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Recent questions tagged remainder-theorem

1 vote
1 answer
1
Consider any integer $I=m^2+n^2$, where $m$ and $n$ are odd integers. Then $I$ is never divisible by $2$ $I$ is never divisible by $4$ $I$ is never divisible by $6$ None of the above
asked Sep 23, 2019 in Numerical Ability Arjun 111 views
1 vote
1 answer
2
The number of positive integers which are less than or equal to $1000$ and are divisible by none of $17$, $19$ and $23$ equals $854$ $153$ $160$ none of the above
asked Sep 23, 2019 in Numerical Ability Arjun 216 views
0 votes
1 answer
3
Let $k$ and $n$ be integers greater than $1$. Then $(kn)!$ is not necessarily divisible by $(n!)^k$ $(k!)^n$ $n! \cdot k! \cdot$ $2^{kn}$
asked Sep 23, 2019 in Numerical Ability Arjun 109 views
1 vote
2 answers
4
Let $S=\{0, 1, 2, \cdots 25\}$ and $T=\{n \in S: n^2+3n+2$ is divisible by $6\}$. Then the number of elements in the set $T$ is $16$ $17$ $18$ $10$
asked Sep 18, 2019 in Numerical Ability gatecse 126 views
1 vote
1 answer
5
Let $a$ be the $81$ – digit number of which all the digits are equal to $1$. Then the number $a$ is, divisible by $9$ but not divisible by $27$ divisible by $27$ but not divisible by $81$ divisible by $81$ None of the above
asked Sep 18, 2019 in Numerical Ability gatecse 86 views
1 vote
1 answer
6
Let $S=\{0,1,2,\cdots,25\}$ and $T=\{n\in S\: : \: n^{2}+3n+2\: \text{is divisible by}\: 6\}$. Then the number of elements in the set $T$ is $16$ $17$ $18$ $10$
asked Sep 18, 2019 in Numerical Ability gatecse 53 views
0 votes
1 answer
7
Let $a$ be the $81$-digit number of which all the digits are equal to $1.$ Then the number $a$ is , divisible by $9$ but not divisible by $27$ divisible by $27$ but not divisible by $81$ divisible by $81$ None of the above
asked Sep 18, 2019 in Numerical Ability gatecse 43 views
1 vote
1 answer
8
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$
asked Sep 18, 2019 in Numerical Ability gatecse 46 views
0 votes
1 answer
9
For all the natural number $n\geq 3,\: n^{2}+1$ is divisible by $3$ not divisible by $3$ divisible by $9$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 67 views
1 vote
2 answers
10
The expression $3^{2n+1}+2^{n+2}$ is divisible by $7$ for all positive integer values of $n$ all non-negative integer values of $n$ only even integer values of $n$ only odd integer values of $n$
asked Sep 18, 2019 in Numerical Ability gatecse 64 views
0 votes
0 answers
11
Suppose a 6 digit number $N$ is formed by rearranging the digits of the number 123456. If $N$ is divisible by 5, then the set of all possible remainders when $N$ is divided by 45 is $\{30\}$ $\{15, 30\}$ $\{0, 15, 30\}$ $\{0, 5, 15, 30\}$
asked Sep 13, 2018 in Numerical Ability jothee 59 views
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