Number System


  1. What least value must be assigned to ‘*’ so that the number 451 * 603 is exactly divisible by 9?









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    If the sum of the digits of a number be divisible by 9, the number is divisible by 9.
    Sum of the digits of 451 * 603 = 4 + 5 + 1 + * + 6 + 0 + 3

    Correct Option: B

    If the sum of the digits of a number be divisible by 9, the number is divisible by 9.
    Sum of the digits of 451 * 603 = 4 + 5 + 1 + * + 6 + 0 + 3
    Sum of the digits of 451 * 603 = 19 + *
    If * = 8, then 19 + 8 = 27 , which is divisible by 9.


  1. What least value must be assigned to ‘*’ so that the number 63576*2 is divisible by 8 ?









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    A number is divisible by 8 if number formed by the last three digits is divisible by 8.

    Correct Option: C

    A number is divisible by 8 if number formed by the last three digits is divisible by 8.
    ∴  If * is replaced by 3, then 632 ÷ 8 = 79
    Hence required answer is 3 .



  1. The least number that must be subtracted from 1294 so that the remainder when divided by 9, 11 and 13 will leave in each case the same remainder 6, is :









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    LCM of 9, 11 and 13 = 9 × 11 × 13 = 1287
    ∴  Required lowest number that leaves 6 as remainder = 1287 + 6 = 1293

    Correct Option: C

    LCM of 9, 11 and 13 = 9 × 11 × 13 = 1287
    ∴  Required lowest number that leaves 6 as remainder = 1287 + 6 = 1293
    ∴  Required answer = 1294 – 1293 = 1


  1. Number of composite numbers lying between 67 and 101 is :









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    Number of numbers lying between 67 and 101
    ⇒  101 – 67 – 1 = 33
    Prime numbers ⇒  71, 73, 79, 83,

    Correct Option: A

    Number of numbers lying between 67 and 101
    ⇒  101 – 67 – 1 = 33
    Prime numbers ⇒  71, 73, 79, 83,
    89 and 97 = 6
    ∴  Composite numbers = 33 – 6 = 27



  1. The least number that must be added to 8961 to make it exactly divisible by 84 is :









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    Correct Option: A


    ∴  Required number = 84 – 57 = 27