How many numbers lie between 300 and 500 in which 4 comes only one time

Explanation

This question asks for the amount of numbers between 300 and 500 where the digit 4 appears exactly once. Option 1 states 99, which is the correct answer. This is due to how the numbers between 300 and 500 are divided into groups of 100. Starting from 300-399, there are 10 instances (304, 314,…,394) where 4 appears once. Then in the next group, 400-499, 4 can`t be counted because it is repeated twice in all numbers. Finally, from 400-500, there are 89 numbers (401, 402,…409, 410, 420,…490) where 4 appears only once. So, 10 (from 300-399) + 89 (from 400-500) = 99 numbers. Option 2 states 100, which is incorrect because it overestimates the amount of valid numbers in the 400-500 range. Option 3 and 4 – 110 and 120, respectively, are incorrect because they grossly overestimate the count. So, the correct answer is 99, the amount of numbers between 300 and 500, where 4 appears only once.