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On January 1st, Olivia deposited a certain amount of money into Bank A, and Ethan deposited a certain amount of money into Bank B. Both accounts earn simple annual interest. If after the initial deposits, no withdrawals or additional deposits were made, did Olivia deposit more money than Ethan?
(1) After one year, the amount of interest Olivia earned on her deposit was 20% greater than the amount of interest Ethan earned on his deposit.
(2) Bank A offers a simple annual interest rate of 5%, and Bank B offers a simple annual interest rate of 4%.
(1) After one year, the amount of interest Olivia earned on her deposit was 20% greater than the amount of interest Ethan earned on his deposit.
(2) Bank A offers a simple annual interest rate of 5%, and Bank B offers a simple annual interest rate of 4%.
29 Apr 2025, 02:31
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Official Solution:
On January 1st, Olivia deposited a certain amount of money into Bank A, and Ethan deposited a certain amount of money into Bank B. Both accounts earn simple annual interest. If after the initial deposits, no withdrawals or additional deposits were made, did Olivia deposit more money than Ethan?
(1) After one year, the amount of interest Olivia earned on her deposit was 20% greater than the amount of interest Ethan earned on his deposit.
More interest does not necessarily mean a greater initial deposit; it would also depend on the interest rate. Not sufficient.
(2) Bank A offers a simple annual interest rate of 5%, and Bank B offers a simple annual interest rate of 4%.
This is also clearly insufficient, since we are asked about the initial deposits.
(1)+(2) Bank A's interest rate is 25% higher than Bank B's (5 is 25% greater than 4). If Olivia and Ethan had deposited equal amounts, then Olivia would have earned exactly 25% more in interest. Since she earned only 20% more, she must have deposited less than Ethan. Sufficient.
Answer: C
On January 1st, Olivia deposited a certain amount of money into Bank A, and Ethan deposited a certain amount of money into Bank B. Both accounts earn simple annual interest. If after the initial deposits, no withdrawals or additional deposits were made, did Olivia deposit more money than Ethan?
(1) After one year, the amount of interest Olivia earned on her deposit was 20% greater than the amount of interest Ethan earned on his deposit.
More interest does not necessarily mean a greater initial deposit; it would also depend on the interest rate. Not sufficient.
(2) Bank A offers a simple annual interest rate of 5%, and Bank B offers a simple annual interest rate of 4%.
This is also clearly insufficient, since we are asked about the initial deposits.
(1)+(2) Bank A's interest rate is 25% higher than Bank B's (5 is 25% greater than 4). If Olivia and Ethan had deposited equal amounts, then Olivia would have earned exactly 25% more in interest. Since she earned only 20% more, she must have deposited less than Ethan. Sufficient.
Answer: C
