What is the sum of the digits of the ID number of my ATM card?
The alphabets PQRSTUVWX represent the nine-digit number with the given property.
Deduction 1 : Since all numbers having even digits have to be divisible by even numbers (i.e., PQ is divisible by 2, PQRS is divisible by 4, PQRSTU is divisible by 6 and PQRSTUVW is divisible by 8), Q, S, U & W must be the 4 even numbers viz. 2, 4, 6 and 8 in some random order. Consequently, P, R, T, V & X (the odd placed digits) must be sharing the odd digits 1,3, 5,7 and 9 in some order.
Deduction 2: Since PQRST is divisible by 5, T must be equal to 5. Thus, the number must be PQRS5UVWX.
Deduction 3: PQR is divisible by 3 and PQRSTU is divisible by 6, hence STU must be divisible by 3, i.e., S + T+U=S+5+U must be divisible by 3. Also, S and U are even numbers. Through trial and error you should realise that there are only two ways this could happen:
(a) If STU represents 258
or (b) If STU represents 654
Note: S can only be 2 or 6 since for PQRS to be divisible by 4, RS should be divisible by 4 and R being an odd number, S can only be 2 or 6.
Deduction 4: The following 4 options of filling in the other two even numbers (4 and 6 in case STU is 258 or 2 and 8 in case STU is 654) emerge:
Sum of digits - 1+2+3+4+5+6+7+8+9=45