What is the number of fives used in numbering a 260-page book?

1. A. 55
2. B. 56
3. C. 57
4. D. 60

Answer: B

Explanation

To count the occurrences of the digit ‘5’ from 1 to 260:
1. From 1 to 100, the digit ‘5’ appears 20 times (e.g., 5, 15, …, 95, and 50-59).
2. From 101 to 200, similarly, ‘5’ appears 20 times (e.g., 105, 115, …, 195, and 150-159).
3. From 201 to 300, ‘5’ appears 20 times (e.g., 205, 215, …, 295, and 250-259).
So, the total occurrences from 1 to 300 would be 20 + 20 + 20 = 60.
However, we only need up to 260. We must subtract the ‘5’s that appear between 261 and 300. These are: 265, 275, 285, 295. There are 4 such numbers.
Therefore, the total number of fives from 1 to 260 is 60 – 4 = 56. This question tests basic counting principles in number systems, a common topic in CSAT.