# Divisibility Rules L1-1

1. A number $N$ is divided by $D$ resulted in quotient $q$ and remainder $r$. Then $N$ can be written as
a. $Dq - r$
b. $\dfrac{D}{q} - r$
c. $Dq + r$
d. $Dr + q$

2. One to ten numbers are written side by side. If this number is divided by 8 then what is the remainder?
a. 5
b. 6
c. 7
d. 0

3. What is the value of $k$ if $8975k$ is divisible by 7
a. 11
b. 16
c. 7
d. 9

4. A number when divided by 69 leaves a remainder of 50. Find the remainder when it is divided by 23.
a. 10
b. 20
c. 6
d. 4

5. A number when divided by a 23 leaves a remainder of 5. Find the remainder when the original number is multiplied by 20 and then divided by the same divisor.
a. 8
b. 10
c. 19
d. 20

6. A number when divided by a 23 leaves a remainder of 5. Find the remainder when square of the number is divided by the same divisor.
a. 1
b. 2
c. 4
d. 8

7. If $358k867$ is divisible by $11$ exactly, then $k=$
a. 1
b. 2
c. 3
d. 4

8. The value of the digit in the number $69k3164$ such that it is divisible by $22$ is
a. 5
b. 6
c. 7
d. 0

9. ${9^{16}} - {5^{16}}$ is divisible by
a. 7
b. 8
c. 56
d. All of the above

10. ${7^{10}} + {4^{10}}$ is divisible by
a. 11
b. 13
c. 65
d. B and C only

11. ${11^{20}} - {4^{20}}$ is divisible by
a. 5
b. 15
c. 137
d. all of the above

12. $K=23^x + 7^x$ where $x$ is an odd natural number. Which of the following need not be a factor of $K$.
a. 10
b. 15
c. 3
d. 8