You divide a 4 digit whole number by a 2 digit divisor. There is no remainder. The sum of the digits in the quotient is 9. What numbers might you have divided.

Question

Please help.

Answer 1

Work backwards. Start with the unknown two digit divisor and an unknown two digit quotient. When multiplied together they must produce four digits.

 

100 times any two digit number has four digits. So does 99 times a two digit number greater than 10. Etc.

 

Pick a two digit number that has digits adding to 9. You can take it from there. One example is 99*36=3564, so 3564 divided by 99.

 

Note you have the choice whether the quotient has two or three digits. Four is not a possibility, because at the very least a four digit number times a two digit number is times 10, so that adds a zero, giving 5 digits. But with three digits we have 10*711 = 7110. Etc.

 

Note you can look at it in the two digit case as (10a + b)(10c + 9 - c), which is (10a+b)9(1+c), and then you find digits a,b,c that produce four digits.

 

I hope that helps!