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# Points A, B, C, and D are on the number line above, and AB = CD = 1/3

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Math Expert
Joined: 02 Sep 2009
Posts: 55758
Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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01 May 2018, 04:55
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:35) correct 34% (02:41) wrong based on 83 sessions

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Points A, B, C, and D are on the number line above, and $$AB = CD = \frac{1}{3}BC$$ What is the coordinate of C ?

A. $$\frac{13}{30}$$

B. $$\frac{9}{20}$$

C. $$\frac{11}{24}$$

D. $$\frac{7}{15}$$

E. $$\frac{29}{60}$$

Attachment:

test.jpg [ 11.38 KiB | Viewed 2110 times ]

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Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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01 May 2018, 05:28
1
1
Bunuel wrote:

Points A, B, C, and D are on the number line above, and $$AB = CD = \frac{1}{3}BC$$ What is the coordinate of C ?

A. $$\frac{13}{30}$$

B. $$\frac{9}{20}$$

C. $$\frac{11}{24}$$

D. $$\frac{7}{15}$$

E. $$\frac{29}{60}$$

Attachment:
test.jpg

Assume Length of AB = x
so AB = CD = x and BC = 3x

so distance between AD = $$5x = \frac{1}{3}-\frac{1}{2} = \frac{1}{6}$$
or $$x= \frac{1}{30}$$
now AC = $$4x+\frac{1}{3} = \frac{4}{30} + \frac{1}{3} = \frac{14}{30} or \frac{7}{15}$$

Hence Option D
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Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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18 May 2018, 01:34
Let B coordinate be x and C be y

So AB=CD=BC/3

x-(1/3)=(1/2)-y=(y-x)/3

x-(1/3)=(y-x)/3 --------(1)

(1/2)-y=(y-x)/3---------(2)

Two equations above

Compare and solve for y
y comes out to be 7/15

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Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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25 May 2019, 07:15
Bunuel wrote:

Points A, B, C, and D are on the number line above, and $$AB = CD = \frac{1}{3}BC$$ What is the coordinate of C ?

A. $$\frac{13}{30}$$

B. $$\frac{9}{20}$$

C. $$\frac{11}{24}$$

D. $$\frac{7}{15}$$

E. $$\frac{29}{60}$$

Attachment:
test.jpg

Let BC is x
Then AB = CD = x/3

Total distance between AD= 1/2 - 1/3 = 5x/3, solve for x.

Now C is D - x/3 = 14/30 Option D 7/15
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Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3   [#permalink] 25 May 2019, 07:15
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