Divisibility Rule for Powers of 2 & 5

Q.

A two – digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

1. 24

2. 42

3. 81

4. None of these

5. 18

Q. The sum of all the factors of 45000 which are exactly the multiples of 10 is:

1. 141960
2. none of these
3. 152295
4. 600

Q. Find the number of numbers between 200 and 300, both included, which are not divisible by 2, 3, 4 and 5.

1. 28
2. 27
3. 26
4. 25

Q. What is the remainder when (1! + 2! + 3!+...1000!) is divided by 5?

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

Q. How many numbers are there in the set S = {200, 201, 202, . . . , 800} which are divisible by neither of 5 nor 7?

1. 411
2. 412
3. 410
4. none of these

Q. Find the sum of all the three digit numbers divisible by 5.

1. 98550
2. 97560
3. 96000
4. 99550

Q.

There are three events X, Y and Z, out of which only one must happen. If the odds are 8:3 against X, 5:2 against Y, the odds against Z must be:

1. 34:43

2. 43:34

3. None of these

4. 8:11

5. 7:5

Q. Find the sum of all odd three -digit numbers that are divisible by 5.

1. 50, 500
2. 50, 250
3. 50, 000
4. 49, 500

Q. Total number of numbers lying in the range of 1331 and 3113 which are neither divisible by 2, 3 or 5 is:

1. 477
2. 594
3. 653
4. None of these

Q.

What is the remainder of $1421\times 1423\times 1425$ when divided by 12 ?

1. 0

2. 1

3. 3

4. 2

Q. Find the remainder when the number represented by 22334 raised to the power $(1^2+2^2+...+{66}^2)$ is divided by 5?

1. 2
2. 4
3. 1
4. None of these

Q. What will be the tens place digit in the following expression:
1! + 2! + 3! + ... + 70!?

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

Q. $N=7{!}^3.$ How many factors of N are multiples of 10?

1. 736
2. 1008
3. 1356
4. 894

Q.

X is a two – digit number, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144. Then the number is:

1. 24

2. 26

3. 42

4. 46

5. 29

Q. Find the sum of all the three digit numbers divisible by 5.

1. 99550
2. 97560
3. 98550
4. 96000
5. 98545

Q. The remainder when 888222888222888222 . . . upto 9235 digits is divided by $5^3$ is:

1. can't be determined
2. none of these
3. 103
4. 38

Q. What is the remainder when ${11}^{10}-11$ is divided by 100?

1. 0
2. 10
3. 20
4. 90

Q.

The remainder obtained when $(1^3+2^3+3^3+4^3+\dots \dots {100}^3)$ is divided by 9 is

1. 1

2. 0

3. 3

4. 2

Q. Find the remainder when $9^{178}$ is divided by 4.

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

Q. Let A be the set of integers N such that
(i) 100 $\le N\le 500$
(ii) N is even
(iii) N is divisible by either 2 or 3 or 4 but not by 7.
How many elements are there in set A?

1. 170
2. 173
3. 171
4. 172

Q. If x, y, z and w are natural numbers, then what is the sum of all the possible distinct remainders when $9^x+6^y+4^z+{11}^z$ divided by 10? ___

Q.

The remainder when 786786 is divided by 7 is

Q. If ${22}^3+{23}^3+{24}^3+\cdots +{87}^3+{88}^3$ is divided by 110, then the remainder will be:

1. 55
2. 0
3. 44
4. 1

Q. The remainder obtained when 100*(99${}^{10}$) is divided by (100*99) + 1 is

1. 0
2. 1
3. 100
4. 9900
5. none of these

Q. Find the number of factors of 150.

Q. The remainder when $6^{6^{6^{6^{6^{\cdots \infty times}}}}}$

1. 0
2. 6
3. 3
4. can't be determined

Q.

The remainder obtained when ${2681}^{2681}$ is divided by 3 is

1. 0

2. 1

3. 2

4. 3

Q.

There are three events X, Y and Z, out of which only one must happen. If the odds are 8:3 against X, 5:2 against Y, the odds against Z must be:

1. 7:5

2. 43:34

3. None of these

4. 8:11

Q. When $(629{)}^{24}$ is divided by 21, find the remainder.

1. 1
2. 5
3. 11
4. 2

Q. Find the remainder when ${402}^{12}$ is divided by 1000?

1. 296
2. None of these
3. 696
4. 496