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A certain species of banana has been genetically engineered to never go soft if the skin is purple. In a sample of unknown size, $50\%$ of bananas are purple and firm and $25\%$ of non-purple bananas are soft.

If there are two fewer non-purple firm bananas than purple firm bananas, how many bananas are in the sample?

A

$20$

B

$16$

C

$12$

D

$10$

E

Insufficient information was​ given to answer the question.

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