In 1998 Jean's annual salary was greater than Kevin's annual salary

Question

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%

JeffTargetTestPrep · Accepted Answer

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

gmatophobia · Answer

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 =  \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

nazii · Answer

hello Dear friend
would you pls explain how I should understand this? "Since a factor of 1.0609 corresponds to a 6.09% increase, the difference in question increased by 6.09%.". How can I learn this?

sayan640 · Answer

Learn it in this way :-
Initital diff = j -k
final diff = (1.0609)(j – k)
Just simplify this - ((1.0609)(j – k) - (j-k) )/ (j-k) * 100  = increase in the difference

Jake7Wimmer · Answer

Can someone show how to do this with picking numbers. Think I am doing something wrong.

Bunuel · Answer

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%

Since both Kevin's and Jean's salaries increase by the same percentage, the difference between their salaries will likewise increase by that percentage. Assuming an initial difference of $100 in 1998, it would rise to $100*1.03 = $103 in 1999 (a 3% increase) and further to $103*1.03 = $106.09 in 2000 (an additional 3% increase). This results in a total increase of 6.09%.

An even easier approach would be to recognize that the difference increases by 3%, plus 3% of 3%, totaling slightly more than 6%. Therefore, only option D, 6.09%, fits this calculation.

Answer: D.

KarishmaB · Answer

Jean's salary has increased by 3% in two successive years. This will be an overall increase of slightly more than 6%. Kevin's salary has also increased by 3% in two successive years. This will be the same overall increase of slightly more than 6% as Jean's. Say this is 6.1% (we don't really need to calculate) If the difference between their salaries was J - K initially, now the difference between their salaries has also increased by the same 'slightly more than 6%' The only possible answer here is 6.09% (slightly more than 6%) Answer (D) If you are not sure, think about this: When something increases by 10% say, the multiplier is 11/10. If both a and b increase by 10% each, their difference becomes (11/10)a - (11/10)b = (11/10)(a - b) Hence their difference also increases by 10%. Check this video on using multipliers with percentages: https://youtu.be/HxnsYI1Rws8 and this post on successive percentage changes https://anaprep.com/arithmetic-successi ... e-changes/

mayankdgmat · Answer

Let their respective salaries be j & k. Where j>k

Difference in 1998 = j-k

Difference in 2000=1.03^2 (j-k)

let j-k is some variable a

Increase in difference = a(1.03^2-1^2) ........use a^2-b^2 = (a+b)(a-b)
=a*2.03*0.03

So % increase= ((2.03*0.03a)/a)*100= 6.09

Prajeesh · Answer

Sure, It's easier if you use numbers.

So we are given that Jean's 1998 salary > Kevin's 1998 salary, so for easing calculation I'll assume,

Jean 1998 Salary = 200

Kevin 1998 salary = 100

The Diff b/w their salaries= 200 - 100 = 100 .

Now for 1999 both salaries increased 3%

Jean 1999 = 200 + 6 = 206

Kevin 1999 = 100 + 3 = 103

Again for 2000, both salaries increased by 3%

Jean 2000 = 206 + (2.06*3) = 212.18

Kevin 2000 = 103 + (1.03*3) = 106.09

Now the difference b/w salaries during 2000 = (212.18 - 106.09) = 106.09

So from a difference of  100  to a difference of  106.09 , that's a  6.09% Increase

Hence D

(Pro tip: Assume values in such a way that the precentage calculation would always be easier)

P_Tripathy · Answer

In 1998 
Let, Jean's annual salary = 200
Kevin's annual salary = 100

For 1999 
Jean = 206 (3% increase)
Kevin = 103 (3% increase)

For 2000 
Jean = 212.18
Kevin = 106.09

Difference -

1998 : 200-100= 100
2000 : 212.18 - 106.06 = 106.09

100 to 106.09 is 6.09% increase.

Hence  D

P_Tripathy · Answer

In 1998 
Let, Jean's annual salary = 200
Kevin's annual salary = 100

For 1999 
Jean = 206 (3% increase)
Kevin = 103 (3% increase)

For 2000 
Jean = 212.18
Kevin = 106.09

Difference -

1998 : 200-100= 100
2000 : 212.18 - 106.06 = 106.09

100 to 106.09 is 6.09% increase.

Hence  D

In 1998 Jean's annual salary was greater than Kevin's annual salary

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In 1998 Jean's annual salary was greater than Kevin's annual salary

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