If Whitney wrote the decimal representations for the first 3

BTGmoderatorDC wrote:If Whitney wrote the decimal representations for the first 300 positive integer multiples of 5 and did not write any other numbers, how many times would she have written the digit 5 ?

A. 150
B. 185
C. 186
D. 200
E. 201

OA E

Source: Official Guide

The smallest multiple of 5 she wrote is 5, and the largest is 300 x 5 = 1,500. So Whitney could have written 5 as the units, tens or the hundreds digit.

Since every odd multiple of 5 has a units digit of 5 and every even multiple of 5 has a units digit of 0, we see that half of the 300 multiples, i.e., 150 of these multiples, will have a units digit of 5.

Now let’s investigate those that have a tens digit of 5. These numbers are 50, 55, 150, 155, …, 1,450, and 1455. We see that there are (1,450 - 50)/100 + 1 = 14 + 1 = 15 numbers that end with 0 and there should be another 15 that end with 5. So there are 30 numbers with a tens digit of 5.

Finally, let’s investigate those that have a hundreds digit of 5. These numbers are 500, 505, 510, … 595, and 1,500. We see that there are (595 - 500)/5 + 1 = 19 + 1 = 20 numbers in the 500’s that have a hundreds digit of 5, and including 1,500, there are 21 such numbers.

Therefore, Whitney has written the digit five 150 + 30 + 21 = 201 times.

Answer: E