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

Question

https://gmatclub.com/forum/download/file.php?id=41111 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} test.jpg

RohitGoyal1123 · Accepted Answer

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

push12345 · Answer

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

Posted from my mobile device

LeoN88 · Answer

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

BrentGMATPrepNow · Answer

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

Answer: D

Cheers,
Brent

jquest68 · Answer

I am not really understanding this. How are you getting 3X and then a 5X in the equation?

Tshenolo · Answer

we have AB=CD=(1/3)BC.

that means BC=3*AB

so (1/3)+AB+BC+CD=1/2

becomes (1/3)+AB+3AB+AB=(1/2)

5*AB=(1/6)

AB=(1/30)

point C =(1/3)+AB+3*AB

---->C =(1/3)+4*AB

sub AB-----> (1/3)+(3/30)=(14/30)=(7/14)

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

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