# Recent questions tagged number-systems

1 vote
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 that of a large shirt. She paid a total of $\text{INR} \; 5000$ for the large shirts, and a total of ... for the small shirts. Then, the price of a large shirt and a small shirt together, in $\text{INR},$ is $200$ $175$ $150$ $225$
1 vote
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
1 vote
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 $15,$ and the tens place digit is $4$ more than the units place digit. Then the highest possible $4$-digit number satisfying the above conditions is
1 vote
4
How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?
1 vote
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 $6090$ $4941$ $6119$ $7471$
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 $\text{N} ?$
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 $\textsf{2x+y}$ equals
1 vote
10
Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ then the smallest possible value of $x_{0}$ is $9$ $10$ $8$ $12$
1 vote
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 : $45$ $36$ $54$ $63$
1 vote
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
$x$ is a whole number. If the only common factors of $x$ and $x2$ are $1$ and $x,$ then $x$ is ________. $1$ a perfect square an odd number a prime number
16
The value of $[(10)^{150}\div (10)^{146}]$: $1000$ $10000$ $100000$ $10^{6}$
1 vote
17
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
1 vote
18
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 equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is _____
1 vote
19
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
20
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
21
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? $5$ $6$ $8$ $7$
22
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
23
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 possible $x$ is _______
24
If the sum of squares of two numbers is $97$, then which one of the following cannot be their product? $-32$ $48$ $64$ $16$
1 vote
25
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 following is true? Neither every member of $\text{A}$ is in $\text{B}$ nor every member of $\text{B}$ ... $\text{B}$ is not in $\text{A}$ Every member of $\text{B}$ is in $\text{A}$ At least one member of $\text{A}$ is not in $\text{B}$
26
The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to $33$ $37$ $39$ $35$
27
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 the sum of squares of the other two numbers is _________
28
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 _______
29
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 of the two diagonals add up to the same value. If the top left and the top right entries of the grid are $6$ and $2$, respectively, then the bottom middle entry is None of the options $1$ $2$ $4$
1 vote
30
If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$ $1785$ $1875$ $1877$
1 vote
31
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 sum of the numbers in the new sequence is $450$, then $a_{5}$ is $50$ $51$ $52$ $49$
32
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 $z\leq 12,$ is $101$ $99$ $87$ $105$
33
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 digits interchanged. The total sales value remained the same, i.e. Rs. $1,148$, but the inventory reduced by $54$. What is the actual price per piece? $\text{Rs. }82$ $\text{Rs. }41$ $\text{Rs. }6$ $\text{Rs. }28$
34
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-rupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought ___________
1 vote
35
If $n$ is any odd number greater than $1$, then $n(n^2 – 1)$ is divisible by $96$ always divisible by $48$ always divisible by $24$ always None of these
36
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 lose and still win more than three fourths of the total number of matches, if it is true that no match can end in a tie _________
1 vote
37
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7$? $666$ $676$ $683$ $777$
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 even Divisible by $3$ Divisible by the sum of the square of first $n$ natural numbers Never divisible by $237$
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 $4$, little finger $5$, then reversed direction, calling the ring finger $6$, middle finger $7$, index ... $10$, middle finger for $11$, and so on. She counted up to $1994$. She ended on her. thumb index finger middle finger ring finger
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 reversed ___________