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 fiftyeight 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 sixdigit 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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