Number System Questions with Solutions

If all the digits 6 in the numbers from 1 to 100 are replaced by 9, by how much does the algebraic sum of these numbers change?

The sum of the numbers from 1 to 100 which are divisible by neither 3 nor 5 is:

A teacher gave a student the task of adding $N$ natural numbers starting from 1. After a while, the student reported his result as 700. The teacher replied that the result was wrong. The student realised he had added one number twice. Find the sum of the digits of the number which the student had added twice.

What is the sum of all 3-digit numbers (with non-zero digits) in which every digit is a perfect square?

Rs. 1074 is to be divided (in whole rupees) into a number of bags so that any amount from Rs. 1 to Rs. 1074 can be given by selecting some of the bags without opening them. What is the minimum number of bags required?

The number of ordered pairs $\left(m,n\right)$, $m,n\in 1,2,\dots ,100$ such that $7^m+7^n$ is divisible by $5$ is

If $x$ and $y$ are the two digits of the number $565xy$ such that the number is divisible by $80$, then $x+y$ equals

If both $7^2$ and $3^3$ are factors of $a\times {11}^3\times 6^2\times {13}^{11}$, then the smallest possible value of $a$ is

The integers 34041 and 32506, when divided by a 3-digit integer n, leave the same remainder. What can be the value of n?

The number of all even integers between 99 and 999 which are not multiples of 3 and 5 is

Consider a sequence formed by concatenating the positive integers in increasing order: 12345678910111213... Which among the following is the 2028th digit in this infinite sequence?