Number System Questions with Solutions

The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's place is 3 more than the digit in the ten's place, then the number is

How many numbers from 1 to 100 are divisible by 8 and have at least one digit equal to 8?

How many numbers between 1 and 1000 (both excluded) are both squares and cubes?

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:

Find the remainder when $X=1!+2!+3!+\cdots +100!$ is divided by $240$.

Find the unit digit of ${\left(13647\right)}^{3265}$.

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?

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

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

Let $x,y,z$ be distinct integers, where $x$ and $y$ are odd positive integers and $z$ is an even positive integer. Which of the following cannot be true?

Choose the correct option for the remainder when $X=1!+2!+3!+\dots +100!$ is divided by 24.

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is

The remainder when $2^{31}$ is divided by 5 is

The last digit of the number obtained by multiplying the numbers 81 x 82 x 83 x 84 x 85 x 86 x 87 x 88 x 89 is

How many numbers between 1 and 1000 are divisible by all the numbers 2, 3, 4, 5 and 6?