LUANDATO wrote:Several people are sitting around a round table playing a card game with a deck of 50 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?
A. 4
B. 5
C. 7
D. 11
E. 13
Algebraic approach:
Let p = the number of people at the table.
After the
p people at the table each receive
c cards -- for a total of
pc cards -- the 1 remaining card is given to Martin, with the result that he receives the last card.
Since the deck is composed of 50 cards, we get:
pc + 1 = 50
pc = 49.
The resulting equation indicates that p must be a FACTOR OF 49.
The correct answer is
C.
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