In writing the integers from 10 to 100, how many times is the digit 7 used?
- A20
- B19
- C10
- D11
Solution & Step-by-step Explanation
Let's count the occurrences of the digit 7 between 10 and 100:
1. In the units place:
The numbers ending in 7 are: 17, 27, 37, 47, 57, 67, 77, 87, 97.
Total occurrences here = 9 times.
2. In the tens place:
The numbers starting with 7 are from 70 to 79:
70, 71, 72, 73, 74, 75, 76, 77, 78, 79.
Total occurrences here = 10 times.
Notice that in the number 77, the digit 7 is used twice—once in the units group count and once in the tens group count.
Total occurrences = times.
1. In the units place:
The numbers ending in 7 are: 17, 27, 37, 47, 57, 67, 77, 87, 97.
Total occurrences here = 9 times.
2. In the tens place:
The numbers starting with 7 are from 70 to 79:
70, 71, 72, 73, 74, 75, 76, 77, 78, 79.
Total occurrences here = 10 times.
Notice that in the number 77, the digit 7 is used twice—once in the units group count and once in the tens group count.
Total occurrences = times.