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A, B, C and D are points on a line, with D the midpoint of segment BC.

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A, B, C and D are points on a line, with D the midpoint of segment BC.  [#permalink]

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New post 12 Jul 2017, 23:41
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

81% (01:59) correct 19% (03:02) wrong based on 41 sessions

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Re: A, B, C and D are points on a line, with D the midpoint of segment BC.  [#permalink]

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New post 13 Jul 2017, 01:05
Bunuel wrote:
A, B, C and D are points on a line, with D the midpoint of segment BC. The lengths of segments AB, AC and BC are 10, 2, 12, respectively. What is the length of segment AD?

(A) 2
(B) 4
(C) 6
(D) 10
(E) 12


To solve this problem we will have to keep thinking about the points on the line while reading the question..
So lets start with point D.
Since D is midpoint of BC
B............D............C
Also BC = 12
B......6......D......6......C

Now, AC = 2.
A can be either left of C or right of C
If A is left of C , AB = 12-2 = 10 (Correct)
If A is right of C AB = 12 +2 = 14 (Incorrect)

So the points placing is as below
B......6......D....4....A..2..C

Length of segment AD = 4

Answer B
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Re: A, B, C and D are points on a line, with D the midpoint of segment BC.  [#permalink]

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New post 13 Jul 2017, 01:09
Bunuel wrote:
A, B, C and D are points on a line, with D the midpoint of segment BC. The lengths of segments AB, AC and BC are 10, 2, 12, respectively. What is the length of segment AD?

(A) 2
(B) 4
(C) 6
(D) 10
(E) 12


Given Information

C.....A........................D.................................B
<----------6-------------->
<-2->

Hence AD is 4 B
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A, B, C and D are points on a line, with D the midpoint of segment BC.  [#permalink]

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New post 13 Jul 2017, 10:18
Bunuel wrote:
A, B, C and D are points on a line, with D the midpoint of segment BC. The lengths of segments AB, AC and BC are 10, 2, 12, respectively. What is the length of segment AD?

(A) 2
(B) 4
(C) 6
(D) 10
(E) 12

Try to find endpoints first. D cannot be one; it's a midpoint.

Consider that BC at 12 has the greatest length. AC and AB sum to BC. Therefore, like D, A is between B and C. They must be the endpoints, with D halfway between, at D = 6.

Start with B, C , and D.

We have either

B_______6________D______6_______C ---------> OR

C_______6________D______6_______B

Now there's A, whose placement will yield which order above is correct. AC(CA) = 2. AB = 10. A is much closer to C, and CA + AB = CB(BC), which is 2 + 10 = 12. Correct. Order and values must be

C_______A___________D_________________B
0_______2___________6_________________12

D=6, A=2. AD = 4.

Answer B
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Re: A, B, C and D are points on a line, with D the midpoint of segment BC.  [#permalink]

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New post 15 Jul 2017, 01:18
Since the longest length of the given line is 12 then the end points are B and C also since D is the midpoint of the line BD=DC , DC= DA+AC DC=6 , AC =2 and so AD= 6-2=4

Am i correct in my explanation?? Thank you
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Re: A, B, C and D are points on a line, with D the midpoint of segment BC.   [#permalink] 15 Jul 2017, 01:18
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A, B, C and D are points on a line, with D the midpoint of segment BC.

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