Maths Olympiad Prep

Track / Stage 5 / 363 of 400 #963 of 1964

Problem 963

AIME late
Number theory Difficulty 5.9 Find the answer

23. a) Show that the number of positive integers less than or equal to xx that are divisible by the positive integer dd is given by [x/d][x / d].
b) Find the number of positive integers not exceeding 1000 that are divisible by 5 , by 25 , by 125 , and by 625 .
c) How many integers between 100 and 1000 are divisible by 7 ? by 49 ?

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

25. .) 200,40,8,1200,40,8,1 c) 128,18

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.