Average


  1. The average of the first 100 positive integers is









  1. View Hint View Answer Discuss in Forum

    As we know that ,

    1 + 2 + 3 +.........+ n =
    n(n + 1)
    2

    Average of these numbers =
    (n + 1)
    2

    Here , n = 100

    Correct Option: C

    As we know that ,

    1 + 2 + 3 +.........+ n =
    n(n + 1)
    2

    Average of these numbers =
    (n + 1)
    2

    Here , n = 100
    ∴ Required average =
    100 + 1
    = 50.5
    2


  1. The average of 7 consecutive numbers is 20. The largest of these numbers is :









  1. View Hint View Answer Discuss in Forum

    Average of 7 consecutive numbers is 20.
    Since the numbers are consecutive, they form an arithmetic series with common difference 1.
    Since, 7 is odd, 20 must be the middle number.
    We can write the series as below,
    17, 18, 19, 20, 21, 22, 23

    Correct Option: B

    Average of 7 consecutive numbers is 20.
    Since the numbers are consecutive, they form an arithmetic series with common difference 1.
    Since, 7 is odd, 20 must be the middle number.
    We can write the series as below,
    17, 18, 19, 20, 21, 22, 23
    ∴ The largest of these numbers is 23.



  1. The average of 15 numbers is 7. If the average of the first 8 numbers is 6.5 and the average of the last 8 numbers is 8.5, then the middle number is :









  1. View Hint View Answer Discuss in Forum

    Given that , The average of 15 numbers = 7
    The average of the first 8 numbers = 6.5
    and the average of the last 8 numbers = 8.5
    Middle i.e. eighth number = 8 × 6.5 + 8 × 8.5 – 15 × 7

    Correct Option: D

    Given that , The average of 15 numbers = 7
    The average of the first 8 numbers = 6.5
    and the average of the last 8 numbers = 8.5
    Middle i.e. eighth number = 8 × 6.5 + 8 × 8.5 – 15 × 7
    Middle i.e. eighth number = 52 + 68 – 105
    Middle i.e. eighth number = 120 – 105 = 15


  1. The average of 8 numbers is 21. If each of the numbers is mulitiplied by 8, the average of the new set of numbers is :









  1. View Hint View Answer Discuss in Forum

    Here , The average of 8 numbers = 21
    When each number is multiplied by 8, the new average gets multiplied by 8.

    Correct Option: D

    Here , The average of 8 numbers = 21
    When each number is multiplied by 8, the new average gets multiplied by 8.
    So , New average = 21 × 8 = 168



  1. The average of 11 numbers is 63. If the average of first six numbers is 60 and the last six numbers is 65, then the 6th number is









  1. View Hint View Answer Discuss in Forum

    Given , Sum of 11 numbers = 63 × 11 = 693
    Sum of the first 6 numbers = 60 × 6 = 360
    and Sum of the last 6 numbers = 65 × 6 = 390
    ∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers

    Correct Option: A

    Given , Sum of 11 numbers = 63 × 11 = 693
    Sum of the first 6 numbers = 60 × 6 = 360
    and Sum of the last 6 numbers = 65 × 6 = 390
    ∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers
    Sixth number = 360 + 390 – 693 = 57