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

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
If AC = BC and CD = DE then, in terms of x, the value of y is  [#permalink]

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25 Oct 2018, 02:44
00:00

Difficulty:

65% (hard)

Question Stats:

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

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

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 [ 2.9 KiB | Viewed 1219 times ]

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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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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

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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Joined: 04 Jan 2015
Posts: 3078
Re: If AC = BC and CD = DE then, in terms of x, the value of y is  [#permalink]

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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

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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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