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

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Joined: 06 Mar 2020
Posts: 77
Location: India
Concentration: Finance
GMAT 1: 660 Q48 V33
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(482^2+2(482)(118)+118^2)/ 306^2−294^2=  [#permalink]

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New post Updated on: 08 Mar 2020, 01:10
1
00:00
A
B
C
D
E

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.
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GMAT 1: 770 Q49 V46
Re: (482^2+2(482)(118)+118^2)/ 306^2−294^2=  [#permalink]

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New post 08 Mar 2020, 05:28
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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

Answer: A

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

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

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