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.** 4^{51} + 4^{52} + 4^{53} + 4^{54} + 4^{55} 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.** (x^{5} - 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 (n^{3} - n^{2})
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 x^{2}(x^{2} – 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} – x^{2}} always divisible by

(a) 5

(b) 6

(c) 8

(d) 10

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

**Answer:**

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)

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