Numbers Worksheet-6

Numbers Worksheet-6

1. The largest natural number which exactly divides the product of any four consecutive natural numbers is :

(a) 6                    (b) 12                  (c) 24                  (d) 120

2. The largest natural number by which the product of three consecutive even natural numbers is always divisible, is :

(a) 16                  (b) 24                 (c) 48                  (d) 96

3. The sum of three consecutive odd numbers is always divisible by :

I. 2        II. 3      III. 5      IV.  6

(a) Only I                                        (b) Only II

(c) Only I and III                          (d) Only II and d I

4. The difference between the squares of two consecutive odd integers is always divisible by :

(a) 3                    (b) 6                    (c) 7                    (d) 8

5. A number is multiplied by 11 and 11 is added to the product. If the resulting number is divisible by 13, the smallest original number is :

(a) 12                  (b) 22                 (c) 26                  (d) 53

6. The sum of the digits of a 3–digit number is subtracted from the number. The resulting number is :

(a) divisible by 6

(b) divisible by 9

(c) divisible neither by 6 nor by 9

(d) divisible by both 6 and 9

7. If x and y are positive integers such that (3x +7y) is a multiple of 11, then which of the following will also be divisible by 11 ?

(a) 4x + 6y                                     (b) x + y + 4

(c) 9x + 4y                                      (d) 4x – 9y

8. The largest number that exactly divides each number of the sequence (I⁵ – 1), (2⁵ – 2), (3⁵ – 3), ....., (n⁵ – n), ..... is :

(a) 1                     (b) 15                  (c) 30                  (d) 120

9. The greatest number by which the product of three consecutive multiples of 3 is always divisible is :

(a) 54                  (b) 81                  (c) 162                (d) 243

10. The smallest number to be added to 1000 so that 45 divides the sum exactly is :

(a) 10                  (b) 20                 (c) 35                  (d) 80

11. The smallest number that must be added to 803642 in order to obtain a multiple of 11 is :

(a) 1                     (b) 4                    (c) 7                    (d) 9

12. Which of the following numbers should be added to 11158 to make it exactly divisible by 77 ?

(a) 5                    (b) 7                    (c) 8                    (d) 9

13. The least number which must be subtracted from 6709 to make it exactly divisible by 9 is:

(a) 2                    (b) 3                    (c) 4                    (d) –5

14. What least number must be subtracted from 427398 so that the remaining number is divisible by 15 ?

(a) 3                    (b) 6                    (c) 11                   (d) 16

15. What least number must be subtracted from 13294 so that the remainder is exactly divisible by 97 ?

(a) 1                     (b) 3                    (c) 4                    (d) 5

16. When the sum of two numbers is multiplied by 5, the product is divisible by 15. Which one of the following pairs of numbers satisfies the above condition ?

(a) 240, 335      (b) 250, 341      (c) 245, 342      (d) None of these

17. The least number by which 72 must be multiplied in order to produce a multiple of 112, is:

(a) 6                    (b) 12                  (c) 14                  (d) 18

18. The number of times 99 is subtracted from 1111 so that the remainder is less than 99, is :

(a) 10                  (b) 11                   (c) 12                  (d) 13

19. Find the number which is nearest to 457 and is exactly divisible by 11.

(a) 450               (b) 451                (c) 460               (d) 462

20. The number nearest to 99547 which is exactly divisible by 687 is :

(a) 98928          (b) 99479          (c) 99615           (d) 100166

Answer Key:

(1)-c; (2)-c; (3)-b; (4)-d; (5)-a; (6)-b; (7)-d; (8)-c; (9)-c; (10)-c; (11)-c; (12)-b; (13)-c; (14)-a; (15)-d; (16)-b; (17)-c; (18)-b; (19)-d; (20)-c