Divisibility Quiz – 1

Question 1

Time: 00:00:00
It is being given that \left ( 2^{32}+1\right ) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

latex]\left ( 2^{16}+1\right )[/latex]

latex]\left ( 2^{16}+1\right )[/latex]

\left ( 2^{16}-1\right )

\left ( 2^{16}-1\right )

\left ( 2^{33}*1\right )

\left ( 2^{33}*1\right )

\left ( 2^{96}+1\right )

\left ( 2^{96}+1\right )

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Question 2

Time: 00:00:00
What least number must be added to 1056, so that the sum is completely divisible by 23 ?

2

2

3

3

18

18

21

21

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Question 3

Time: 00:00:00
How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336

4

4

5

5

6

6

7

7

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Question 4

Time: 00:00:00
The largest 4 digit number exactly divisible by 88 is:

9944

9944

9768

9768

9988

9988

8888

8888

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Question 5

Time: 00:00:00
A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

1,2

1,2

2,3

2,3

3,2

3,2

4,1

4,1

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Question 6

Time: 00:00:00
The difference of the squares of two consecutive even integers is divisible by which of the following integers?

3

3

4

4

6

6

7

7

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Question 7

Time: 00:00:00
Which one of the following numbers is completely divisible by 99?

3572404

3572404

135792

135792

913464

913464

114345

114345

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Question 8

Time: 00:00:00
The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?

7

7

29

29

16

16

13

13

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Question 9

Time: 00:00:00
N^{2} leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?

1,5,7 and 11

1,5,7 and 11

1,5

1,5

5,9 and 11

5,9 and 11

1 and 11

1 and 11

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Question 10

Time: 00:00:00
A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?

8

8

12

12

9

9

15

15

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["0","40","60","80","100"]
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