Sally is thinking of a number. The product of the digits is one half of the number. What is the smallest positive, two-digit integer she could be thinking of?
+1223 Sally's number, AB, can be represented as 10A + B, where A and B are the individual digits.
AB = (10A + B)/2
AB - 5A - B/2 = 0
2AB - 10A - B = 0
(2A - 1)(B - 5) = 5
Case 1: 2A - 1 = 5 and B - 5 = 1
A = 3, B = 6
Case 2: 2A - 1 = 1 and B - 5 = 5
B = 10, so this doesn't work.
The number is 36.
