- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the number of natural numbers between 10 and 300 each of which gives remainder 3 when divided by 4.
Given:
Numbers between 10 and 300.
To do:
We have to find the number of numbers that lie between 10 and 300, which when divided by 4 leave a remainder 3.
Solution:
We know that,
nth term $a_n= a + (n - 1)d$
Numbers which when divided by 4 that leave a remainder 3 are $(4+3), (8+3), (12+3), (16+3), ......, (296+3), (300+3), ......$
Numbers between 10 and 300 which when divided by 4 that leave a remainder 3 are $11, 15, 19, ......, 299$
Here, first number in the series is 7 and the last number is 299.
Clearly, it is an arithmetic progression with first term $a=7$ and the common difference $d=4$.
Let there are $n$ numbers in the series.
So, $299$ will be the nth term
This implies,
$299=11 + (n-1)\times4$
$4n-4= 299–11$
$4n=288+4$
$4n=292$
$n=\frac{292}{4}$
$n=73$.
Therefore, 73 numbers lie between 10 and 300, which when divided by 4 leave a remainder 3.
78 Views
