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## Jason's and Karen's salary percent increase

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 0 member replies
Olga Lapina Junior | Next Rank: 30 Posts
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#### Jason's and Karen's salary percent increase

Mon Feb 17, 2014 10:19 am
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

How to solve this one? Is it simply deviding (4,440 - 2,000) by 2,000?

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Brent@GMATPrepNow GMAT Instructor
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Mon Feb 17, 2014 10:38 am
Olga Lapina wrote:
Jason's salary and Karen's salary were each p percent greater in 1998 than in 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
Target question: What is the value of p?

Given: Jason's salary and Karen's salary were each p percent greater in 1998 than in 1995.
IMPORTANT: If my 1998 salary is p percent greater than my 1995 salary, then: 1998 salary = (1 + p/100)(1995 salary)
For example, if my 1998 salary is 7 percent greater than my 1995 salary, then: 1998 salary = (1 + 7/100)(1995 salary) = 1.07(1995 salary)

Let K = Karen's salary in 1995
Let J = Jason's salary in 1995
So, (1 + p/100)K = Karen's salary in 1998
And (1 + p/100)J = Jason's salary in 1998

Statement 1: In 1995 Karen's salary was $2,000 greater than Jason's So, we get K - J = 2000 So there's no information about p, so we can't determine the value of p Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: In 1998 Karen's salary was$2,440 greater than Jason's
We get: (1 + p/100)K - (1 + p/100)J = 2400
NOTICE that we can rewrite this as: (1 + p/100)(K - J) = 2400
Since we cannot solve this equation for p, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From statement 1, we concluded that K - J = 2000
From statement 2, we concluded that (1 + p/100)(K - J) = 2400

Now take the second equation and replace (K - J) with 2000 to get: (1 + p/100)(2000) = 2400
At this point, we need only recognize that we COULD solve this equation for p, but we're not going to, since this would waste valuable time on the time-sensitive GMAT.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

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GMATGuruNY GMAT Instructor
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Mon Feb 17, 2014 1:39 pm
Quote:
Jasonâ€™s salary and Karenâ€™s salary were each p percent greater in 1998 than in 1995. What is the value of p?
a) In 1995, Karenâ€™s salary was $2,000 greater than Jasonâ€™s b) In 1998, Karenâ€™s salary was$2,400 greater than Jasonâ€™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.

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Jeff@TargetTestPrep GMAT Instructor
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Thu Dec 07, 2017 7:40 am
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 Jasonâ€™s salary in 1998 and (1 + p/100)K is Karenâ€™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

Letâ€™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.

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Jeffrey Miller Head of GMAT Instruction

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