Number System


  1. 999
    998
    × 999 is equal to :
    999









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    999
    998
    × 999
    999

    = 999
    998
    × 999
    999

    Correct Option: A

    999
    998
    × 999
    999

    = 999
    998
    × 999
    999

    Required answer = 9992 + 998
    Required answer = (1000 – 1)2 + 998
    Required answer = 1000000 – 2000 + 1 + 998
    Required answer = 998999


  1. The number which is to be added to 0.01 to get 1.1, is









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    Let p be added to given number .
    According to question ,
    ⇒ p + 0.01 = 1.1
    ⇒ p = 1.1 - 0.01

    Correct Option: B

    Let p be added to given number .
    According to question ,
    ⇒ p + 0.01 = 1.1
    ⇒ p = 1.1 - 0.01
    ∴ Required number = 1.1 – 0.01 = 1.09



  1. If [n] denotes the greatest integer < n and (n) denotes the smallest integer > n, where n is any real number, then
    1
    1
    ×1
    1
    1
    1
    ÷1
    1
    + (1.5) is
    5555









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    [n] < n (integer); (n) > n (integer)
    ∴ Expression

    1
    1
    ×1
    1
    1
    1
    ÷1
    1
    + (1.5) = 2 × 1 – 2 ÷ 1 + 2
    5555

    Correct Option: B

    [n] < n (integer); (n) > n (integer)
    ∴ Expression

    1
    1
    ×1
    1
    1
    1
    ÷1
    1
    + (1.5) = 2 × 1 – 2 ÷ 1 + 2 = 2
    5555


  1. Which one of the following will completely divide 571 + 572 + 573 ?









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    571 + 572 + 573 = 571 (1 + 5 + 52)

    Correct Option: C

    571 + 572 + 573 = 571 (1 + 5 + 52)
    ⇒ 571 + 572 + ⇒ 573 = 571 × which is exactly divisible by 155.
    Hence required answer is 155 .



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









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    ∴ The required number = 11 – 4 = 7
    2nd Method to solve this question :
    Sum of digits at odd places = 2 + 6 + 0 = 8

    Correct Option: C


    ∴ The required number = 11 – 4 = 7
    2nd Method to solve this question :
    Sum of digits at odd places = 2 + 6 + 0 = 8, sum of digits at even places = 4 + 3 + 8 = 15. For divisibility by 11, difference i.e., (15 – 8) = 0 or mutiple of 11.
    ∴ The required number = 7