Question

On this monthly calendar, the date behind one of the letters is added to the date behind $C$ . If this sum equals the sum of the dates behind $A$ and $B$ , then the letter is

$P$

$Q$

$R$

$S$

$T$

Solution:

Moving one column right adds $1$ to the date, and moving one row down adds $7$ . Let $C$ have date $n$ . Then $A$ , one column to the right, is $n+1$ . The letter $P$ sits two rows directly below $C$ , so $P = n+14$ , and $B$ , one column left of $P$ in the bottom row, is $n+13$ .

We need a letter whose date $d$ satisfies $d + n = (n+1) + (n+13)$ , so $d = n + 14$ . That date is behind $P$ .

Thus, the correct answer is A .

1990 AMC 8 Problem 10

Solution:

Problem 10 in Other Years