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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: 59628
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:

67% (02:34) correct 33% (02:51) wrong based on 119 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 3199 times ]

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Joined: 05 Dec 2017
Posts: 52
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WE: Analyst (Commercial Banking)
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
3
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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Joined: 02 Oct 2017
Posts: 708
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
1
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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Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
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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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Joined: 12 Sep 2015
Posts: 4131
Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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29 Jul 2019, 10:34
Top Contributor
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

Distance from A to D = 1/2 - 1/3
= 3/6 - 2/6
= 1/6

Let x = the distance from A to B
This means that 3x = the distance from B to C
And x = the distance from C to D
So, the TOTAL DISTANCE from A to D = x + 3x + x = 5x

So, we can conclude that 5x = 1/6
Divide both sides by 5 to get: x = 1/30

We want the coordinate of C.
C is 1/30 LESS THAN 1/2 (the coordinate of D)
1/2 - 1/30 = 15/30 - 1/30
= 14/30
= 7/15

Cheers,
Brent
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Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3   [#permalink] 29 Jul 2019, 10:34
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