A book of one hundred pages has its pages numbered from 1 to 100. How many sheets of this book have the digit 5 in their numbering? (NOTE: a sheet has two pages.)
(a) 13
(b) 14
(c) 15
(d) 16
(e) 17
The correct option is (c).

Between 1 and 100, the digit 5 appears in the numbers $5,15,25,35,45,50,51,52,53$, $54,55,56,57,58,59,65,75,85$ and 95. The first sheet contains pages 1 and 2, the second sheet contains pages 3 and 4, the third sheet contains pages 5 and 6, and so on. Therefore, the two pages that make up each sheet are numbered as follows: an odd number and the next even number. Thus, the pairs of numbers on the same sheet are 49, $50 ; 51,52 ; 53,54 ; 55,56 ; 57,58 ; 59,60$, and in this group, we have six sheets. On the other hand, from 1 to 48, we have five sheets with the pages $5,15,25,35$ and 45, and from 61 to 100, we have four sheets with the pages $65,75,85$ and 95. We conclude that the total number of sheets with the digit 5 in their numbering is $6+5+4=15$.