Growth in Salaries

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actofman: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Tue Oct 30, 2012 9:48 am

by actofman » Tue Apr 23, 2013 12:59 am

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

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 23, 2013 12:59 am

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by Anju@Gurome » Tue Apr 23, 2013 1:36 am

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.

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Quant Expert, Gurome

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 23, 2013 2:27 am

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

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, let p=10%.
Difference in 1995: K-J.
Difference in 1998: 1.1K - 1.1J = 1.1(K-J).
The difference increases by p=10%.

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.

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