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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) \(100m + 100n + mn = 4300\)
M24-19
(1) \(mn = 300\)
(2) \(100m + 100n + mn = 4300\)
M24-19
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28 Aug 2023, 08:52
Kudos
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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?
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
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
General Discussion
03 Jan 2011, 19:50
Kudos
Bookmarks
1991------------------1992-------------------1993
x ------------------ x(1+M/100)------------------x(1+M/100)(1+N/100)
% Increase from 1991 to 1993
(x(1+M/100)(1+N/100) - X) * 100
--------------------------------------- = N+M+MN/100 = (100N+100N+MN)/100 = 4300/100 = 43 %
x
So only B is needed.
x ------------------ x(1+M/100)------------------x(1+M/100)(1+N/100)
% Increase from 1991 to 1993
(x(1+M/100)(1+N/100) - X) * 100
--------------------------------------- = N+M+MN/100 = (100N+100N+MN)/100 = 4300/100 = 43 %
x
So only B is needed.
