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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Points A, B, C, and D are on the number line above, and AB = CD = 1/3

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Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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Difficulty:   55% (hard)

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

HideShow timer Statistics  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 2116 times ]

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Manager  S
Joined: 05 Dec 2017
Posts: 53
Location: India
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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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
Director  P
Joined: 02 Oct 2017
Posts: 729
Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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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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ISB School Moderator G
Joined: 08 Dec 2013
Posts: 470
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: Points A, B, C, and D are on the number line above, and AB = CD = 1/3  [#permalink]

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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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I never gave up what I wanted- 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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Points A, B, C, and D are on the number line above, and AB = CD = 1/3  