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On the number line shown, the distance between 0 and a, a

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by BTGmoderatorDC » Wed Aug 01, 2018 6:32 pm

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B

C

D

E

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Difficulty—

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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
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answer

by Karishma BL » Thu Aug 02, 2018 3:18 am
BTGmoderatorDC wrote:Image
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?
Karishma
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