We Can Figure Something Out
I have 2 distinct positive integers.
The sum of these two integers is either 4 or 5.
The product of these two integers is either 4 or 6.
What can we deduce from the information above?
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1 solution
Moderator note:
Great explanation of this problem. I was quite amazed at the complexity of these simple statments.
If the sum is 4, then because the two positive integers are distinct, they must be 1 and 3. But then their product is 3, none among the available choices. So the sum must be 5 .
Note that we don't know the product. For a sum of 5, we can have either 1 and 4, or 2 and 3. The first gives product 4, and the second gives product 6, and both are valid.