Divisibility Rule for 7 & 13

Q.

The difference between a two – digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the tenths digit to that of the units digit of the number is 2:1?

1. 8

2. 16

3. 9

4. 6

5. 4

Q. When ${2222}^{5555}+{5555}^{2222}$ is divided by 7, the remainder is

1. 0
2. 2
3. 4
4. 5

Q. What is the remainder of ${2000}^{1000}$ divided by 13?

1. 11
2. 3
3. 4
4. 8

Q. The H.C.F. and L.C.M. of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is ____.

1. 16
2. 26
3. 48
4. 36
5. 24

Q. The remainder when ${10}^{10}+{10}^{100}+{10}^{1000}+....+{10}^{10000000000}isdividedby7$ is

1. 1
2. 0
3. 2
4. 5

Q. The remainder when $3^0+3^1+3^2+\cdots +3^{200}$ is divided by 13 is:

1. 0
2. 12
3. 3
4. none of these

Q. What is the remainder when $5^{79}$ is divided by 7?

1. 1
2. 0
3. 4
4. 5

Q. How many natural numbers upto 1155 are divisible by either 5 or 7 but not by 11?

1. 105
2. 330
3. 333
4. none of these

Q. How many number between 200 and 400 are divisible by 13?

1. 14
2. 15
3. 16
4. 17

Q. Find the remiander when ${33}^{{34}^{35}}$ is divided by 7.

1. 5
2. 2
3. 4
4. 6

Q.

What is the remainder obtained when 100!+100 is divided by 101?

1. 0

2. 100

3. 1

4. 99

Q. The remainder obtained when 1! + 2! + 3! + . . . + 77! is divided by 7 is:

1. 0
2. 5
3. 4
4. can't be determined

Q.

The difference between the numerator and the denominator of a fraction is 5. If 5 is added to its denominator, the fraction is decreased by$1\frac{1}{4}$. Find the value of the fraction.

1. (1/6)

2. 2(1/4)

3. 3(1/4)

4. None of these

5. 6

Q. Find the number of 4 digit numbers which are divisible by 11 or 13 but not by 17?

1. 1363
2. 1455
3. 1463
4. 1123
5. 1133

Q. What is the remainder when ${90}^{91}$ is divided by 13?

1. 0
2. 7
3. 12
4. 1

Q. Find the remainder when 17³⁶ is divided by 36?

1. 0
2. 1
3. 17
4. 2
5. -1

Q.

The relation between A.M.(arithmetic mean), G.M.(geometric mean) and H.M. (harmonic mean ) of any two distinct positive numbers is

1. A.M > G.M < H.M

2. A.M> H.M> G.M

3. A.M > H.M < G.M

4. A.M > G.M > H.M

Q. When I distribute a packet of chocolates to 7 students, I am left with 4 chocolates. When I distribute the same packet of chocolates to 11 students, I am left with 6 chocolates. How many chocolates will be left with me if I distribute the same packet of chocolates among 13 students (a packet of chocolate contains total number of N chocolates, where 1000 < N <1050)?

1. 2
2. 0
3. 6
4. 7

Q.

A number when divided by by 9 gives 8 as a remainder. What will be the remainder obtained when the same number is divided by 3.

1. 0

2. 1

3. Can’t say

4. 2

Q. For what values of x is $({25}^x+1$) divisible by 13?

1. Odd natural values of x
2. All real values of x
3. All the integral values of x
4. Even values of x

Q. Find the remainder when 123123…. upto 300 digits is divided by 7, 9, 11, 13 and 37 respectively.

1. 0, 3, 0, 0, 16
2. 0, 6, 0, 0, 16
3. 0, 6, 0, 0, 21
4. 0, 3, 0, 0, 21

Q. N= 4! + 5!+6!.........200!. Find the last two digits of N

1. 13
2. 00
3. 04
4. 54
5. 24

Q. Find the remainder when $5^{2p}$ divided by 13, given that $p=(1!{)}^2+(2!{)}^2+\dots \dots (10!{)}^2$.

1. 1
2. 6
3. 8
4. 12

Q. What is the remainder when ${}_{32}{33}^{34}$ is divided by 7?

1. 4
2. 2
3. 3
4. 1

Q. X is a number formed by writing 9 for 99 times. What will be the remainder of this number when divided by 7?___

Q. A number is formed by writing the same digit 8 times. That number is always divisible by?

1. none of these
2. 7
3. 13
4. 19

Q. $\left[\right(144{)}^2÷48\times ?]÷22=216$

1. 23
2. 16
3. 11
4. 32
5. None of these

Q. S is a number formed by writing 8 for 88 times. What will be the remainder of this number when divided by 7?

1. 4
2. 5
3. 8
4. 1

Q.

The remainder obtained when$\left({104}^{303}\right)$ is divided by 101 is

1. 3

2. 27

3. 55

4. 98

Q. Srini wrote his class 10th board examination this year. When the result was out, he searched for his hall ticket to see his roll number, but could not trace it. He could remember only the first three digits of the six-digit number as 267. However, his father remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the units digit of the number?

1. Cannot be determined
2. 5
3. 2
4. 7