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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?

 Feb 22, 2021
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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.

 Feb 22, 2021

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