Olga Lapina wrote:Jason's salary and Karen's salary were each p percent greater in 1998 than n 1995.
What is the value of p?
1. In 1995 Karen's salary was $2,000 greater than Jason's
2. In 1998 Karen's salary was $2,440 greater than Jason's
We are given that Janson's salary and Karen's salary were each p percent greater in 1998 than in 1995, and we need to determine the value of p.
We can let J = Janson's salary in 1995 and K = Karen's salary in 1995. Therefore, (1 + p/100)J is Jason's salary in 1998 and (1 + p/100)K is Karen's salary in 1998.
Statement One Alone:
In 1995 Karen's salary was $2,000 greater than Janson's.
This means K = J + 2000. However, that is not enough information to determine the value of p. Statement one alone is not sufficient. We can eliminate answer choices A and D.
Statement Two Alone:
In 1998 Karen's salary was $2,440 greater than Janson's.
Using the information in statement two, we can create the following equation:
(1 + p/100)K = (1 + p/100)J + 2440
However, this is still not enough information to determine p. Statement two alone is not sufficient. We can eliminate answer choice B.
Statements One and Two Together:
From the two statements, we have the following:
K = J + 2000
(1 + p/100)K = (1 + p/100)J + 2440
Let's simplify the second equation:
We can start by dividing both sides by (1 + p/100) and obtain:
K = J + 2440/(1 + p/100)
K - J = 2440/(1 + p/100)
From our first equation, we know that K - J = 2,000. Thus, we can substitute 2,000 for K - J in our second equation and we have:
2000 = 2440/[(1 + p/100)]
Since we know that we can determine p, we can stop here. The two statements together are sufficient.
Answer:
C
