Find sum of all the 3 digit number formed by using digits 2, 5, 7 & 9 (repetition being not allowed)

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10 Jan 2018 Sum of Digits

Find sum of all the 3 digit number formed by using digits 2, 5, 7 & 9 (repetition being not allowed).

OPtion

1) 14112
2) 15246
3) 13860
4) 12466
5) 13986
6) 15600
7) 12726
8) 14238
9) 12978
10)None of these

Solution

Total combination are
{2,5,7}, {2,5,9}, {2,7,9} and {5,7,9}

2*(13)*111+2*15*111+ 2*17*111 + 2*18*111

In every set of 3 numbers, 6 arrangements are possible - with each digit being 2 times at hundred place, 2 times at tens place and 2 times at units place. For example in case of {2,5,7} = 257, 275, 527, 572, 725, 752

So Sum of all numbers formed from set {2,5,7} = 2*(2+5+7)*100 + 2*(2+5+7)*10 + 2*(2+5+7)*1 = 3108
Similarly,
Sum of all numbers formed from set {2,5,9} = 2*(2+5+9)*100 + 2*(2+5+9)*10 + 2*(2+5+9)*1 = 3552
Sum of all numbers formed from set {2,7,9} = 2*(2+7+9)*100 + 2*(2+7+9)*10 + 2*(2+7+9)*1 = 3996
Sum of all numbers formed from set {5,7,9} = 2*(5+7+9)*100 + 2*(5+7+9)*10 + 2*(5+7+9)*1 = 4662

Sum of all = 15318

Correct Option: 10 Best Solution (1)

G.S.Kantharao   6 years AGO

Numbers are 257+259+275+279+295+297+527+529+572+579+592+597+725+729+752+759+792+795+925+927+952+957+972+975=15318
Hence my option is 10👈

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