Brainteasers....

sydtech2515

Question 1:
A bag contains 100 cards with letters on them. There are 50 cards with a letter A on them, 25 cards with a letter B, and 40 cards with a letter C.
There are only 30 seconds remaining for this question. Referring to the scenario above, if only 10 cards have both letters A and B, how many cards definitely have only the letter C and NOT the letter A or B on them?

Question 2:
The 20 balls in a box have either 0 (blank), 1, or 2 letters on them. If five balls have only a C on them, two balls have only a B on them, and two balls have an A and a C on them, what is the maximum number of balls that can be blank?

AKG

1. # of cards with either A or B = # of cards with A + # of cards with B - # of cards with both A and B = 50 + 25 - 10 = 65. I assume when you say, "only 10 cards have both letters A and B" that means that ten cards have either AB or ABC on them. Anyways, # of cards with just C on them = # of cards with no A and no B = 100 - # of cards with A or B - 100 - 65 = 35.

2. Is this a trick? 20 - 5 - 2 - 2 = 11.