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06 Aug 2026, 03:54
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At the beginning of 2024, Elena divided $1,200 between two savings accounts, Account A and Account B. The amount placed in Account A earned simple interest at 9% per year, and the amount placed in Account B earned simple interest at 5% per year. If no additional deposits or withdrawals were made in either account, by the end of 2024 was the interest earned by Account A greater than the interest earned by Account B?
(1) Elena placed less than one-third of the $1,200 in Account A.
(2) By the end of 2024, the total interest earned by the two accounts was $74.
(1) Elena placed less than one-third of the $1,200 in Account A.
(2) By the end of 2024, the total interest earned by the two accounts was $74.
06 Aug 2026, 03:54
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Official Solution:
At the beginning of 2024, Elena divided $1,200 between two savings accounts, Account A and Account B. The amount placed in Account A earned simple interest at 9% per year, and the amount placed in Account B earned simple interest at 5% per year. If no additional deposits or withdrawals were made in either account, by the end of 2024 was the interest earned by Account A greater than the interest earned by Account B?
Let \(x\) be the amount placed in Account A. Then the amount placed in Account B was \(1,200 - x\).
Since the money stayed in the accounts for one year, the interest earned by Account A was \(0.09x\), and the interest earned by Account B was \(0.05(1,200 - x)\).
The question asks:
Is \(0.09x > 0.05(1,200 - x)\)?
Is \(0.09x > 60 - 0.05x\)?
Is \(0.14x > 60\)?
Is \(\frac{7}{50} * x > 60\)?
Is \(x > \frac{3,000}{7}\)?
Since \(\frac{3,000}{7} \approx 430\), Account A earned more interest than Account B only if \(x > \frac{3,000}{7} \approx 430\).
(1) Elena placed less than one-third of the $1,200 in Account A.
One-third of 1,200 is 400, so \(x < 400\). Since \(x < 400\), Account A definitely did not earn more interest than Account B.
Sufficient.
(2) By the end of 2024, the total interest earned by the two accounts was $74.
So:
\(0.09x + 0.05(1,200 - x) = 74\)
\(0.09x + 60 - 0.05x = 74\)
\(0.04x = 14\)
\(x = 350\)
Since \(x = 350\), Account A did not earn more interest than Account B.
Sufficient.
Answer: D
At the beginning of 2024, Elena divided $1,200 between two savings accounts, Account A and Account B. The amount placed in Account A earned simple interest at 9% per year, and the amount placed in Account B earned simple interest at 5% per year. If no additional deposits or withdrawals were made in either account, by the end of 2024 was the interest earned by Account A greater than the interest earned by Account B?
Let \(x\) be the amount placed in Account A. Then the amount placed in Account B was \(1,200 - x\).
Since the money stayed in the accounts for one year, the interest earned by Account A was \(0.09x\), and the interest earned by Account B was \(0.05(1,200 - x)\).
The question asks:
Is \(0.09x > 0.05(1,200 - x)\)?
Is \(0.09x > 60 - 0.05x\)?
Is \(0.14x > 60\)?
Is \(\frac{7}{50} * x > 60\)?
Is \(x > \frac{3,000}{7}\)?
Since \(\frac{3,000}{7} \approx 430\), Account A earned more interest than Account B only if \(x > \frac{3,000}{7} \approx 430\).
(1) Elena placed less than one-third of the $1,200 in Account A.
One-third of 1,200 is 400, so \(x < 400\). Since \(x < 400\), Account A definitely did not earn more interest than Account B.
Sufficient.
(2) By the end of 2024, the total interest earned by the two accounts was $74.
So:
\(0.09x + 0.05(1,200 - x) = 74\)
\(0.09x + 60 - 0.05x = 74\)
\(0.04x = 14\)
\(x = 350\)
Since \(x = 350\), Account A did not earn more interest than Account B.
Sufficient.
Answer: D
