BTGmoderatorLU wrote:Source: e-GMAT
In 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
Using info given (figure included) we have DATA and FOCUS as below:
\[0 < a < b < c\,\,\left( * \right)\]
\[{\text{dist}}\left( {0,a} \right) = a\]
\[\left. \begin{gathered}
{\text{dist}}\left( {a,b} \right) = 2a\, \hfill \\
{\text{dist}}\left( {a,c} \right) = 3a \hfill \\
\end{gathered} \right\}\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,{\text{dist}}\left( {b,c} \right) = 3a - 2a = a\]
\[? = c = {\text{dist}}\left( {0,c} \right) = 4a\]
From the fact that
\[{\text{dist}}\left( {b,15} \right) = 2 \cdot {\text{dist}}\left( {a,15} \right)\,\,\,\,\,\]
We have three possibilities:
\[b < 15:\,\]
\[15 - b = 2\left( {15 - a} \right)\,\,\,\, \Rightarrow \,\,\,\,15 = 2a - b = 2a - 3a = - a\,\,\,\, \Rightarrow \,\,\,a < 0\,\,\,\,{\text{impossible}}\,\,\]
\[a < 15 \leqslant b:\]
\[b - 15 = 2\left( {15 - a} \right)\,\,\,\, \Rightarrow \,\,\,\,3 \cdot 15 = 2a + b = 2a + 3a = 5a\,\,\,\, \Rightarrow \,\,? = 4a = 4 \cdot 9 = 36\]
From the fact that we have already found (one viable) correct alternative choice, no need to evaluate the third scenario!
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
c = 1:3:4.
