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Number System Question Answers

Solved Examples:


  1. What is the difference in the place value and the face value of 8 in 78975?
    Ans : The place value of 8 is 8000
    The face value of 8 is 8
    Therefore the required difference = 8000 - 8 = 7992

  2. The numbers p, p + 2, p + 4 are all primes. Find the value of p.
    Ans : When p = 3, the given numbers are 3, 5, 7; which are prime.

  3. If 42 k 8 is a multiple of 9, find the value of k
    Ans : Sum of digits = (4 + 2 + k +8) = (14 + k).
    Now, least value of k for which (14 + k) is divisible by 9 is k = 4.


  4. Find the least number of five digits that is exactly divisible by 456.
    Ans : The least five digit number = 10000.
    when 10000 is divided by 456, the remainder is 424.
    Therefore the required number
    = 10000 + (456 -424) = 10032

  5. A certain number consists of two digits whose sum is 9. If the order of the digits is reversed, the new number is 9 less than the original number. The original number is :
    Ans : Let ten's digit be x and unit's digit be y.
    Then x + y = 9
    (10x + y) - (10y + x ) = 9 ⇒ x - y = 1
    Solving x + y = 9 & x- y =1,
    we get x = 5 & y = 4
    Therefore the required number = 54


Practise Test:


  1. 24 is divided into two parts such that 6 times the first part exceeds 4 times the second part by 4. Find the first part.
    1) 14   2) 16   3) 10   4) 12

  2. The sum of 11 results is 55. The sum of the first 6 results is 30 and that of the last 6 is 48. Find the sixth result.
    1) 20   2) 24   3) 13   4) 23

  3. The total age of 9 boys is 128. The total age of the first 4 boys is 62 and that of the next 4 boys is 48. Find the age of the 9th boy.
    1) 16   2) 18   3) 12   4) 17

  4. 340 soldiers are arranged in a parade such that the number of soldiers in each column is the same as the number of columns. Find how many soldiers are excluded from the group to make such an arrangement possible.
    1) 16   2) 21   3) 14   4) 24

  5. 25. The smallest number which must be subtracted from 1300 to make it a perfect square is
    1) 2   2) 3   3) 4  4) 6

Answers Practise Test:


1. (3)   2. (4)   3. (2)   4. (1)   5. (3)

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