CEMC Pascal, 1998

Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

A deck of 100 cards is numbered from 1 to 100. Each card has the same number printed on both sides. One side of each card is red and the other side is yellow. Barsby places all the cards, red side up, on a table. He first turns over every card that has a number divisible by 2. He then examines all the cards, and turns over every card that has a number divisible by 3. How many cards have the red side up when Barsby is finished?

(A) $83$ (B) $17$ (C) $66$ (D) $50$ (E) $49$

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