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# In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng

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Joined: 02 Sep 2009
Posts: 50730
In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng  [#permalink]

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23 Oct 2018, 20:21
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:45) correct 12% (00:56) wrong based on 42 sessions

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In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the length of line segment BC?

Note: Figure not drawn to scale

A. 2
B. 3
C. 4
D. 5
E. 6

Attachment:

GMAT_PS_Magoosh_315.png [ 3.1 KiB | Viewed 389 times ]

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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng  [#permalink]

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23 Oct 2018, 20:25
Bunuel wrote:
In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the length of line segment BC?

Note: Figure not drawn to scale

A. 2
B. 3
C. 4
D. 5
E. 6

Attachment:
GMAT_PS_Magoosh_315.png

Let,
AB = a
BC = b
CD = c
DE = d

AE = a+b+c+d = 20

i.e. d = 20 - 14 = 6

CD = c = 6

EB = b+c+d = 17
i..e b+6+6 = 17
i.e. b = 5

i.e. a = 14 - 5 - 6 = 3

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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng  [#permalink]

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23 Oct 2018, 23:11
Bunuel wrote:
In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the length of line segment BC?

Note: Figure not drawn to scale

A. 2
B. 3
C. 4
D. 5
E. 6

Attachment:
The attachment GMAT_PS_Magoosh_315.png is no longer available

$$AE = AB + BC + CD + DE$$

Or, $$AE = AD + DE$$

So, $$20 = 14 + DE$$

Or, $$DE = 6$$

Now, break down parts and solve ...
Attachment:

Solution.png [ 4.14 KiB | Viewed 311 times ]
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Joined: 04 Jan 2015
Posts: 2213
Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng  [#permalink]

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24 Oct 2018, 02:58

Solution

Given:
• AE = 20
• CD = 6
• EB = 17

To find:
• The length of BC

Approach and Working:
• BC = BE – CD – DE
• DE = AE – AD
• Thus, BC = BE – CD – (AE - AD)
• Therefore, BC = 17 – 6 – (20 - 14) = 11 – 6 = 5

Hence, the correct answer is Option D

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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng  [#permalink]

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27 Oct 2018, 23:17
In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the length of line segment BC?

A. 2
B. 3
C. 4
D. 5
E. 6

Using the given info we can find :
Total length is 20 AE

BE 17, CD 6, AD 14 ( given )
Info we can find using given details,
DC 6, DE 6

DC+DE+BC=BE
6+6+BC=17

BC=5

IMO D
Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng &nbs [#permalink] 27 Oct 2018, 23:17
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