Question
A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold ?
Answer: Option C
Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.
Let the number of spades be x. Then, number of clubs = (7 - x).
Number of diamonds = 2 x number of spades = 2x;
Number of hearts = 2 x number of diamonds = 4x.
Total number of cards = x + 2x + 4x + 7 - x = 6x + 7.
Therefore 6x + 7 = 13 ⇔ 6x = 6 ⇔ x - 1.
Hence, number of clubs = (7 - x) = 6.
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Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.
Let the number of spades be x. Then, number of clubs = (7 - x).
Number of diamonds = 2 x number of spades = 2x;
Number of hearts = 2 x number of diamonds = 4x.
Total number of cards = x + 2x + 4x + 7 - x = 6x + 7.
Therefore 6x + 7 = 13 ⇔ 6x = 6 ⇔ x - 1.
Hence, number of clubs = (7 - x) = 6.
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