# Worksheet on Divisibility Tests

Practice the questions given in the worksheet on divisibility tests.

1. What least positive integral value must be given to * so that the number 541*326 is divisible by 9?

(a) 1

(b) 7

(c) 6

(d) 4

2. Which of the following numbers is not exactly divisible by 99?

(a) 4476285

(b) 838827

(c) 7812288

(d) 854727

3. 451 + 452 + 453 + 454 + 455 is divisible by

(a) 17

(b) 13

(c) 11

(d) 3

4. The digits indicated by * in 47417** so that this number is divisible by 99 are:

(a) 0, 4

(b) 4, 0

(c) 0, 7

(d) 5, 6

5. (x5 - x) always divisible by (where x is a natural integer)

(a) only 10

(b) only 6

(c) both 6 and 10

(d) neither 6 or 10

6. Among common multiples of 25 and 35, the nearest to 1600 is

(a) 1605

(b) 1315

(c) 1575

(d) 1750

7. When a certain number is multiplied by 37, the product consists entirely of fives. The smaller such number is:

(a) 15051

(b) 10515

(c) 10525

(d) 15015

8. The sum of all integers between 200 and 400 divisible by 9 is

(a) 3366

(b) 6633

(c) 6336

(d) 6363

9. The largest number, by which the expression (n3 - n2) is divisible by all positive integral value, of n, is

(a) 2

(b) 4

(c) 5

(d) 6



10. What is the 507th term of the sequence 1, -1, 2, -2, 1, -1, 2, -2, 1, .................. ?

(a) -1

(b) 1

(c) -2

(d) 2

11. The sum of first 85 natural numbers will be divisible by

(a) 89

(b) 43

(c) 44

(d) 46

12. If x is a whole number, then x2(x2 – 1) is always divisible by

(a) 12

(b) multiple of 12

(c) 12 - x

(d) 24

13. The sum of the first fifty-eight numbers divisible by

(a) 29

(b) 23

(c) 57

(d) 56

14. If x and y are the two digits of the number 7717xy such that this number is divisible by 90, then (x + y) is equal to

(a) 0

(b) 5

(c) 6

(d) 3

15.  676767 is a six-digit number. It is divisible by

(a) 7 only

(b) 37 only

(c) 3 and 13 only

(d) All 3, 7, 13 and 37

16. If ‘x’ is a natural positive odd integer, then {(x + 2)2 – x2} always divisible by

(a) 5

(b) 6

(c) 8

(d) 10

Answers for the worksheet on worksheet on divisibility tests are given below.

1. (c)

2. (d)

3. (c)

4. (a)

5. (c)

6. (c)

7. (d)

8. (b)

9. (a)

10. (d)

11. (b)

12. (a)

13. (a)

14. (b)

15. (d)

16. (c)