab =  [#permalink]

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

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

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

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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3091
If a + b = x, and a – b = y, then ab =  [#permalink]

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1
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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