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Jason's salary and Karen's salary were each p percent

Expert replies
by AAPL » Sat Dec 15, 2018 4:50 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

GMAT Prep

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 Janson's.

OA C
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Source: — Data Sufficiency |

by Brent@GMATPrepNow » Sat Dec 15, 2018 5:40 am
AAPL 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 Janson'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
There's no information about p, so we can't determine the value of p
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

Answer = C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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