Even and Odd Draws

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The player of a certain game drew a number of cards from a deck in which each card was labeled with an integer from 1 to 10. Four more even than odd numbers were drawn. How many times were even numbers drawn?

(1) The player drew 12 cards.

(2) The player received 4 points for each even number and 2 points for each odd number drawn, for a total of 40 points.