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24 May 2018, 06:03
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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:
15%
(low)
Question Stats:
88% (01:51) correct
12%
(01:54)
wrong
based on 70
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A pianist agreed to perform one concert at a fee 12.5 percent less than her usual fee and a second concert at a fee 20 percent greater than the first fee. The fee for the second concert was what percent greater than her usual fee?
A. 5%
B. 7.5%
C. 15%
D. 16.25%
E. 32.5%
A. 5%
B. 7.5%
C. 15%
D. 16.25%
E. 32.5%
24 May 2018, 07:43
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Bunuel
Let usual fee be 40
So, The fee for 1st Concert is 35
And ,The fee for 2nd Concert is 42
Quote:
ie, \(\frac{42 - 40}{40}*100\) = \(5\)%, Answer must be (A)
25 May 2018, 12:48
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Bunuel
If there is successive percent change, we can
Use multipliers. Two ways:
(1) Formula for successive percent change
If there are only two successive percent changes, overall percent change can be found with a very simple formula
\(A + B + \frac{A*B}{100}\) [percent]
\(A\) = first percent change \(= -12.5\)
\(B\) = second percent change = \(+20\)
Overall percent change:
\(-12.5 + 20 + (\frac{-12.5*20}{100})\) [percent]
\(-12.5 + 20 + (-\frac{250}{100})\) [percent]
\((-12.5+20-2.5) = 5\) percent greater than original (because 5 is positive)
(2) Multiply the multipliers:
Numbers:(.875*1.2=1.05)
Fractions
Multiplier for percent decrease: \(12.5 =.125=\frac{1}{8}\)
\(1-\frac{1}{8}=\frac{7}{8}\) of usual fee
Multiplier for percent increase: \(20=.20=\frac{1}{5}\)
\(1+\frac{1}{5}=\frac{6}{5}\)
Multiply the multipliers:
\((\frac{7}{8}*\frac{6}{5})=\frac{21}{20}=1\frac{1}{20}\)
Subtract 1 to find percent change.
\((1\frac{1}{20}-1)=(\frac{1}{20}*100)=.05*100=5\)% greater than original
Answer A
