How many numbers between 1 and 100 contain the digit 5?

How many numbers between 1 and 100 contain the digit 5?

• A. 18
• B. 19
• C. 20
• D. 21

Answer: (C)

Counting numbers that have a 5 anywhere in their digits means checking both the ones place and the tens place. There are ten numbers with a 5 in the ones place: 5, 15, 25, 35, 45, 55, 65, 75, 85, 95. There are also ten numbers with a 5 in the tens place: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59. The number 55 appears in both groups, so we don’t double-count it. Subtract one to account for the overlap: 10 + 10 − 1 = 19. The numbers between 1 and 100 that contain the digit 5 total 19.

Counting numbers that have a 5 anywhere in their digits means checking both the ones place and the tens place. There are ten numbers with a 5 in the ones place: 5, 15, 25, 35, 45, 55, 65, 75, 85, 95. There are also ten numbers with a 5 in the tens place: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59. The number 55 appears in both groups, so we don’t double-count it. Subtract one to account for the overlap: 10 + 10 − 1 = 19. The numbers between 1 and 100 that contain the digit 5 total 19.