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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 ?
  • a)
    4
  • b)
    5
  • c)
    6
  • d)
    7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A player holds 13 cards of four suits, of which seven are black and si...
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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Most Upvoted Answer
A player holds 13 cards of four suits, of which seven are black and si...
To solve this question, we need to use the given information and apply logical reasoning to find the number of clubs the player holds.

Given information:
- The player holds 13 cards in total.
- There are four suits: clubs, spades, diamonds, and hearts.
- There are seven black cards and six red cards.
- There are twice as many diamonds as spades.
- There are twice as many hearts as diamonds.

Step 1: Identify the number of each suit
Let's assume the number of clubs is 'C', spades is 'S', diamonds is 'D', and hearts is 'H'.
According to the given information, we can write the following equations:

1. C + S + D + H = 13 (total number of cards)
2. C + S = 7 (number of black cards)
3. D + H = 6 (number of red cards)
4. D = 2S (twice as many diamonds as spades)
5. H = 2D (twice as many hearts as diamonds)

Step 2: Solve the equations
Using equations 4 and 5, we can substitute the values of D and H in terms of S:

D = 2S
H = 2D = 2(2S) = 4S

Now, substitute these values in equation 3:

D + H = 6
2S + 4S = 6
6S = 6
S = 1

Now we can substitute the value of S in equation 2 to find C:

C + S = 7
C + 1 = 7
C = 6

Therefore, the player holds 6 clubs (option C)
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