Hi, there. I'm happy to help with this.
Jason's salary and Karen's salary were each p percent greater in 1998 than in 1995. What is the value of p?
(1) In 1995 Karen's salary was $2000 greater than Jason's.
(2) In 1998 Karen's salary was $2240 greater than Jason's.
Statement #1:
In 1995 Karen's salary was $2000 greater than Jason's.
Let K be Karen's salary in 1995, and J, Jason's salary in 1995. This tell us
K - J = 2000
Absolutely no information about p. This statement, by itself, is wildly
insufficient.
Statement #1:
In 1998 Karen's salary was $2240 greater than Jason's.
Here, p is an integer percent --- change it into a multiplier: M = (1 + p/100). Then
M*K - M*J = M*(K - J) = 2440.
Here, with this statement only, we have no information about J - K, so we can't solve for M, which would allow us to solve for p. Statement #2, by itself, is
insufficient.
Combined statements:
We have
(i) K - J = 2000
(ii) M*(K - J) = 2440
Combining, we have M*2000 = 2440 ---> M = 2440/2000 = 1.22
M = 1 + p/100 = 1.22
p/100 = 0.22
p = 22%
Combining the statements allows us to solve for the percent. The moral is: the difference between two quantities increases by the same percent by which the individual quantities increase. Combined, the statements are
sufficient.
Answer =
C
Does all this make sense? Let me know if you have any further questions.
Mike
