Hi AndrewRivera7793,

This question is essentially about arithmetic and manipulating fractions. If you were to see this as an Official GMAT question, there would be 5 answer choices to choose from (which might provide some hints as to how to solve or include answers that are "too big" or "too small" to be correct. Without the answers, we're forced to do calculations to solve.

We're given the positions of point A and point D. With this information, we can calculate the distance between THOSE 2 points:

1/2 - 1/3 = 3/6 - 2/6 = 1/6

So the total length of AB + BC + CD = 1/6

Next, we're told...

AB = CD = BC/3

We can use this to count up "parts" of that section of the number line.

AB = 1 part
CD = 1 part
BC = 3 parts

You could use larger numbers for the "parts" if you wanted, but the ratio of the three numbers would be the same.

Now, since there are 5 equal "parts" in the space between A and D, we can calculate what each "part" equals

5 parts = 1/6
1 part = (1/6)/5
1 part = 1/30

So...
AB = 1/30
BC = 3/30 = 1/10
CD = 1/30

To confirm that these values are correct, we can add them up...
1/30 + 3/30 + 1/30 = 5/30 = 1/6

This matches our original calculation, so we now know the length of all the various line segments.

We're asked for the co-ordinate of C

C = D = 1/30
C = 1/2 - 1/30 = 15/30 - 1/30 = 14/30

Final Answer: [spoiler]14/30 = 7/15[/spoiler]

GMAT assassins aren't born, they're made,
Rich