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08 Jan 2025, 04:49
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Warren has exactly three types of coins in his piggy bank: $0.25, $0.50, and $1. If the number of $0.25 coins is 8, and the number of $0.50 coins is 4, how many $1 coins does he have?
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
08 Jan 2025, 04:49
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Official Solution:
Warren has exactly three types of coins in his piggy bank: $0.25, $0.50, and $1. If the number of $0.25 coins is 8, and the number of $0.50 coins is 4, how many $1 coins does he have?
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
If the total value of the $1 coins is 50% of the total value of all the coins, the value of the $0.25 and $0.50 coins must account for the other 50%. The value of the $0.25 and $0.50 coins is $0.25 * 8 + $0.50 * 4 = $4. Since the value of the $1 coins is also $4, the number of $1 coins is $4 / $1 = 4. Sufficient.
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
The total number of $0.25 and $0.50 coins is 8 + 4 = 12. This represents 75% of the total number of coins. If 75% corresponds to 12 coins, then 25% corresponds to 12/3 = 4 coins. Thus, the number of $1 coins is 4. Sufficient.
Answer: D
Warren has exactly three types of coins in his piggy bank: $0.25, $0.50, and $1. If the number of $0.25 coins is 8, and the number of $0.50 coins is 4, how many $1 coins does he have?
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
If the total value of the $1 coins is 50% of the total value of all the coins, the value of the $0.25 and $0.50 coins must account for the other 50%. The value of the $0.25 and $0.50 coins is $0.25 * 8 + $0.50 * 4 = $4. Since the value of the $1 coins is also $4, the number of $1 coins is $4 / $1 = 4. Sufficient.
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
The total number of $0.25 and $0.50 coins is 8 + 4 = 12. This represents 75% of the total number of coins. If 75% corresponds to 12 coins, then 25% corresponds to 12/3 = 4 coins. Thus, the number of $1 coins is 4. Sufficient.
Answer: D
