Question

A two-digit positive integer x has the property that when 109 is divided by x, the remainder is 4. What is the sum of all such two-digit positive integers x

Answer 1

The sum of the two digits integers which divide 109 with a remainder of 4 is 71

Explanation:

The given parameters are;

109/x = Q + 4/x

Therefore, we have;

109 = Q·x + 4

∴ Q·x = 109 - 4 = 105

x = 105/Q

Therefore, x is a factor of 105

The possible two digits integers which x represents includes the two digit factors of 105 which are;

15, 21, and 35

Which gives;

15 × 7 = 105

21 × 5 = 105

35 × 3 = 105

The sum of the two digits integers which divide 109 with a remainder of 4 is 15 + 21 + 35 = 71.