The problem should read as follows:
Jason's salary and Karen's salary were each p percent greater in 1998 than in 1995. What is the value of p?
a) In 1995, Karen's salary was $2,000 greater than Jason's
b) In 1998, Karen's salary was $2,400 greater than Jason's
Since Jason's salary grew by p%, and Karen's salary grew by p%, the DIFFERENCE between their salaries also grew by p%.
To illustrate:
Case 1: Karen's 1995 salary = 150, Jason's 1995 salary = 100, p=10%.
Difference in 1995: 150-100 = 50.
Karen's 1998 salary = 150 + .1(150) = 165.
Jason's 1998 salary = 100 + .1(100) = 110.
Difference in 1998 = 165-110 = 55.
The difference increases from 50 to 55 -- an increase of p=10%.
Case 2: Karen's 1995 salary = 200, Jason's 1995 salary = 100, p=20%.
Difference in 1995: 200-100 = 100.
Karen's 1998 salary = 200 + .2(200) = 240.
Jason's 1998 salary = 100 + .2(100) = 120.
Difference in 1998 = 240-120 = 120.
The difference increases from 100 to 120 -- an increase of p=20%.
Clearly, neither statement alone is sufficient.
When the two statements are combined, the difference between the salaries increases from 2000 to 2400 -- an increase of 20%.
Thus, p=20.
The correct answer is
C.
Algebraic approach:
To make the math easier, let F be the FACTOR by which each salary increases.
Statement 1:
K-J = 2000.
No information about F.
Statement 2:
K's salary = (F)(K).
J's salary = (F)(J).
Since the difference between the two salaries is $2400, we get:
(F)(K) - (F)(K) = 2400.
F(K-J) = 2400.
No way to solve for F.
Statements combined:
Substituting K-J=2000 into F(K-j) = 2400, we get:
F(2000) = 2400
F = 2440/2000 = 240/200 = 120/100 = 120%.
Since each salary increases by a factor of 120%, the value of p -- the percent increase from 1995 to 1998 -- is 20%.
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