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

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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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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.

Please explain your answer


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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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.

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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

answer is definitely C.


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.

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Re: jason's salary & karen's salary [#permalink]

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anilnandyala wrote:
jason's salary & karen's salary were each P percent greater in 1998 then in 1995 what is the value of
P?

a in 1995 karen's salary was $2000 greater then jason's

b in 1998 karen's salary was $2400 greater then 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%.

Answer: C.
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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.

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let salaries at 95 be K and J each.
salaries in 98 will be p*k and p*j each. Considering p as percentage value.

in 95, k-j = 2000

in 98, p(k-j) = 2440

thus p's value can be found using these equations. Hence C.
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New post 19 Oct 2010, 03:36
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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%.
Answer is C.

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udaymathapati wrote:
Attachment:
M-Q29.JPG


Note that both of their salary increase by same p percent. In 1995 let jason's and karen's salary be j and k resp. And in 1998, let that be j1 and k1.
j1 = pj
k1 = pk

St 1 --> in 1995, k = j+2000
Not sufficient doesn't provide any info about 1998 year.

St 2--> in 1998, k1 = j1+2440
Not sufficient doesn't provide any info about 1995 year.

Both together, solve the equations -
k1 = pk
j1+2440 = p(j+2000)
j1+2440 = j1+p2000 --> p = 12.2

Answer is C

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

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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
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New post 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.



Please explain your answer


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

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New post 11 Dec 2007, 16:39
I get E.

A, Alone: K = J + 2000. Insuff
B alone: K (1 +P/100) = J(1 + P/100) + 2440. Insuff.


Together, we have three unknowns and two equations, we can't solve the equations. We must know at least one of either Janson's or Karen's salary in 1995 in order to solve for P.

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New post 12 Dec 2007, 02:24
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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jasons salary and karen salary were each p percent greater [#permalink]

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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

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New post 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%

Not sure if this is at all right. Please help

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New post 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%

So the answer is C.
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Re: jason's salary & karen's salary [#permalink]

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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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Re: jason's salary & karen's salary [#permalink]

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New post 03 May 2011, 21:42
J = (1+p/100)j

K = (1+p/100)k

(1)

k = j + 2000

Not sufficient

(2)


K = J + 2440

Not Sufficient

(1) + (2)

J/K = j/k


1 - 2440/K = 1 - 2000/k

=> K/k = 2440/2000

Substituting this in above equation 2440/2000 = (1 + p)/100



Answer - C
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Re: Percents : Jason's salary and karen's salary were P % [#permalink]

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New post 23 Apr 2013, 04:38
My answer is C
In 1995 Jason's salary J. In 1998 it would be (1+p/100)*J
In 1995 Karen's salary K. In 1998 it would be (1+p/100)*K
Stmt 1 :
K= J+2000 in 1995. We dont know about either of their salaries in 1998. Hence insufficient

Stmt 2:
(1+p/100)K=(1+p/100)J + 2440. We dont know the values of J and K . Hence insufficient.

combining. let (1+p/100)= a .
a*(j+2000) = a*J +2440.

and we can solve for a or (1+p/100) and we can find the value of P.

Hope its clear.

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

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New post 23 Apr 2013, 16:15
Look at it like it's a rate problem between two separate objects.

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Re: Janson's salary and Karen's salary were each p percent   [#permalink] 23 Apr 2013, 16:15

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