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Which of the following equals x + xy + (x + xy)y?

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Which of the following equals x + xy + (x + xy)y?  [#permalink]

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New post 21 Nov 2019, 00:47
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

85% (01:31) correct 15% (01:29) wrong based on 40 sessions

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Which of the following equals x + xy + (x + xy)y?  [#permalink]

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New post 21 Nov 2019, 01:04
1
2 ways to solve. First pure algebra (my least beloved thing and most needed on Gmat :) ) and second brute force (I like to waste up to 5 minutes brute-forcing everything :) )

1) Algebra
x+xy+(x+xy)y
Open the brackets: \(x+xy+xy+xy^2\)=\(x+2xy+xy^2\)
factor out common variable: \(x(1+2y+y^2)\)
Observe that \(1+2y+y^2=(1+y)^2\)
So we have \(x(1+y)^2\)
Look for such option

2) Brute force
Open the brackets: \(x+xy+xy+xy^2\)=\(x+2xy+xy^2\)
Open the brackets for every answer choice to see the match

Hope you will choose the first option and score 700+ on actual test
Have a nice day
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Re: Which of the following equals x + xy + (x + xy)y?  [#permalink]

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New post 21 Nov 2019, 21:06
Bunuel wrote:
Which of the following equals \(x + xy + (x + xy)y\)?

(A) \(x(1 + y)^2\)

(B) \(x(2 + y + y^2)\)

(C) \(2x(1 + y) + y\)

(D) \(2xy(1 + y)\)

(E) \(x^2(1 + y^2)y\)


Explanation:
Approach, opening the brackets, taking common out as in option, common is out
= x + xy + (x+xy).y
= x + xy + xy + xy^2
Taking x (common out)
= x (1+ 2y + y^2)
= x ( 1 + y)^2--- Option A

:please Please give kudos, if you find my explanation good enough :please
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Re: Which of the following equals x + xy + (x + xy)y?  [#permalink]

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New post 24 Nov 2019, 19:08
Bunuel wrote:
Which of the following equals \(x + xy + (x + xy)y\)?

(A) \(x(1 + y)^2\)

(B) \(x(2 + y + y^2)\)

(C) \(2x(1 + y) + y\)

(D) \(2xy(1 + y)\)

(E) \(x^2(1 + y^2)y\)


We can factor out x + xy first, and we have:

(x + xy)(1 + y)

Now we can factor out x from the first factor:

x(1 + y)(1 + y)

x(1 + y)^2

Answer: A
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Re: Which of the following equals x + xy + (x + xy)y?   [#permalink] 24 Nov 2019, 19:08
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