SOLUTION: Find digits a and b such that the number 34a47b5893 is divisible by 99.

Question 75181: Find digits a and b such that the number 34a47b5893 is divisible by 99.
Answer by nilan(17) (Show Source): You can put this solution on YOUR website!
Suppose 34a47b5893 is divisible by 99
Then obviously it is divisible by 9
If a number is divisible by 9 the sum of all the digits should divisible by 9 (this can be easily proved)
For example let the number abcd divisible by 9 then
where k is positive integer
Then

then a+b+d+c is divisible by 9
This can be proved for any number (can be given a general proof. Try it)
Again to the problem
Then the sum of 34a47b5893 is divisible by 9
Then 3+4+a+4+7+b+5+8+9+3 is divisible by 9
Then
43+a+b is divisible by nine
Then a=0 and b=2
Or a=2 and b = 0
RELATED QUESTIONS
Numbers are to be built using only the digits 1,2,3,4, and 5 in such a way that each... (answered by lotusjayden,greenestamps)

find a number that; The last digit is even Sum of the digits is divisible by 3 The... (answered by jim_thompson5910)

Dee finds that she has an extraordinary social security number. Its nine digits contain... (answered by ankor@dixie-net.com)

find the least 5 digit number which is exactly divisible by 20,25,30? and find the... (answered by Edwin McCravy)

Find the smallest number such that if 35 is subtracted from that number the result is... (answered by josgarithmetic)

If the sum of the digits is divisible by 9 that number is also divisible by A 9 B 6 C... (answered by jim_thompson5910)

If the sum of the digits is divisible by 9 that number is also divisible by 9,6,4,and... (answered by solver91311)

A five digit number is formed using digits 0 1 2 3 and 4 without repetition. Find the... (answered by Alan3354,ikleyn)

Find the three digit number such that the sum of its digits is equal to 12, the product... (answered by CPhill)