A number is greater than twice its reciprocal by $31/4$. Find the number.

Let the number be $x$.According to the problem statement:
$$x-\frac{2}{x}=\frac{31}{4}$$
Let's test the given options to find a match quickly:Option A ($x=7$): $7-\frac{2}{7}=\frac{47}{7}\ne \frac{31}{4}$ Option B ($x=8$): $8-\frac{2}{8}=8-\frac{1}{4}=\frac{32-1}{4}=\frac{31}{4}$ Since Option B perfectly satisfies the equation, the required number is 8.