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If x represents the sum of all the positive three-digit

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Re: If x represents the sum of all the positive three-digit  [#permalink]

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New post 28 May 2020, 13:05
3 digit number (pqr) can be written as 100p + 10q +r

Given: x is the sum of all possible number that cn be formed using digits a,b,c once in a 3 digit number:

x= (100a + 10b + c) + (100a + 10c + b) + (100b + 10c + a) + (100b + 10a +c) + (100c + 10b + a) + (100c + 10a +b)
x = 222 * (a+b+c)


Hence the largest number by which x will be divisible will be 222


Assumption method: Let three digits be 1,2,3

x = 123 + 213 + 132 + 312 + 231 + 321 = 1332 = 222 * 6
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Re: If x represents the sum of all the positive three-digit  [#permalink]

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New post 13 Jul 2020, 08:54
There are 6 arrangements of 'a', 'b', and 'c'. i.e. 'abc', 'acb'...etc

try a few values to identify the pattern

let a,b,&c = 4,5,&6 respectively

in units, tens and hundreds the sum would be 2(15) hence the sum of all 6 variations would 3330 (considering the carry over too)
Now, 3330 = 333*10= 3*111*2*5 (hightest 222)

try for any other value youll arrive at the same ans
let a,b,&c = 1,2,&3respectively
sum = 1332
1332 = 3*111*2*2
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Re: If x represents the sum of all the positive three-digit   [#permalink] 13 Jul 2020, 08:54

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If x represents the sum of all the positive three-digit

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