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If AC = BC and CD = DE then, in terms of x, the value of y is

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If AC = BC and CD = DE then, in terms of x, the value of y is  [#permalink]

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New post 25 Oct 2018, 02:44
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (02:12) correct 46% (01:18) wrong based on 31 sessions

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Joined: 06 Jan 2015
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Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
If AC = BC and CD = DE then, in terms of x, the value of y is  [#permalink]

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New post Updated on: 25 Oct 2018, 07:05
Bunuel wrote:
If AC = BC and CD = DE then, in terms of x, the value of y is
Image
Note: Figure not drawn to scale

A. x
B. 180 - 2x
C. 90 - 2x
D. 4x - 180
E. 45 + x/4


Attachment:
GMAT_PS_Magoosh_359.png


Since AC = BC

angle CAB = angle CBA =x

And CD = DE

angle DCE = angle CED = z

And angle ACB = DCE = z

and z=180-2x

2x + z = 2z+y

On Simplification

z=180+2x

180=360+4x + y

y=4x-180

Hence D
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Resource: GMATPrep RCs With Solution

Originally posted by NandishSS on 25 Oct 2018, 03:02.
Last edited by NandishSS on 25 Oct 2018, 07:05, edited 1 time in total.
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Re: If AC = BC and CD = DE then, in terms of x, the value of y is  [#permalink]

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New post 25 Oct 2018, 06:20

Solution


Given:
    • AC = BC
    • CD = DE

To find:
    • The value of y, in terms of x

Approach and Working:
    • ∠ABC = ∠BAC = x, since, AC = BC
      o Implies, ∠ACB = 180 – (x + x) = 180 – 2x

    • Thus, ∠BCE = 180 - ∠ACB = 180 – 180 + 2x = 2x
    • Now, ∠ECD = 180 - ∠BCE = 180 – 2x
    • In triangle CDE, given, CD = DE
      o Implies, ∠CED = ∠ECD = 180 - 2x
      o And, ∠CDE + ∠ DEC + ∠ECD = 180
         Implies, y + 180 -2x + 180 – 2x = 180

    • Therefore, y = 4x -180

Hence, the correct answer is Option D

Answer: D
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Re: If AC = BC and CD = DE then, in terms of x, the value of y is   [#permalink] 25 Oct 2018, 06:20
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If AC = BC and CD = DE then, in terms of x, the value of y is

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