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Let Z be the largest number that is made up of each of the digits 1 through 9 exactly once and is
divisible by 99. Wh

Question

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Let Z be the largest number that is made up of each of the digits 1 through 9 exactly once and is
divisible by 99. What is the digit in the hundredth place, in such a number? Please note – A number
passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.​

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Allison 4 weeks 2021-09-18T22:32:04+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-09-18T22:33:33+00:00

    Given : Z be the largest number that is made up of each of the digits 1 through 9 exactly once and is

    divisible by 99.

    To Find :   digit in the hundredth place, in such a number

    Solution:

    Largest  number possible = 987654321

    Number should be divisible by 99 means 9 * 11

    sum of 9 digits = 45 hence Divisible by 9  

    Divisible by 11

    9 – 8 + 7 – 6 + 5 – 4 + 3 – 2  + 1

    = ( 25) – (20)

    = 5

    we need to make this 5 as 0  or  11

    it can not be made 0 as  sum of all numbers = 45 Hence one sum will be odd and one will be even

    so we nee to get 11

    for that we need to get  28  – 17  = 11

    Swap 1 with 4   or  3 with 6  or  5 with  8  

    but Swap 1 with 4   will give the largest number

    Hence

    987651324  is the largest is divisible by 99

    9 – 8 + 7 – 6 + 5 – 1 + 3 – 2  + 4

    = 28  – 17  =  11

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