BTGmoderatorDC wrote:
On the number line shown, the distance between 0 and a, a and b, and a and c is in the ratio of 1:2:3. If the distance of point b from 15 is twice the distance of point a from 15, what is the value of |c|?
A. 9
B. 27
C. 36
D. 45
E. 54
OA
C
Source: e-GMAT
15 must lie between a and b.
Say distance between a and 15 is x units. Then distance between 15 and b is 2x units.
------------------------ 0 ------------------------ a ----------- 15 -------------------------- b -------------------------------------- c ------------------
----------------------------------------------------<-----x-----><------------ 2x ----------->
So distance between a and b is total x + 2x = 3x units
But ratio of distance between 0 and a and that between a and b is 1:2.
So point a = 3x/2 away from 0
------------------------ 0 ------------------------ a ----------- 15 -------------------------- b -------------------------------------- c ------------------
-------------------------<---------3x/2---------><-----x-----><------------ 2x ----------->
3x/2 + x = 15
x = 6
So a = 3*6/2 = 9 units away from 0.
Distance between a and c is 3 times of this distance 9 so distance between a and c is 27.
|c| is simply distance of point c from 0 which is 9 + 27 = 36
Answer (C)
Something to think about:
Why can 15 not lie to the left of a?
