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# (482^2+2(482)(118)+118^2)/ 306^2−294^2=

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Manager
Joined: 06 Mar 2020
Posts: 84
Location: India
Concentration: Finance
GMAT 1: 660 Q48 V33

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Updated on: 08 Mar 2020, 01:10
1
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:30) correct 23% (02:43) wrong based on 26 sessions

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$$\frac{482^2+2(482)(118)+118^2}{ 306^2−294^2}=$$

A) 50
B) 100
C) 125
D) 216
E) 300

Originally posted by 770GMAT on 07 Mar 2020, 23:34.
Last edited by Bunuel on 08 Mar 2020, 01:10, edited 1 time in total.
Renamed the topic, edited the question and formatted properly.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4879
GMAT 1: 770 Q49 V46

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08 Mar 2020, 05:28
3
Top Contributor
770GMAT wrote:
$$\frac{482^2+2(482)(118)+118^2}{ 306^2−294^2}=$$

A) 50
B) 100
C) 125
D) 216
E) 300

3 special factorizations:

#1: $$x^2 + 2xy +y^2 = (x + y)(x + y) = (x + y)^2$$

#2: $$x^2 - 2xy +y^2 = (x - y)(x - y) = (x - y)^2$$

#3: $$x^2 -y^2 = (x + y)(x - y)$$

Take: $$\frac{482^2+2(482)(118)+118^2}{ 306^2−294^2}$$

Apply factorization #1 to the numerator, and factorization #3 to the denominator to get: $$\frac{(482+118)(482+118)}{ (306+294)(306-294)}$$

Evaluate the parts in brackets: $$\frac{(600)(600)}{ (600)(12)}$$

Simplify: $$\frac{600}{ 12}$$

Evaluate: 50

Cheers,
Brent
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Re: (482^2+2(482)(118)+118^2)/ 306^2−294^2=   [#permalink] 08 Mar 2020, 05:28