Practice the questions given in the worksheet on test of divisibility.
1. The largest natural number which exactly divides the product of any five consecutive natural number is:
(a) 6
(b) 12
(c) 24
(d) 120
2. The sum of the cubes of any three consecutive natural numbers are always divisible by
(a) sum of squares of three numbers
(b) product of three numbers
(c) 27
(d) sum of three numbers.
3. The difference between the squares of two consecutive
even integers is always divisible by:
(a) 12
(b) 6
(c) 4
(d) 8
4. How many threedigit numbers are divisible by 6?
(a) 102
(b) 150
(c) 151
(d) 966
5. The smallest number of five digits exactly divisible by 476 is
(a) 47600
(b) 10000
(c) 10476
(d) 10472
6. What minimum number should be added to 936261 to make it exactly divisible by 7?
(a) 12
(b) 5
(c) 9
(d) 6
7. 2^8 × 3^6 is divisible by
(a) 2^7 × 3^7
(b) 2^6 × 3^5
(c) 2^4 × 3^7
(d) 2^5 × 3^8
8. One less than (49)^15 is exactly divisible by
(a) 50
(b) 51
(c) 49
(d) 8
9. In a sixdigit number, the sum of the digits in the even places is 13 but the sum of the digits in the odd place is 24. All such numbers are divisible by
(a) 7
(b) 9
(c) 11
(d) None of these
10. In a sixdigit even number, the sum of the digits in the even places is 12 and the sum of the digits in the odd places is 15. All such numbers are divisible by
(a) 17
(b) 18
(c) 21
(d) none
`11. The sum of all possible threedigit numbers formed from three different onedigit natural numbers when divided by the sum of the original three digits is equal to
(a) 313
(b) 121
(c) 222
(d) 444
12. If the number 357*25*is divisible by 3 and 5, the missing digits in the unit’s place and the thousand’s place respectively are
(a) 0, 6
(b) 5, 1
(c) 5, 4
(d) none of these
13. The total number of integers between 100 and 200 which are divisible by both 9 and 6 is
(a) 5
(b) 6
(c) 7
(d) 8
14. What should be the value of K so that 1623K is divisible by 99?
(a) 5
(b) 6
(c) for no value
(d) any value
15.If x and y are positive integers such that 3x + y is multiple of 11, then which of the following will also be divisible by 11?
(a) 4x + 6y
(b) x +y + 5
(c) 9x + 3y
(d) 4x  9y
16. A number lies between the cubes of 15 and 16. If the number is divisible by the square of 12 as well as 7, what is the number?
(a) 3469
(b) 4032
(c) 4096
(d) 5249
17. How many numbers between 300 and 700 are divisible by 2, 3 and 7 together?
(a) 9
(b) 8
(c) 12
(d) 11
18. The greatest number by which n(n + 1)(n +2)(n + 3) is divisible where n is any positive integer is:
(a) 24
(b) 35
(c) 15
(d) 48
`Answers for the worksheet on worksheet on test of divisibility are given below.
Answers:
1. (d)
2. (d)
3. (c)
4. (b)
5. (d)
6. (d)
7. (b)
8. (d)
9. (c)
10. (b)
11. (c)
12. (d)
13. (b)
14. (b)
15. (c)
16. (b)
17. (a)
18. (d)
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