## Divisibility

A **divisibility** rule is a shorthand way of determining whether a given integer is **divisible** by a fixed divisor without performing the division, usually by examining its digits. Let’s try an objective problem number 3 based on this rule from B. Stat Hons. Admission Test 2005.

## Try the problem

B.Stat. (Hons.) Admission Test 2005 – Objective problem 3

Divisibility

4/10

Challenges and Thrills in Pre College Mathematics

Excursion of Mathematics

## Knowledge Graph

## Use some hints

First Hint

All the numbers between 1 to 1000 that are divisible by 2 but not by 4 are the set of AP whose first term is 2 and common difference is 4.

And the list is

2,6,10,14,.......998

and thre are 250 terms. nd the sum of all these numbers is 125000.

Second Hint

Now we need to add all the numbers which are divisible by 5, an off cource they will not be divisible by 4.

But we have already added the even numbers. so we just need to add the odd numbers only.

Final Hint

The sum of all the odd numbesr will be

(5+15+25+35+……….995= 50000).

An now we just need to add to get the total sum.

## Other useful links

- https://www.cheenta.com/quadratic-equation-isi-entrance-b-stat-hons-2003-problem-4/
- https://www.youtube.com/watch?v=ANExXtIQXPo&list=PLTDTcDkWcXuxeaAMvWpx4vGIul38dKOQp&index=1