Number System


  1. When a number is divided by 357 the remainder is 39. If that number is divided by 17, the remainder will be :









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    Here, 357 is exactly divisible by 17.
    ∴  Required remainder = Remainder obtained on dividing 39 by
    17

    Correct Option: C

    Here, 357 is exactly divisible by 17.
    ∴  Required remainder = Remainder obtained on dividing 39 by
    17
    ⇒ 39 = ( 17 × 2 ) + 5
    Hence required answer is 5 .


  1. A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively.
    When it is successively divided by 5 and 4 the respective remainders will be









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    According to question ,
    The least number X in this case will be determined as follows:
    Y = 5 × 1 + 4 = 9

    X = 4 × Y + 1 = 4 × 9 + 1 = 37
    Now,

    Correct Option: C

    According to question ,
    The least number X in this case will be determined as follows:
    Y = 5 × 1 + 4 = 9

    X = 4 × Y + 1 = 4 × 9 + 1 = 37
    Now,

    Hence, the respective remainders are 2, 3.



  1. Each member of a picnic party contributed twice as many rupees as the total number of members and the total collection was 3042. The number of members present in the party was









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    Let the required number of persons be N.
    According to the question,
    2N2 = 3042

    Correct Option: A

    Let the required number of persons be N.
    According to the question,
    2N2 = 3042

    ⇒   N2 =
    3042
    = 1521
    2

    ⇒   N = √1521 = 39


  1. In a division problem, the divisor is 4 times the quotient and 3 times the remainder. If remainder is 4, the dividend is









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    Given , Remainder = 4
    According to question ,
    Divisor = 3 × Remainder
    ⇒ Divisor = 3 × 4 = 12
    Again, divisor = 4 × quotient
    ⇒ 4 × quotient = 12

    Correct Option: B

    Given , Remainder = 4
    According to question ,
    Divisor = 3 × Remainder
    ⇒ Divisor = 3 × 4 = 12
    Again, divisor = 4 × quotient
    ⇒ 4 × quotient = 12

    ⇒ Quotient =
    12
    = 3
    4

    ⇒ Dividend = 3 × 12 + 4 = 40



  1. How many natural numbers divisible by 7 are there between 3 and 200 ?









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    Number just greater than 3 which is divisible by 7 = 7
    Number just smaller than 200
    which is divisible by 7 = 196
    Here, a = 7, an = 196,
    d = 7, n = 8

    Correct Option: B

    Number just greater than 3 which is divisible by 7 = 7
    Number just smaller than 200
    which is divisible by 7 = 196
    Here, a = 7, an = 196,
    d = 7, n = 8
    ∴ an = a + (n –1)d
    ⇒ 196 = 7 + (n – 1) × 7

    ⇒ n − 1 =
    196 − 7
    = 27
    7

    ⇒  n = 27 + 1 = 28
    2nd method to solve this question
    We can find the answer after dividing 200 by 7.
    The quotient is our answer.