How many two-digit prime numbers have digits that add up to 10?

Explanation

1. 01

   Two-digit numbers with digit sum 10: 19, 28, 37, 46, 55, 64, 73, 82, 91.

2. 02

   Even numbers and 55 are out, leaving 19, 37, 73, 91.

3. 03

   $91 = 7 \times 13$ is composite, so the primes are 19, 37 and 73: 3 numbers.