actofman wrote: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
Let us assume that Jason's and Karen's salary in 1995 was $J and $K, respectively.
So, Jason's salary in 1998 = J + p% of J = J + (p/100)*J = J*(1 + p/100)
and, Karen's salary in 1998 = K + p% of K = K + (p/100)*K = K*(1 + p/100)
To simplify the representation, let us assume (1 + p/100) = n
So, Jason's and Karen's salary in 1998 was nJ and nK, respectively.
Statement 1: (K - J) = 2,000
We cannot determine p from this information.
Not sufficient
Statement 2: (nK - nJ) = 2,400
We cannot determine p from this information.
Not sufficient
1 & 2 Together: From statement 2, n(K - J) = 2,400
So, n(K - J)/(K - J) = 2,400/2,000
--> n = 6/5
--> (1 + p/100) = 6/5
We can uniquely determine the value of p from the above equation.
Sufficient
The correct answer is C.
