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04 Aug 2023, 05:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (01:50) correct
28%
(02:02)
wrong
based on 1116
sessions
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Kylie invested a certain amount of money at r% yearly interest compounded at the end of each year and the same amount of money at (r + 2)% yearly interest compounded at the end of each year. What was the amount of money that Kylie invested at the (r + 2)% yearly interest rate?
(1) At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.
(2) r = 3
(1) At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.
(2) r = 3
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04 Aug 2023, 05:15
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Bunuel
Let's assume the amount Kylie invests = p
Statement 1
(1) At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.
For the first year, the interest obtained via compound interest and the interest obtained via simple interest are the same.
Interest Obtained at the end of the first year :
Investment 1 : \(\frac{p * 1 * r}{100}\)
Investment 2 : \(\frac{p * 1 * (r+2)}{100}\)
Given
\(\frac{p * 1 * (r+2)}{100} - \frac{p * 1 * r}{100} = 200\)
\(\frac{2p}{100} = 200\)
We can find p. The statement alone is sufficient. We can eliminate B, C, and E.
Statement 1
(2) r = 3
Just by knowing the rate, we cannot find the principal amount.
The statement alone is not sufficient.
Option A
06 Sep 2023, 18:15
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Bunuel
If x dollars was invested at r%, and x dollars was invested at (r + 2)%, then we need to answer the question:
x = ?
Statement One Alone:
=> At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.
The following equation represents the relationship between the amounts of interest earned on the two investments:
x[(r + 2)/100] = x(r/100) + 200
xr + 2x = xr + 20,000
2x = 20,000
x = $10,000
Statement one is sufficient. Eliminate answer choices B, C, and E.
Statement Two Alone:
=> r = 3
Since no information is given about any actual dollar amounts, we can’t answer the question. Statement two is not sufficient.
Answer: A
