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02 Jul 2023, 07:28
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D
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Difficulty:
45%
(medium)
Question Stats:
77% (02:21) correct
23%
(02:40)
wrong
based on 1042
sessions
History
Date
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Not Attempted Yet
In 1998 Jean's annual salary was greater than Kevin's annual salary. In each of 1999 and 2000, Jean's annual salary was 3 percent greater in that year than in the preceding year and Kevin's annual salary was also 3 percent greater in that year than in the preceding year. By what percent did the difference between Jean's and Kevin's annual salaries increase from 1998 to 2000 ?
A. 3%
B. 3.03%
C. 6%
D. 6.09%
E. 9.03%
A. 3%
B. 3.03%
C. 6%
D. 6.09%
E. 9.03%
04 Jul 2023, 04:47
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MasteringGMAT
difference_1998 = j - k
Since “3 percent greater” corresponds to a factor of 1.03, we have:
difference_1999 = j(1.03) – k(1.03)
difference_2000 = j(1.03)^2 – k(1.03)^2 = (j – k)(1.03)^2
So,
difference_2000 = (1.0609)(j – k)
Since a factor of 1.0609 corresponds to a 6.09% increase, the difference in question increased by 6.09%.
Answer: D
02 Jul 2023, 07:56
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MasteringGMAT
We can use two approaches to solve this question -
1) Logic Approach
As both Kevin's and Jean's salaries have increased by the same percentage the percentage of difference will remain constant.
Assume that the initial difference between their salaries = d
Difference in the first year = 1 + (1 * \(\frac{3}{100}\)) d = 1.03d
Difference in the second year = [1.03 + (1.03 * \(\frac{3}{100}\))] d = 1.0609 d
% change = \(\frac{0.0609 d }{ d} * 100 = 6.09\) %
2) Formula
If \(x_1\) represents the percentage change in year 1 and \(x_2\) represents the percentage change in year 2, the cumulative percentage change is given by \(x_1 + x_2 + \frac{x_1*x_2}{100}\)
In this problem, both \(x_1\) and \(x_2\) are 3
Cumulative change (%) = \(3 + 3 + \frac{3*3}{100 }= 6 + 0.09 = 6.09\)%
Option D
