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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Anju@Gurome
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Let us assume that Jason's and Karen's salary in 1995 was $J and $K, respectively.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
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.
Anju Agarwal
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Since Jason's salary grew by p%, and Karen's salary grew by p%, the DIFFERENCE between their salaries also grew by p%.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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