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.

Answer: C

Source: GMAT Prep

## 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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VJesus12 wrote: ↑Sat Oct 16, 2021 4:51 amJanson'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.

Answer: C

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

Answer: C

Cheers,

Brent