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29 Jul 2024, 07:10
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Charlie invested \($x\) in Fund A for one year at an annual simple interest rate of \(p\) percent. What would be the total value of this investment at the end of that period?
(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.
(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.
(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.
(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.
29 Jul 2024, 07:10
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Official Solution:
Charlie invested \($x\) in Fund A for one year at an annual simple interest rate of \(p\) percent. What would be the total value of this investment at the end of that period?
This is a fairly straightforward question, but some might fall into the C-trap or mistakenly choose D as the answer.
Essentially, we need to find the value of \(x(1 + \frac{p}{100})\).
(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.
This implies that \((2x)(1 + \frac{p}{100}) = 220\), which, by dividing by 2, yields \(x(1 + \frac{p}{100}) = 110\). This is exactly what we want to find. Sufficient.
Or, by simple reasoning, if doubling the initial investment amounts to $220 in one year, the initial investment will amount to half of that, so $110.
(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.
This implies that \(x(1 + \frac{2p}{100}) = 120\), which cannot be simplified to get the value of \(x(1 + \frac{p}{100})\) nor can it be solved to get the individual values of \(x\) and \(p\) to calculate \(x(1 + \frac{p}{100})\). Not sufficient.
Answer: A
Charlie invested \($x\) in Fund A for one year at an annual simple interest rate of \(p\) percent. What would be the total value of this investment at the end of that period?
This is a fairly straightforward question, but some might fall into the C-trap or mistakenly choose D as the answer.
Essentially, we need to find the value of \(x(1 + \frac{p}{100})\).
(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.
This implies that \((2x)(1 + \frac{p}{100}) = 220\), which, by dividing by 2, yields \(x(1 + \frac{p}{100}) = 110\). This is exactly what we want to find. Sufficient.
Or, by simple reasoning, if doubling the initial investment amounts to $220 in one year, the initial investment will amount to half of that, so $110.
(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.
This implies that \(x(1 + \frac{2p}{100}) = 120\), which cannot be simplified to get the value of \(x(1 + \frac{p}{100})\) nor can it be solved to get the individual values of \(x\) and \(p\) to calculate \(x(1 + \frac{p}{100})\). Not sufficient.
Answer: A
23 Apr 2025, 19:46
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Question says simple interest and not compound interest.
Incase of SI, From statement 1, value of investment should be 110 while value from statement should be 60 thus contradictory. Thus, answer should be "E"
Incase of SI, From statement 1, value of investment should be 110 while value from statement should be 60 thus contradictory. Thus, answer should be "E"
