Bunuel wrote:

What is the sum of all four digit integers formed using the digits 1, 2, 3 and 4 (repetition is allowed)

A) 444440

B) 610000

C) 666640

D) 711040

E) 880000

Total Numbers that can be formed by using digits 1, 2, 3 and 4 = 4x4x4x4 = 256

Now sum of all these numbers can be calculated by looking at an observation that

Any digit can come at any of the 4 places i.e. each digit will appear at unit digit 256/4 = 64 times

i.e. 1 will be used as Unit digit in 64 numbers

i.e. 2 will be used as Unit digit in 64 numbers

i.e. 3 will be used as Unit digit in 64 numbers

i.e. 4 will be used as Unit digit in 64 numbers

i.e. Sum of Unit digits of all the number = 64(1+2+3+4) = 640

i.e. Number becomes

_ _ _ 0 AND 64 GOES AS CARRY FORWARD

Any digit can come at any of the 4 places i.e. each digit will appear at ten's digit 256/4 = 64 times

i.e. 1 will be used as Tens digit in 64 numbers

i.e. 2 will be used as Tens digit in 64 numbers

i.e. 3 will be used as Tens digit in 64 numbers

i.e. 4 will be used as Tens digit in 64 numbers

i.e. Sum of Tens digits of all the number = 64(1+2+3+4) = 640

with carry forward 64, the sum becomes (640+64=704)

i.e. Number becomes

_ _ 4 0 AND 70 GOES AS CARRY FORWARD

Any digit can come at any of the 4 places i.e. each digit will appear at Hundreds digit 256/4 = 64 times

i.e. 1 will be used as Hundreds digit in 64 numbers

i.e. 2 will be used as Hundreds digit in 64 numbers

i.e. 3 will be used as Hundreds digit in 64 numbers

i.e. 4 will be used as Hundreds digit in 64 numbers

i.e. Sum of Hundreds digits of all the number = 64(1+2+3+4) = 640

with carry forward 64, the sum becomes (640+70=710)

i.e. Number becomes

_ 0 4 0 AND 71 GOES AS CARRY FORWARD

Any digit can come at any of the 4 places i.e. each digit will appear at Thousands digit 256/4 = 64 times

i.e. 1 will be used as Thousands digit in 64 numbers

i.e. 2 will be used as Thousands digit in 64 numbers

i.e. 3 will be used as Thousands digit in 64 numbers

i.e. 4 will be used as Thousands digit in 64 numbers

i.e. Sum of Thousands digits of all the number = 64(1+2+3+4) = 640

with carry forward 64, the sum becomes (640+71=711)

i.e. Number becomes

7 1 1 0 4 0 Answer: option D

Shocking solution process.