The number a = \frac{p}{q}, where p and q are relatively prime positive integers, has the property that the sum of all real numbers x satisfying
\lfloor x \rfloor \cdot \{x\} = a \cdot x^2
is 420, where \lfloor x \rfloor denotes the greatest integer less than or equal to x and \{x\} = x − \lfloor x \rfloor denotes the fractional part of x. What is p + q?
Answer Choices
A. 245
B. 593
C. 929
D. 1331
E. 1332