Data Sufficiency

Jason's salary and Karen's salary were both p percent greater in 1998 than 1995. What is value of p?

1)In 1999 Karen's salary was $2000 greater than Jason's
2) In 1995 Karen's salary was $24440 greater than Jason's

Not sure if we are assuming p percent as same increase for both of them?

Thanks

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%.
SUFFICIENT.

Is there any shortcut for this method? and May I know if this is a hard or medium level question?

parulmahajan89 wrote:Is there any shortcut for this method? and May I know if this is a hard or medium level question?

Hi Parul,

Percent is same, but we cannot assume the increment same too, as that depends on the respective base salaries. Statement (2) is very impractical salary-wise. Further, this question is not copied correctly. I have seen this question before and answered [spoiler]C[/spoiler] without any math. In most of the occasions on DS, common sense saves all the hard work and time for us.

The correct question as suggested by Mitch is:

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.

Key fact here is that the difference in salaries would also increase by the same percent, and the two differences are given in the two statements, [spoiler]hence C, and this is a hard problem for the beginners[/spoiler].