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The sum of two positive real numbers is 100. Find their maximum possible product?

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The sum of two positive real numbers is 100. Find their maximum possible product?
posted Sep 5, 2015 by anonymous

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+1 vote

In a sequence of eleven real numbers, only two are shown. The product of every 3 successive boxes is 120. Find the sum of all the numbers in the boxes (including the two already open).

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Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: ‘I am not aware of those numbers.’
Jacob: ‘I knew you wouldn’t be. I am not aware myself.’
John: ‘Now I know them!’
Jacob: ‘Now I know them, too!’

What are the two numbers?

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