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

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VP
Joined: 21 Jul 2006
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Janson's salary and Karen's salary were each p percent  [#permalink]

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11 Dec 2007, 15:22
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Question Stats:

67% (01:00) correct 33% (01:10) wrong based on 704 sessions

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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 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.
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Janson's salary and Karen's salary were each p percent  [#permalink]

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02 Nov 2010, 07:25
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anilnandyala wrote:
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.

Given: $$j_2=j_1(1+\frac{p}{100})$$ and $$k_2=k_1(1+\frac{p}{100})$$. Qurestion: $$p=?$$

(1) $$k_1-j_1=2,000$$. Not sufficient to calculate $$p$$.
(2) $$k_2-j_2=2440$$. Not sufficient to calculate $$p$$.

(1)+(2) $$k_2-j_2=2440=k_1(1+\frac{p}{100})-j_1(1+\frac{p}{100})$$ --> $$2440=k_1(1+\frac{p}{100})-j_1(1+\frac{p}{100})=(1+\frac{p}{100})(k_1-j_1)=(1+\frac{p}{100})2,000$$ --> $$2440=(1+\frac{p}{100})2,000$$. Sufficient to to calculate $$p$$.

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%.

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11 Dec 2007, 16:11
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Answer is C. Right off the bat without doing any math.

Taken separately we don't know anything.

Taken together...

We know that their salaries grew further apart by $440. They started off in 1995 as$2,000 apart. That means the $440 increase must have come from the$2,000 difference.

440/2000 = P

(using a calculator to prove it)

440/2000 = 22% (or 2,440/2000 = 1.22)

10,000(1.22) = 12,200
12,000(1.22) = 14, 640
14,640-12,200 = 2,440

50,000(1.22) = 61,000
52,000(1.22) = 63,440
63,440-61,000 = 2,440

No need to do the math on the real test. Just realize that you know how much their salaries started and that if there is any change in the difference it must've come from the original difference in salary.

C it is.
##### General Discussion
Intern
Joined: 25 Nov 2007
Posts: 38
Re: DS: Percentage Salary Increase  [#permalink]

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11 Dec 2007, 16:19
tarek99 wrote:
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.

A insufficient
B Insufficient

Combining
From A,
In 1995

Janson's salary = J
Karen's salary = J+2000

In 1998

Janson's salary = J*0.p + J
Karen's salary = ((J+2000) * 0.p) + (J +2000)

Also, from B
((J+2000) * 0.p) + (J +2000) = (J*0.p + J) +2440
2000*0.p=440

Ans C

Whats the OA
Director
Joined: 12 Jul 2007
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11 Dec 2007, 16:56
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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. Director Joined: 12 Jul 2007 Posts: 853 ### Show Tags 11 Dec 2007, 17:09 7 1 tnguyen707 wrote: eschn3am wrote: 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

I tested this method, and it works. I still can't visualize it. Oh well, I guess whatever works!

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.
VP
Joined: 21 Jul 2006
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12 Dec 2007, 02:24
1
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
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Joined: 29 Aug 2007
Posts: 2420
Re: DS: Percentage Salary Increase  [#permalink]

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12 Dec 2007, 21:32
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1
tarek99 wrote:
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.

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%
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19 Oct 2010, 03:13
C it is.

1) insuff. as info given: J + 2000 = K, and no time scale to relate to P.
2) insuff. as above

both - I assumed suff as I think we had enough data.
solve the two equations:
J + 2000 = k
J + (J*P) + 2400 = k + (k*P)

P = 22%

Manager
Joined: 15 Apr 2010
Posts: 157

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19 Oct 2010, 03:28
Both statements alone do not help, so we have to look at both statements together.

In 1995:
Ka = Ja + 2000

In 1998:
Kb = Jb + 2400

Since Kb = Ka(1 + p/100),

Ka(1 + p/100) = Ja(1 + p/100) + 2400

Substitute Ka

(Ja + 2000)(1 + p/100) = Ja(1 + p/100) + 2400

solving we get p = 20%

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19 Oct 2010, 03:36
1
satishreddy wrote:
jasons salary and karen salary were each p percent greater in 1998 than in 1995, what is the value of p

1) in 1995 karens salary was $2000 greater than jasons 1) in 1998 karens salary was$2400 greater than jasons

Combining these 2 statement we can get the value of p.
Because 2000 would also have increased with the same percentage p.
means, 2000 + 2000(p/100) = 2400
or p = (400* 100)/2000 = 20%.

Consider KUDOS if u find this helpful to u .Thanks
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Re: jason's salary & karen's salary  [#permalink]

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02 Nov 2010, 17:59
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
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(2) In 1998 Karen's salary was $2,440 greater than Jason's. Here's how I did it. (1) 95 increased by p 98 Jason S Karen (S+2000) Not sufficient (2) 95 increased by p 98 Jason Y Karen Y+ 2 400 Not Suffictient. So combining: (S+2000)xP/100-2440=SP/100 2000P/100=2440 20P=2440 P=2440/20 P=122 22% increase Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2727 Re: Janson's salary and Karen's salary were each p percent [#permalink] ### Show Tags 11 Nov 2016, 08:07 1 tarek99 wrote: 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. 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 _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions CEO Joined: 12 Sep 2015 Posts: 2702 Location: Canada Re: Janson's salary and Karen's salary were each p percent [#permalink] ### Show Tags 13 Jan 2018, 07:28 Top Contributor tarek99 wrote: 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. 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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Re: Janson's salary and Karen's salary were each p percent &nbs [#permalink] 13 Jan 2018, 07:28
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