Modular arithmetic

Question 1

What is 72%7 ?

Answer 1

2

Question 2

What is -19%8 ?

Answer 2

5

Question 3

What is range of a%m?

Answer 3

[0, m-1]

Question 4

What is -60%9 in python ?

Answer 4

3

Question 5

What is -60%9 in c/c++/java/js/c# ?

Answer 5

-6 (In case of these language to calculate correct a%m add m to the answer so -6+9 = 3(correct ans))

Question 6

Why do we need modular arithmetic?

Answer 6

It’s is used is concepts like consistent hashing, hash table, encryption etc.

Question 7

True or False

((a+b)%m) == (a%m + b%m)

Answer 7

False eg. (7+7)%4

Question 8

True or False

((a+b)%m) == (a%m + b%m)%m

Answer 8

True

Question 9

True or False

(a*b)%m == ((a%m)*(b*m))%m

Answer 9

True

Question 10

Which number is divisible by 3?
* 4351
* 3521
* 7326
* 8236

Answer 10

7326
*sum of all digits should be divisible by 3.

Question 11

Which number is dvisible by 4?
* 42234
* 64262
* 87118
* 43256

Answer 11

43256
*Last two digit should be divisible by 4.

Question 12

What is 534259%3 ?

Answer 12

1
*(Sum of all the digits)%3

Question 13

What is 63493%4 ?

Answer 13

1
*(Last two digits) % 4

Question 14

A number is divisible by 8 if….

Answer 14

A number is divisible by 8 if its last three digits are divisible by 8.

Question 15

A number is divisible by 6 if…

Answer 15

A number is divisible by 6 if it is divisible by 2 and 3

Question 16

A number is divisible by 9 if…

Answer 16

A number is divisible by 9 if its digits add up to a number divisible by 9

Question 17

A number is divisible by 7 if…

Answer 17

if a number is divisible 7, then the difference between twice the unit digit of the given number and the remaining part of the given number should be equal to 0, or the multiples of 7.

Question 18

What is Reminder in following statement?
~~~
Dividend = Divisor x Quotient + Remainder.
~~~

Answer 18

Reminder = Dividend - num;
*num = Largest mulitple of divisor <= Dividend

Question 19

How to use power function in java?

Answer 19

Math.pow(a, b)

Question 20

What is return type of Math.pow() in Java?

Answer 20

Double