Register

ISI2016-DCG-12

• recategorized by
277 views

1 Answer

0 votes
0 votes
Answer $C$

Highest power can be calculated in the following way:

$$\Bigg\lfloor\frac{1000}{3}\Bigg\rfloor  + \Bigg\lfloor\frac{1000}{3^2}\Bigg\rfloor + \Bigg\lfloor\frac{1000}{3^3}\Bigg\rfloor + \Bigg\lfloor\frac{1000}{3^4}\Bigg\rfloor + \Bigg\lfloor\frac{1000}{3^5}\Bigg\rfloor + \Bigg\lfloor\frac{1000}{3^6}\Bigg\rfloor + \Bigg\lfloor\frac{1000}{3^7}\Bigg\rfloor = 333 + 111 + 37+12+4+1 + 0 = 498 $$

$\therefore C$ is the correct option.
User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
1 answer
1
gatecse asked Sep 18, 2019
248 views
ISI2016-DCG-8
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 $16$ $17$ $18$ $10$
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$
User Avatar
0 votes
0 votes
1 answer
2
gatecse asked Sep 18, 2019
272 views
ISI2016-DCG-10
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
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 di...
User Avatar
0 votes
0 votes
1 answer
3
gatecse asked Sep 18, 2019
333 views
ISI2016-DCG-13
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
For all the natural number $n\geq 3,\: n^{2}+1$ isdivisible by $3$not divisible by $3$divisible by $9$None of these
User Avatar
1 votes
1 votes
2 answers
4
gatecse asked Sep 18, 2019
447 views
ISI2016-DCG-19
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 $n$
The expression $3^{2n+1}+2^{n+2}$ is divisible by $7$ forall positive integer values of $n$all non-negative integer values of $n$only even integer values of $n$only odd i...
User Avatar
Link Copied!