self Maths Puzzle

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.

Read Solution (Total 2)

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,

new number = 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
10 years agoHelpfull: Yes(7) No(1)

6 is the digit struck off bcoz if the 4 digit number is 4281 then the sum of its digits is 15 and 4281-15 is 4266 ,so if we struck off the units place digit i.e. 6,the remaining 3 digits are 2,4,6.
10 years agoHelpfull: Yes(2) No(1)

self Other Question

On planet Jupiterthe people use a certain number system to the base 'n' (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of 'n' is the least possible value there the decimal representation of the difference between Jerk's correct wage for the day is A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?
option
1. a must be 2
2. c must be 2
3. b must be 0
4. None of these