Suppose $m$ and $n$ are positive integers with $m<n$. The value of $\frac{m+3}{n+3}$ will be

(A) equal to 1

(B) equal to 3

(C) less than the value of $\frac{m}{n}$

(D) greater than the value of $\frac{m}{n}$

(E) equal to the value of $\frac{m}{n}$
Since the result must work no matter what positive integers $m$ and $n$ we choose with $m\frac{m}{n}$, so the answer must be (D).

(We could also prove this algebraically by starting with $m<n$, which gives $3 m<3 n$, which gives $m n+3 m<m n+3 n$, which gives $m(n+3)<n(m+3)$ which gives $\frac{m}{n}<\frac{m+3}{n+3}$.)

ANSWER: (D)