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

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Bunuel
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In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink] New post   23 Oct 2018, 21:21
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E

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Question Stats:

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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


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D
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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink] New post   23 Oct 2018, 21:25
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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


Show Spoiler
Attachment:
GMAT_PS_Magoosh_315.png


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

AE = a+b+c+d = 20

AD = a+b+c = 14

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

Answer: Option D
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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink] New post   24 Oct 2018, 00:11
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


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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
Solution.png [ 4.14 KiB | Viewed 3597 times ]
Answer must be (D) 5
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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink] New post   24 Oct 2018, 03:58
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Solution


Given:
    • AE = 20
    • AD = 14
    • 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

Answer: D

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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink] New post   28 Oct 2018, 00:17
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
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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink] New post   17 Oct 2020, 12:54
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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



Solution:

Since AE = 20 and AD = 14, then DE = AE - AD = 20 - 14 = 6. Since CD = 6 and DE = 6 and EB = 17, we see that BC = EB - CD - DE = 17 - 6 - 6 = 5.

Answer: D
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Re: In the diagram, AE = 20, AD = 14, CD = 6 and EB = 17. What is the leng [#permalink]
17 Oct 2020, 12:54
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