Number System


  1. The digit in the unit’s place of the product (2464)1793 × (615)317 × (131)491 is









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    (4)2m gives 6 at unit digit.
    (4)2m +1 gives 4 at unit digit.
    (5)n gives 5 at unit place.

    Correct Option: A

    (4)2m gives 6 at unit digit.
    (4)2m +1 gives 4 at unit digit.
    (5)n gives 5 at unit place.
    The same is the case with 1.
    ∴  Required digit = Unit’s digit in the product of 4× 5 × 1 = 0


  1. The digit in unit’s place of the product 81 × 82 × 83 × ... × 89 is









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    The digit in unit’s place = unit’s digit in the product 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
    See the 5 and 8 from given unit place of product will multiply and give 0 at unit place.

    Correct Option: A

    The digit in unit’s place = unit’s digit in the product 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
    See the 5 and 8 from given unit place of product will multiply and give 0 at unit place and then other unit place number will multiply with 0 and final number will be 0 at unit place.



  1. The sum of three consecutive integers is 51. The middle one is :









  1. View Hint View Answer Discuss in Forum

    Let us assume the 3 consecutive numbers are x, x + 1 and x + 2.
    According to question,
    ∴  x + x + 1 + x + 2 = 51

    Correct Option: D

    Let us assume the 3 consecutive numbers are x, x + 1 and x + 2.
    According to question,
    ∴  x + x + 1 + x + 2 = 51
    ⇒  3x + 3 = 51
    ⇒  3x = 51 – 3 = 48

    ⇒  x =
    48
    = 16
    3

    ⇒ Middle number = 16 + 1= 17


  1. Six numbers are arranged in decreasing order. The average of the first five numbers is 30 and the average of the last five numbers is 25. The difference of the first and the last numbers is :









  1. View Hint View Answer Discuss in Forum

    Let us assume that six numbers are p, q, r, s, t, u.
    According to the given question, Numbers are in decreasing order :
    p > q > r > s > t > u
    Again according to the question,
    p + q + r + s + t = 5 × 30

    q + r + s + t + u = 5 × 25

    Correct Option: B

    Let us assume that six numbers are p, q, r, s, t, u.
    According to the given question, Numbers are in decreasing order :
    p > q > r > s > t > u
    Again according to the question,
    p + q + r + s + t = 5 × 30
    ⇒ p + q + r + s + t = 150     --- (i)
    q + r + s + t + u = 5 × 25
    ⇒ q + r + s + t + u = 125     --- (ii)
    By equation (i) – (ii)
    p – u = 150 – 125 = 25



  1. If the difference between the reciprocal of a positive proper fraction and the fraction itself be 9/20 then the fraction is









  1. View Hint View Answer Discuss in Forum

    Let us assume that the fraction is P.

    Therefore Reciprocal of the given fraction P  = 
    1
    .
    P

    According to given question,
    P
    =
    9
    1P20

    Correct Option: C

    The required fraction is  
    4
    ,
    5

    because
    5
    4
    =
    25 − 16
    =
    9
    452020