Number System


  1. A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, the remainder is :









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    According to question ,
    Number = 269 × 68 + 0
    Number = 269 × (67 + 1)

    Correct Option: B

    According to question ,
    Number = 269 × 68 + 0
    Number = 269 × (67 + 1)
    Number = 269 × 67 + 269
    Clearly, remainder is obtained on dividing 269 by 67 that is 1.
    Thus , required remainder is 1.


  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. (719 + 2) is divided by 6, the remainder is :









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    Using the Binomial expansion , we have
    (x + 1)n = xn + nc1 xn–1 +
    nc2 xn– 2 + ..... + ncn–1 x +1
    Here, each term except the last term contains x. Obviously, each term except the last term is exactly divisible by x.

    Correct Option: B

    Using the Binomial expansion , we have
    (x + 1)n = xn + nc1 xn–1 +
    nc2 xn– 2 + ..... + ncn–1 x +1
    Here, each term except the last term contains x. Obviously, each term except the last term is exactly divisible by x.
    Following the same logic,
    ∴ 719 = (6 + 1)19 has each term except last term divisible by 6.
    Hence, 719 + 2 when divided by 6 leaves remainder
    ⇒ 719 + 2 = 1 + 2 = 3
    Hence the remainder is 3.


  1. A number, when divided by 119, leaves a remainder of 19. If it is divided by 17, it will leave a remainder of :









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    On dividing the given number by 119, let k be the quotient and 19 as remainder.
    Then, number = 119k + 19

    Correct Option: D

    On dividing the given number by 119, let k be the quotient and 19 as remainder.
    Then, number = 119k + 19
    number = 17 × 7k + 17 × 1 + 2
    number = 17 (7k + 1) + 2
    Hence, the given number when divided by 17, gives (7k + 1) as quotient and 2 as remainder.
    Hence , required remainder is 2.



  1. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is :









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    Let the numbers be p and q and p is greater than q.
    As given,
    The product of two numbers = 9375
    pq = 9375     .......(i)
    Again,

    p
    = 15
    q

    Correct Option: C

    Let the numbers be p and q and p is greater than q.
    As given,
    The product of two numbers = 9375
    pq = 9375     .......(i)
    Again,

    p
    = 15
    q

    ⇒ p = 15q
    ∴ From equation (i),
    15q × q = 9375
    ⇒  q2 =
    9375
    = 625
    15

    ⇒ q = √625 = 25
    ∴ p = 15y = 15 × 25 = 375
    ∴ p + q = 375 + 25 = 400
    Hence , The sum of the numbers is 400 .