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14 November, 19:54

11.1.30

How many three-digit even numbers are possible if the leftmost digit cannot be zero?

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  1. 14 November, 20:17
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    The total number of 3 digit even numbers is 450

    Step-by-step explanation:

    Step 1:

    We need to determine the number of 3 digit numbers which is even and the leftmost digit is not zero.

    The 3 digits with left most digit not equal to zero starts from 100 and goes up to 998

    If we consider only the even 3 digit numbers in this interval, this would form an arithmetic progression with the first number a = 100 and the common difference d = 2.

    Step 2:

    The last number l in this series is 998.

    So we have

    a = 100

    l = 998

    d = 2

    The nth term in the arithmetic progression is given by a + (n-1) d

    so substituting the above values we get

    100 + (n-1) 2 = 998

    2n = 900 = > n = 450

    Step 3:

    Answer:

    The total number of 3 digit even numbers is 450
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