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Sample Question 24:
All three vertices of an equilateral triangle are on the parabola \(y=x^2\), and one of its sides has a slope of \(2\). The \(x\)-coordinates of the three vertices have a sum of \(m/n\), where \(m\) and \(n\) are relatively prime positive integers. What is the value of \(m+n\)?
\(\mathrm{(A)}\ {{{14}}} \qquad \mathrm{(B)}\ {{{15}}} \qquad \mathrm{(C)}\ {{{16}}} \qquad \mathrm{(D)}\ {{{17}}} \qquad \mathrm{(E)}\ {{{18}}}\)