Number System · Basic Numeracy · UPSC Civil Service

$222^{333} + 333^{222}$ is divisible by which of the following numbers?

Consider the following statements in respect of the sum $S = x + y + z$, where $x, y$ and $z$ are distinct prime numbers each less than 10: 1. The uni...

Let $X$ be a two-digit number and $Y$ be another two-digit number formed by interchanging the digits of $X$. If $(X + Y)$ is the greatest two-digit nu...

$32^5 + 2^{27}$ is divisible by

Consider the following in respect of prime number p and composite number c. 1. $\frac{\mathrm{p}+\mathrm{c}}{\mathrm{p}-\mathrm{c}}$ can be even. 2....

Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?

A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The ...

Which number amongst 240, 321, 418 and 812 is the smallest?

What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?  ...

Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number : 1. p × q...

What is the number of numbers of the form 0·XY, where X and Y are distinct non-zero digits?

If 32019 is divided by 10, then what is the remainder?

The number 3798125P369 is divisible by 7. What is the value of the digit P?

Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?

The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. Consider the following statements...

When a certain number is multiplied by 7, the product entirely comprises ones only (1111....). What is the smallest such number?