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16 Sep 2014, 01:21
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Price increased by \(m\%\) from 1991 to 1992 and by \(n\%\) from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?
(1) \(mn = 300\)
(2) \(100m + 100n + mn = 4300\)
(1) \(mn = 300\)
(2) \(100m + 100n + mn = 4300\)
20 Apr 2016, 01:55
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herein
Check below links for theory and practice on percents:
Percentages, Interest and More
Compound Interest Problems from our Special Questions Directory.
Theory on Percent and Interest Problems
DS Percent and Interest Problems
PS Percent and Interest Problems
General Discussion
16 Sep 2014, 01:21
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Official Solution:
Price increased by \(m\%\) from 1991 to 1992 and by \(n\%\) from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?
Increasing some value by \(x\%\) is the same as multiplying by \(1 + \frac{x}{100}\). For example, if you increase something by 10% you multiply by \(1 + \frac{10}{100}= 1.1\). Hence, after the increase by \(m\%\) and then by \(n\%\), the price would become \((1 + \frac{m}{100})(1 + \frac{n}{100}) = 1 + \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}\) times the original price.
(1) \(mn = 300\).
From the above, we cannot deduce the value of \((1 + \frac{m}{100})(1 + \frac{n}{100}) \). Not sufficient.
(2) \(100m + 100n + mn = 4300\).
Dividing the above by 10,000 gives \(\frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}=0.43\). Adding 1 to both sides gives \(1 + \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}=1.43\). Therefore, the price increased by 43%. Sufficient.
Answer: B
Price increased by \(m\%\) from 1991 to 1992 and by \(n\%\) from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?
Increasing some value by \(x\%\) is the same as multiplying by \(1 + \frac{x}{100}\). For example, if you increase something by 10% you multiply by \(1 + \frac{10}{100}= 1.1\). Hence, after the increase by \(m\%\) and then by \(n\%\), the price would become \((1 + \frac{m}{100})(1 + \frac{n}{100}) = 1 + \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}\) times the original price.
(1) \(mn = 300\).
From the above, we cannot deduce the value of \((1 + \frac{m}{100})(1 + \frac{n}{100}) \). Not sufficient.
(2) \(100m + 100n + mn = 4300\).
Dividing the above by 10,000 gives \(\frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}=0.43\). Adding 1 to both sides gives \(1 + \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}=1.43\). Therefore, the price increased by 43%. Sufficient.
Answer: B
