Number System

Number System

1. Which of the following numbers is divisible completely by both 9 and 11?

1. 277218
2. 10098
3. 12345
4. 181998

b. 10098

2. Which of the following numbers is NOT divisible by 9?

1. 49104
2. 77832
3. 35253
4. 45390

d. 45390

3. Which of the following number is NOT divisible by 8?

1. 35792
2. 35112
3. 35412
4. 35552

c. 35412

4. If the 7 digit number 504x5y3 is divisible by 11, then one of the values of the sum of x and y is:

1. 11
2. 5
3. 17
4. 7

c. 17

5. If 11-digit number 88p554085k6, k ≠ p, is divisible by 72, then what is the value of (3k +2p)?

1. 12
2. 7
3. 13
4. 23

c. 13

6. Find the remainder, when 171×172×173 is divided by 17.

1. 9
2. 8
3. 6
4. 7

c. 6

7. When a number is divided by a divisor, the remainder is 16. When twice the original number is divided by the same divisor, the remainder is 3. Find the value of that divisor

1. 29
2. 51
3. 23
4. 53

a. 29

8. If the number 6484y6 is divisible by 8, then find the least value of y?

1. 3
2. 4
3. 1
4. 7

c. 1

9. If the 15 digit number 4a5124356789734 is divisible by 9, then the value of "a" is

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

b. 4

10. If the 8 digit number 3x5479y4 is divisible by 88 and the 8 digit number 425139z2 is divisible by 9, then find the maximum possible value of (3x+2y-z).

1. 33
2. 37
3. 25
4. 35

a. 33

11. When a number n is divided by 5, the remainder is 2. When n² is divided by 5, the remainder will be:

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

c. 4

12. How many numbers of the first 100 positive integers are divisible by 3 or 4 without a remainder?

1. 50
2. 5
3. 58
4. 85

a. 50

13. How many numbers between 1 and 700 are completely divisible by 17?

1. 42
2. 41
3. 45
4. 46

b. 41

14. When 19³⁰⁰ is divided by 20, find the remainder.

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

a. 1

15. Which of the following is the greatest three digit number that is divisible by 13?

1. 990
2. 575
3. 988
4. 908

c. 988

16. The number 93248x6 are divisible by 11. Then digit x is equal to.

1. 2
2. 5
3. 7
4. 8

c. 7

17. (41⁴³+ 43⁴³) is divisible by:

1. 86
2. 74
3. 12
4. 84

d. 84

18. If pq is a two-digit number, then pq-qp will be completely divisible by:

1. 9
2. 7
3. 6
4. 5

a. 9

19. If n is a natural number then n³-n is always divisible by...........

1. 8
2. 6
3. 5
4. 4

b. 6

20. A number when divided by 7 leaves a remainder 4. What will be the remainder when the square of the same number is divided by 7?

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

a. 2

21. The smallest positive number which must be added to the greatest number of 4 digits in order that the sum may be exactly divisible by 307 is:

1. 307
2. 132
3. 306
4. 176

b. 132

22. How many numbers between 300 and 1000 are divisible by 7?

1. 994
2. 301
3. 101
4. 100

d. 100

23. How many numbers from 3 to 60 are odd numbers that are exactly divisible by 5?

1. 7
2. 5
3. 8
4. 6

d. 6

24. Find the greatest number of five digits, which is exactly divisible by 468.

1. 99684
2. 99486
3. 99864
4. 99468

a. 99684

25. In between 250-1000, how many numbers are completely divisible by 5, 6 & 7.

1. 5
2. 7
3. 6
4. 3

d. 3

26. The largest four-digit number that is exactly divisible by 83 is:

1. 9936
2. 9954
3. 9960
4. 9966

c. 9960

27. (47)²⁵-1 is exactly divisible by:

1. 21
2. 24
3. 23
4. 19

c. 23

28. If 111….....1 (n digits) is divisible by 9, then the least value of n is:

1. 18
2. 12
3. 3
4. 9

d. 9

29. A number when divided by 280 leaves 73 as the remainder. When the same number is divided by 35, the remainder will be:

1. 4
2. 2
3. 3
4. 7

c. 3

30. The least number that is divisible by all the numbers from 2 to 10 is-

1. 2520
2. 100
3. 504
4. 9

a. 2520

31. How many numbers greater than 2 and less than 30 are divisible by 1 and themselves

1. 9
2. 29
3. 27
4. 11

a. 9

32. 3⁷¹+3⁷²+3⁷³+3⁷⁴+3⁷⁵ is divisible by:

1. 8
2. 5
3. 11
4. 7

c. 11

33. The smallest 5 digit number that leaves a remainder of 6 when divided by 7 is:

1. 10009
2. 10002
3. 10003
4. 10007

b. 10002

34. N is a whole number which when, divided by 6 leaves the remainder 4. Find the remainder when 2N is divided by 6.

1. 4
2. 8
3. 2
4. 0

c. 2

35. Find the largest number of four digit that is completely divisible by 49.

1. 9998
2. 9994
3. 9992
4. 9996

d. 9996

36. What should be added to 135642 to get the largest six digit number?

1. 864350
2. 863357
3. 864357
4. 864347

c. 864357

37. Find the smallest four digit number that is divisible by 47.

1. 1200
2. 1025
3. 1034
4. 1360

c. 1034

38. Find the least 6 digit number that is a multiple of 18.

1. 100000
2. 999900
3. 100008
4. 100006

c. 100008

39. A student divided a number by 12 instead of 21 and received 35. Find the correct answer.

1. 20
2. 15
3. 26
4. 25

a. 20

40. Find the least number to be added to 231228 to make it exactly divisible by 33.

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

a. 3

41. Which of the following numbers is not divisible by 8?

1. 12676
2. 11504
3. 12832
4. 12360

a. 12676

42. 276x1, is divisible by 3. What is the sum of the possible values of x?

1. 18
2. 21
3. 12
4. 15

d. 15

43. By dividing 14528 by a certain number, Suresh gets 83 as quotient and 3 as remainder. What is the divisor?

1. 165
2. 185
3. 195
4. 175

d. 175

44. If the number x4461 is divisible by 11, find the value of x.

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

d. 5

45. Which number is divisible by 9?

1. 56112
2. 89445
3. 49653
4. 58556

c. 49653

46. Which of the following numbers is divisible by 6?

1. 12378
2. 12363
3. 12370
4. 12388

a. 12378

47. Choose the missing digit 'x' from the options given for the number 987x54, so that the number is completely divisible by 6.

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

c. 3

48. What number should be deducted from 1265 to make it divisible by 29 exactly?

1. 15
2. 16
3. 18
4. 17

c. 18

49. Find the least number to be added to 1739 so that it is exactly divisible by 11.

1. 11
2. 2
3. 1
4. 10

d. 10

50. Find the remainder, when 3¹⁰ is divided by 7.

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

a. 4