Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

ABJeIIy Apr 2, 2024

#1**+2 **

We want all numbers in this form:

_ _ 3

_ _ 4

_ _ 5

An integer can't be part of both groups, since an integer has only one ending number.

For all of these, the first two can cycle from 10 to 99 which is 90 numbers

Sum of numbers ending in 3 is (sum of numbers 10 - 99) * 10 + 90*3 = 49320

Sum of numbers ending in 4 is (sum of numbers 10 - 99) * 10 + 90*4 = 49410

Sum of numbers ending in 5 is (sum of numbers 10 - 99) * 10 + 90*5 = 49500

49320 + 49410 + 49500 = **148230**.

hairyberry Apr 3, 2024