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16 Sep 2014, 00:37
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Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?
A. 14%
B. 27%
C. 30%
D. 34%
E. 35%
THIS QUESTION HAS BEEN RETIRED,
A. 14%
B. 27%
C. 30%
D. 34%
E. 35%
THIS QUESTION HAS BEEN RETIRED,
16 Sep 2014, 00:37
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Official Solution:
Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?
A. 14%
B. 27%
C. 30%
D. 34%
E. 35%
The price of $216 is irrelevant to finding the answer.
For any price \(X\) the customer would pay:
The percentage difference = \(100\% * \frac{1.7X - 1.2X}{1.7X} = 100\% * \frac{0.5}{1.7} \approx 100\% * \frac{0.51}{1.7} = 30\%\)
Answer: C
Two payment schemes are available for customers in the N'K store. The first scheme includes a down payment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a down payment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?
A. 14%
B. 27%
C. 30%
D. 34%
E. 35%
The price of $216 is irrelevant to finding the answer.
For any price \(X\) the customer would pay:
- First scheme: \(0.2X + 10*0.1X = 1.2X\)
- Second scheme: \(0.1X + 20*0.08X = 1.7X\)
The percentage difference = \(100\% * \frac{1.7X - 1.2X}{1.7X} = 100\% * \frac{0.5}{1.7} \approx 100\% * \frac{0.51}{1.7} = 30\%\)
Answer: C
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