Q45. What is the number of fives used in numbering a 260-page book?
Detailed Solution
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.
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