GAUSS8 2014 Problem 25

Residents were surveyed in order to determine which owers to plant in the new Public Garden. A total of N people participated in the survey. Exactly \frac{9}{14} of those surveyed said that the color of the flower was important. Exactly \frac{7}{12} of those surveyed said that the smell of the flower was important. In total, 753 people said that both the color and smell were important. How many possible values are there for N?

Answer Choices
A. 22
B. 23
C. 21
D. 24
E. 25