Recent questions tagged number-systems

1 votes
4 answers
82
Convert the number $1982$ from base $10$ to base $12.$ The result is$1182$$1912$$1192$$1292$
0 votes
1 answer
84
Let $\text{N} = 55^3 + 17^3 – 72^3.\; \text{N}$ is divisible byboth $7$ and $13$both $3$ and $13$both $17$ and $7$both $3$ and $17$
0 votes
0 answers
86
The integers $34041$ and $32506$ when divided by a three-digit integer $ n\text{’}$ leave the same remainder. What is $ n\text{’}?$$289$$367$$453$$307$
1 votes
1 answer
87
Let $\text{N} = 1421 \times 1423 \times 1425.$ What is the remainder when $\text{N}$ is divided by $12?$$0$$9$$3$$6$
0 votes
0 answers
88
Let $\text{S}$ be the set of prime numbers greater than or equal to $2$ and less than $100.$ Multiply all elements of $\text{S}.$ With how many consecutive zeros will the...
0 votes
0 answers
89
Let $\text{S}$ be the set of integers $x$ such that$100 < x < 200$$x$ is odd$x$ is divisible by $3$ but not by $7$How many elements does $\text{S}$ contain?$16$$12$$11$$1...
0 votes
0 answers
92
The remainder when $2^{256}$ is divided by $17$ is$7$$13$$11$$1$
0 votes
0 answers
93
If $\text{U, V, W}$ and $m$ are natural numbers such that $\text{U}^m + \text{V}^m = \text{W}^m$, then which of the following is true?$m < \min\text{(U, V, W)}$$m \max\t...
1 votes
0 answers
95
For all integers $n>0, \: \: 7^{6n} - 6^{6n}$ is divisible by$13$$128$$549$None of these
1 votes
0 answers
96
1 votes
1 answer
97
Number $\text{S}$ is equal to the square of the sum of the digits of a $2$ digit number $\text{D}.$ If the difference between $\text{S}$ and $\text{D}$ is $27,$ then $\te...
0 votes
3 answers
98
On dividing a number by $3, 4,$ and $7,$ the remainders are $2, 1,$ and $4$ respectively. If the same number is divided by $84$ then the remainder is$80$$76$$53$None of t...
0 votes
0 answers
99
Let T be the set of integers $\{3, 11, 19,27, \dots ,451, 459, 467\}$ and S be a subset of T such that the sum of no two elements of S is $470.$ The maximum possible numb...
0 votes
0 answers
100
The number of positive integers $n$ in the range $12 \leq n \leq 40$ such that the product $(n-1)(n-2) \dots 3 \cdot 2 \cdot 1$ is not divisible by $n$ is$5$$7$$13$$14$
0 votes
0 answers
101
0 votes
0 answers
102
If the product of $n$ positive real numbers is unity, then their sum is necessarily a multiple of $n$equal to $n+\left(\frac{1}{n}\right)$never less than $n$a positive in...
0 votes
0 answers
104
How many even integers $n,$ where $100 \leq n \leq 200$, are divisible neither by $7$ nor by $9?$$40$$37$$39$$38$
0 votes
1 answer
108
Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? $3$ $2$ $4$ $1$
0 votes
0 answers
109
John bought five toffees and ten chocolates together for forty rupees. Subsequently, he returned one toffee and got two chocolates in exchange. The price of an chocolate ...
0 votes
0 answers
110
The remainder, when $(15^{23} + 23^{23})$ is divided by $19,$ is$4$$15$$0$$18$
0 votes
1 answer
112
Suppose $n$ is an integer such that the sum of the digits of $n$ is $2,$ and $10^{10} < n < 10^{11}$. The number of different values for $n$ is$11$$10$$9$$8$
0 votes
0 answers
116
Let $\text{S}$ be a positive integer such that every element $n$ of $\text{S}$ satisfies the conditions$1000 \leq n \leq 1200$every digit in $n$ is oddThen how many elem...
0 votes
1 answer
117
1 votes
1 answer
118
The rightmost non-zero digit of the number $30^{2720}$ is ______$1$$3$$7$$9$
0 votes
0 answers
120
Let $n! = 1 \times 2 \times 3 \times \dots \times n$ for integer $n \geq 1$. If $p = 1! (2 \times 2!) + (3 \times 3!) + \dots + (10 \times 10!)$, then $p+2$ when divided ...