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Recent questions tagged number-systems

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CAT 2021 Set-3 | Quantitative Aptitude | Question: 18
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
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 votes
1 answer
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CAT 2021 Set-1 | Quantitative Aptitude | Question: 1
How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?
How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?
1 votes
1 answer
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CAT 2021 Set-1 | Quantitative Aptitude | Question: 3
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 $6090$ $4941$ $6119$ $7471$
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$$...
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CAT 2020 Set-3 | Question: 66
How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$
How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$
0 votes
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CAT 2020 Set-3 | Question: 67
Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} > 25,$ then how many distinct values are possible for $\text{N} ?$
Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} 25,$ then how many distinct values are possible for $\...
2 votes
1 answer
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CAT 2020 Set-3 | Question: 71
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$ $40$ $42$ $43$ $41$
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$$40$$42$$43$$41$
2 votes
1 answer
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CAT 2020 Set-2 | Question: 67
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ equals
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ eq...
2 votes
2 answers
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NIELIT 2019 Feb Scientist D - Section D: 5
How many pair of natural numbers are there, the differences of whose squares is $45$ ? $1$ $2$ $3$ $4$
How many pair of natural numbers are there, the differences of whose squares is $45$ ? $1$$2$$3$$4$
1 votes
1 answer
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NIELIT 2019 Feb Scientist D - Section C: 6
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 : $45$ $36$ $54$ $63$
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 ...
3 votes
1 answer
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NIELIT 2019 Feb Scientist D - Section C: 28
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 : $18$ $24$ $81$ $42$
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$$42$
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1 answer
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NIELIT 2019 Feb Scientist C - Section D: 21
Find the number of numbers between $300$ to $400$ (both included) that are not divisible by $2,3,4$ and $5$ $50$ $33$ $26$ $17$
Find the number of numbers between $300$ to $400$ (both included) that are not divisible by $2,3,4$ and $5$$50$$33$$26$$17$
0 votes
1 answer
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NIELIT 2019 Feb Scientist C - Section C: 5
By which one of the following should we multiply $152207$ so that the product is $11111111$? $53$ $63$ $73$ $83$
By which one of the following should we multiply $152207$ so that the product is $11111111$?$53$$63$$73$$83$
1 votes
1 answer
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NIELIT 2017 OCT Scientific Assistant A - Section A: 4
$x$ 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
$x$ 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
1 votes
1 answer
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CAT 2019 Set-2 | Question: 70
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
4 votes
1 answer
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CAT 2019 Set-2 | Question: 85
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
2 votes
1 answer
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CAT 2018 Set-2 | Question: 69
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
3 votes
1 answer
22
CAT 2018 Set-2 | Question: 68
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? $5$ $6$ $8$ $7$
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?...
2 votes
1 answer
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CAT 2018 Set-2 | Question: 80
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
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
2 votes
1 answer
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CAT 2018 Set-2 | Question: 79
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 _______
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...
3 votes
2 answers
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CAT 2018 Set-2 | Question: 90
If the sum of squares of two numbers is $97$, then which one of the following cannot be their product? $-32$ $48$ $64$ $16$
If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?$-32$$48$$64$$16$
2 votes
1 answer
27
CAT 2018 Set-2 | Question: 92
The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to $33$ $37$ $39$ $35$
The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to$33$$37$$39$$35$
2 votes
1 answer
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CAT 2018 Set-1 | Question: 79
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 _________
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...
2 votes
1 answer
29
CAT 2018 Set-1 | Question: 92
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 _______
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 _______
1 votes
1 answer
31
CAT 2017 Set-2 | Question: 87
If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$ $1785$ $1875$ $1877$
If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$$1785$$1875$$1877$
1 votes
1 answer
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CAT 2017 Set-2 | Question: 93
Let $a_{1},a_{2},a_{3},a_{4},a_{5}$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_{3}$. If the sum of the numbers in the new sequence is $450$, then $a_{5}$ is $50$ $51$ $52$ $49$
Let $a_{1},a_{2},a_{3},a_{4},a_{5}$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_{3}$. If the s...
0 votes
0 answers
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CAT 2017 Set-1 | Question: 91
The number of solutions $\left ( x, y, z \right )$ to the equation $x-y-z=25$, where $x, y,$ and $z$ are positive integers such that $x\leq 40,y\leq 12,$ and $z\leq 12,$ is $101$ $99$ $87$ $105$
The number of solutions $\left ( x, y, z \right )$ to the equation $x-y-z=25$, where $x, y,$ and $z$ are positive integers such that $x\leq 40,y\leq 12,$ and $z\leq 12,$ ...
1 votes
1 answer
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CAT 2016 | Question: 75
If $n$ is any odd number greater than $1$, then $n(n^2 – 1)$ is divisible by $96$ always divisible by $48$ always divisible by $24$ always None of these
If $n$ is any odd number greater than $1$, then $n(n^2 – 1)$ isdivisible by $96$ alwaysdivisible by $48$ alwaysdivisible by $24$ alwaysNone of these
1 votes
1 answer
38
CAT 2016 | Question: 97
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$ $666$ $676$ $683$ $777$
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$$666$$676$$683$$777$
0 votes
1 answer
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CAT 2015 | Question: 70
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 $237$
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 ...
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