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?

Guest Feb 22, 2021

#1**-1 **

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.**

CubeyThePenguin Feb 22, 2021