# Recent questions tagged number-systems

1

A shop owner bought a total of $64$ shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was $\text{INR} \; 50$ less than th...

2

If $n$ is a positive integer such that $( \sqrt[7]{10}) ( \sqrt[7]{10})^{2} \dots ( \sqrt[7]{10})^{n} 999,$ then the smallest value of $n$ is

3

For a $4$-digit number, the sum of its digits in the thousands, hundreds and tens places is $14,$ the sum of its digits in the hundreds, tens and units places is $15,$ an...

4

How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?

5

The natural numbers are divided into groups as $(1), (2,3,4), (5,6,7,8,9), \dots $ and so on. Then, the sum of the numbers in the $15 \text{th}$ group is equal to $6090$$...

6

How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$

7

Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} 25,$ then how many distinct values are possible for $\...

8

How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$$40$$42$$43$$41$

9

If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ eq...

10

Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ t...

11

How many pair of natural numbers are there, the differences of whose squares is $45$ ? $1$$2$$3$$4$

12

A certain number consists of two digits whose sum is $9$. It the order of digits is reversed, the new number is $9$ less than the original number. The original number is ...

13

A two digit number is such that the product of the digits is $8$. When $18$ is added to the number, the digits are reversed. The number is :$18$$24$$81$$42$

14

Find the number of numbers between $300$ to $400$ (both included) that are not divisible by $2,3,4$ and $5$$50$$33$$26$$17$

15

By which one of the following should we multiply $152207$ so that the product is $11111111$?$53$$63$$73$$83$

16

$x$ is a whole number. If the only common factors of $x$ and $x2$ are $1$ and $x,$ then $x$ is ________.$1$a perfect squarean odd numbera prime number

17

The value of $[(10)^{150}\div (10)^{146}]$:$1000$$10000$$100000$$10^{6}$

18

How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______

19

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is e...

20

How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______

21

The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is

22

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?...

23

Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals

24

If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest...

25

If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?$-32$$48$$64$$16$

26

If $\text{A}=\left \{6^{2n} – 35n – 1: n=1,2,3 \dots \right \}$ and $\text{B}= \left \{35\left (n – 1 \right ) : n=1,2,3\dots \right \}$ then which of the followin...

27

The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to$33$$37$$39$$35$

28

While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of...

29

The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x +2$ is perfectly divisible by either $3$ or $4$, is _______

30

The numbers $1, 2,\dots$,$9$ are arranged in a $3 \times 3$ square grid in such a way that each number occurs once and the entries along each column, each row, and each o...

31

If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$$1785$$1875$$1877$

32

Let $a_{1},a_{2},a_{3},a_{4},a_{5}$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_{3}$. If the s...

33

The number of solutions $\left ( x, y, z \right )$ to the equation $x-y-z=25$, where $x, y,$ and $z$ are positive integers such that $x\leq 40,y\leq 12,$ and $z\leq 12,$ ...

34

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their dig...

35

Once I had been to the post office to buy five-rupee, two- rupee and one-rupee stamps. I paid the clerk Rs. $20$, and since he had no change, he gave me three more one-ru...

36

If $n$ is any odd number greater than $1$, then $n(n^2 – 1)$ isdivisible by $96$ alwaysdivisible by $48$ alwaysdivisible by $24$ alwaysNone of these

37

Out of two-thirds of the total number of basketball matches, a team has won $17$ matches and lost $3$ of them. What is the maximum number of matches that the team can los...

38

What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$$666$$676$$683$$777$

39

For the product $n\left ( n+1 \right )\left ( 2n+1 \right ),n \in \mathbf{N}$, which one of the following is not necessarily true? It is evenDivisible by $3$Divisible by ...

40

A young girl counted in the following way on the fingers of her left hand. She started calling the thumb $1$, the index finger $2$, middle finger $3$, ring finger $4$, li...