SOLUTION: Given that the number 5913d8 is divisible by 12, what is the sum of all the digits that could replace d?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Given that the number 5913d8 is divisible by 12, what is the sum of all the digits that could replace d?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 220710: Given that the number 5913d8 is divisible by 12, what is the sum of all the digits that could replace d?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5913d8 is only divisible by 12 only if 5913d8 is divisible by both 3 and 4.





5913d8 is divisible by 4 only if the last two digits are divisible by 4. In other words, 5913d8 is divisible by 4 only if d8 is divisible by 4. This restricts the choices of d to: 0, 2, 4, 6, and 8

5913d8 is divisible by 3 only if the sum of the digits are divisible by 3. So add them up to get: 5+9+1+3+d+8=26+d. Now just plug in the possible values of d to determine if 26+d is divisible by 3.

d=0: 26+0=26 which is NOT divisible by 3. So d=0 is eliminated.
d=2: 26+2=28 which is NOT divisible by 3. So d=2 is eliminated.
d=4: 26+4=30 which is divisible by 3. So d=4 is one digit.
d=6: 26+6=32 which is NOT divisible by 3. So d=6 is eliminated.
d=8: 26+8=34 which is NOT divisible by 3. So d=8 is eliminated.


So the only number that is divisible by 12 is 591348. So the sum of all the digits that could replace 'd' is 4.