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

Not at all.

All we have to do is realize that a $2,000 difference grew to a $2,440 when multiplied by P. This makes for a 22% increase and the information holds true for any two numbers $2,000 apart.

500,000*1.22 = 610,000
502,000*1.22 = 612,440

2,000*1.22 = 2440
4,000*1.22 = 4880

answer is definitely C.

Try thinking of it like this.

We know that in 1995 Karen's salary was $2,000 greater than Jason's
We know that in 1998 Karen's salary was $2,440 greater than Jason's

Between 1995 and 1998 each of their salaries increased by the same percentage (P)

If Jason makes $10,000 and Karen makes $12,000 then we know that Jason's 10K and Karen's first 10K each increased by the same amount. They would be dead even in 1998 if Karen didn't make $2,000 more.

This means that Karen's $2,000 had to increase by $440 (to get to $2,440) all on it's own. So what percentage increase do you need for $2,000 to become $2,440? this is your answer. and that's why you can choose C without doing any math.

I'm not the best with explanations, but I hope this helps somewhat.

OA is C. but the way i saw this, the difference of 440 didn't make any sense to me. I thought C is possible ONLY if the 2 people have the exact same salary from the beginning. but we don't even know that. a 5% increase on a salary of $10 will not yield the same as a salary of $100. that's why i picked E. both could yield different dollar amounts, but both have the same percentage increase. but after looking at the explanation, i guess if this works, then so be it. i never realised you could get to such an answer by only having the gaps between the 2 actually amounts. cool

1995: Janson's salary = j
Karen's salary = k

1998: Janson's salary = j (1+p)
Karen's salary = k (1+p)

1: in 1995, k = j + 2000
2: in 1998, k(1+p) = j (1+p) + 2440

togather: k(1+p) = j (1+p) + 2440
(j + 2000) (1+p) = j (1+p) + 2440
2000 + 2000p = 2440
p = (2440 - 2000)/2000
p = 22%

Since question asks for the comparison between 1995 and 1998 salaries, a quick look at the statements will tell you that neither alone is sufficient. Now the question remains whether together they are sufficient. Let's analyze.

In 1995:
J salary - J;
K salary - J + 2000

In 1998: (Their salaries are now p% greater)
J salary- J + p% of J;
K salary- (J + 2000) + p% of (J + 2000)= J + p% of J + 2000 + p% of 2000

Compare the salaries in red. According to second statement, their difference is 2440.
So we can say p% of 2000 = 440. On solving, we get p = 22

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 Jason’s salary in 1998 and (1 + p/100)K is Karen’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

Let’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.

Answer: C

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:
Cheers,
Brent

What if you thought of it this way: There are 2 rules that must remain valid throughout: 1. the difference between Karen's and Jason's salary each year and 2. The percentage change for each person must be the same. Therefore:

- Is there anyway to get a another difference between Karen's and Jason's salary (i.e. 2000 and 2440) for each year respectively while keeping the percentage change for each person the same? No.
- Could you have the percentage change for each person different while keeping the difference between the two salaries for each respective year the same? No.

Can you change one of the input factors on this chart while keeping the output factors the same?

If not, (without breaking one of the rules, you can't), then the answer is C.

Video solution from Quant Reasoning starts at 9:30
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Folks above have provided many equations so I won't add to those. However, in this particular what I found helpful was taking x and y variables for salaries of Jason and Karen. It is evident that it can only be done through algebra. I didn't find taking hypothetical figures as easy for this one and stuck with lettered variables.

I made a simpler version -
1995 ( j) 1998(j)
4 10
1995 (k) 1998(k)
16 40

Now on combi both statements the % will remain the same i.e the difference in salary = % change from 1995 ( j) to 1998(j)
The only diff. you need to pull out is the change factor 40 - 10 = 10(4 - 1) and 16 -4 = 4(4-1)
10/4 change factor = 150% and 1995 ( j) 1998(j) = 10/4 same 150%

Bunuel

You have mentioned above "Or another way: difference between their salaries increased by 2440-2000=440, which is 440/2000*100=22%, but difference increases proportionally with the salaries, so increase in salary is also 22%."

but this will not always be the case

for eg let's say A & B are having salaries 10$ and 14$ respectively so difference is 4$
Now let's say after salary increase difference increased to 8$ so difference increased by 100%.

But if we talk about their individual salary increase it's not always the case that individual salaries should also increase by 100%.
Let's say if A's salary increased from 10$ to 12$ and B's salary increased from 14$ to 20$ , then in this case though salary difference increased by 100% but individual salaries did not increase by 100%

The question stated that both salaries were EACH increased by p percent. Your scenario violate this condition. If both salaries are increased by the same percentage, p, then the difference between them will also increase by p percent.

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