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Apples and Oranges - Answer

There are 800 inhabitants of Pennsville, Pennsylvania.

In this puzzle, oranges represent truth. Apples represent lies. From the statement that each man says his sister likes apples, we can deduce that in each brother/sister pair, one lies and one tells the truth. Therefore, there are as many lying men as truthful women and visa versa.

From the statement that each wife says her husband likes oranges, we can deduce that in each married couple, one lies and one does not.

From there deductions, we can deduce further as follows:

1. The statement that 100 inhabitants like oranges and 80 men like apples are either both true or both false.
   
   
2. One of the statements that 80 women like apples and that 20 men like oranges is true and one is false.
   
   
3. One of the statements that 4/5 of the men like apples and that 80 women like oranges is true and one is false.

The only solution that satisfies these requirements is 80 men and 320 women like oranges and 80 women and 320 men like apples.

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