I take a four-digit number and subtract from it the sum of its digits. In the result I strike off one of the digits and the remaining three digits of the result are 2, 4 and 6 (not necessarily in that order). Find the digit struck off by me.  Pick one:
A) 6 B) 7 C) 8 D) 9 E) 10
Sol:   Let us assume the four digit number as wxyz. Then in base system 10 it can written as 1000w + 100x + 10y + z. Now given that,   wxyz = 1000w + 100x + 10y + z - (w + x + y + z) = 999w + 99x + 9y which is a multiple of 9   Hence the sum of digits must be a multiple of 9.   Hence 2 + 4 + 6 + x is equal to either 9, 18, 27 ...   But if the sum is equal to 9 then x is negative number. Therefore x = 6.   6nswer 6
<result>A</result>
I take a four-digit number and subtract from it the sum of its digits. In the result I strike off one of the digits and the remaining three digits of the result are 2, 4 and 6 (not necessarily in that order). Find the digit struck off by me.