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# In the figure above, which one of the following is true?

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
In the figure above, which one of the following is true?  [#permalink]

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05 Feb 2019, 04:03
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:38) correct 36% (02:03) wrong based on 22 sessions

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In the figure above, which one of the following is true?

A. x = 2y
B. y = 2x
C. x + y = 80
D. x − y = 30
E. x = y

Attachment:

2019-02-05_1502.png [ 24.04 KiB | Viewed 423 times ]

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In the figure above, which one of the following is true?  [#permalink]

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05 Feb 2019, 04:40
Bunuel wrote:

In the figure above, which one of the following is true?

A. x = 2y
B. y = 2x
C. x + y = 80
D. x − y = 30
E. x = y

Attachment:
2019-02-05_1502.png

I'd go with A.

Sum of interior angles of a triangle = 180º

So, we have 2 sums that both add up to 180

2x + 5y
4x + y

Putting them together we have

2x + 5y = 4x + y
5y - y = 4x - 2x
4y = 2x
2y = x

Which leads us to option A
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Re: In the figure above, which one of the following is true?  [#permalink]

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05 Feb 2019, 06:24
Bunuel wrote:

In the figure above, which one of the following is true?

A. x = 2y
B. y = 2x
C. x + y = 80
D. x − y = 30
E. x = y

Attachment:
2019-02-05_1502.png

we have two triangles
4x+y=180
2x+5y= 180
subtract
2x-4y=0
x-2y=0
x=2y
IMO A
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Re: In the figure above, which one of the following is true?  [#permalink]

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05 Feb 2019, 21:50
Bunuel wrote:

In the figure above, which one of the following is true?

A. x = 2y
B. y = 2x
C. x + y = 80
D. x − y = 30
E. x = y

Attachment:
2019-02-05_1502.png

Sum of interior angles of a triangle is 180 degrees. Therefore, we have-
1) 5y+x+x=180==>2x+5y=180
2) 2x+2x+y=180==>4x+y=180

==>2x+5y=4x+y
2x=4y
==>x=2y

Ans:A
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GMAT:710 (Q49,V38,IR8,AWA5)
Re: In the figure above, which one of the following is true?   [#permalink] 05 Feb 2019, 21:50
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