Janson's salary and Karen's salary were each $$p$$ percent greater in $$1998$$ than in $$1995.$$ What is the value of

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Janson's salary and Karen's salary were each $$p$$ percent greater in $$1998$$ than in $$1995.$$ What is the value of

by VJesus12 » Sat Oct 16, 2021 4:51 am
Janson'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.

Source: GMAT Prep

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Re: Janson's salary and Karen's salary were each $$p$$ percent greater in $$1998$$ than in $$1995.$$ What is the value o

by [email protected] » Sat Oct 16, 2021 5:57 am
VJesus12 wrote:
Sat Oct 16, 2021 4:51 am
Janson'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.

Source: GMAT Prep
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