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Gardo picks a number. He doubles the number, squares the result, divides the square by three, subtracts 30 from the quotient, and gets 18.

Gardo picks a number. He doubles the number, squares the result, divides the square by three, subtracts 30 from the quotient, and gets 18. What are the possible numbers that Gardo could have picked? What operation does Gardo perform which prevents us from knowing the exact number he picked?

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