## 22Let Z be the largest number that is made up of each of the digits 1 through 9 exactly once and isdivisible by 99. Wh

Question

22
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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4 weeks 2021-09-18T22:32:04+00:00 1 Answers 0 views 0

1. 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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