Number System-Exercise Questions

                                                            Number System


    1. The difference between the local value and face value of 7 in the numeral             657903 is:

a. 0                 b. 7896            c. 6993                        d. 903

2. The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:

a. 7                 b. 29                c. 41                d. 67

3. The unit’s digit in the product (3127)173  is:

a. 1                 b. 3                  c. 7                  d. 9

4.  (51+52+53+………+100) is equal to:

a. 2525           b. 2975            c. 3225                        d. 3775

5. 5b2 is a three-digit number with b as a missing digit. If the number is divisible by 6, the missing digit is:

a. 2                 b. 3                  c. 6                  d. 7

6. How many of the following numbers are divisible by 3 but not by 9?

2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

a. 5                 b. 6                  c. 7                  d. None of these

7. The value of P, when 4864 x 9P2 is divisible by 12, is:

a. 2                 b. 5                  c. 8                  d. None of these.

8. How many of the following numbers are divisible by 132?

264, 396, 462, 792, 968, 2178, 5184, 6336

a. 4                 b. 5                  c. 6                  d. 7

9. The number 311311311311311311311 is:

a. divisible by 3 but not by 11           b. divisible by 11 but not by3 c. divisible by both 3 and 11   d. neither divisible by 3 nor by 11.

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

a. 6                 b. 12                c. 24                d. 120

11. 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 II           d. Only II and IV

12. 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

13. 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

14. On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is:

a. 364724       b. 365387        c. 365737        d. 366757

15. When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder?

a. 11               b. 13                c. 15                d. Data inadequate

16. A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is:

a. 0                 b. 1                  c. 2                  d. 3

17. If x is a whole number, then x2(x2-1) is always divisible by:

a. 12               b. 24                c. 12-x             d. multiple of 12

18. A number when divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:

a. 214             b. 476              c. 954              d. 1908

19. A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?

a. 2                 b. 3                  c. 4                  d. 5

20. A number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is:

a. 1220                       b. 1250            c. 2 2030         d. 22030

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