JASON'S SALARY AND KAREN'S SALARY WERE EACH P PERCENT GREATE

[Guest]

JASON'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 2,400 GREATER THAN JASON'S

HOW CAN I SOLVE THIS PROBLEM?

GMAT-PREP (DATA SUFF)

ANSWER IS C

[Guest]

JASON'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 2,400 GREATER THAN JASON'S

HOW CAN I SOLVE THIS PROBLEM?

GMAT-PREP (DATA SUFF)

ANSWER IS C

1. k=2000+j
2. (1+p%)k = 2400+ (1+p%)j => (1+p%)(2000+j)= 2400+(1+p%)j
i.e. (1+p%)2000 = 2400 u get P

[Guest]

Could someone explain how one went about solving this problem?
THANKS

[RonPurewal]

1. k=2000+j
2. (1+p%)k = 2400+ (1+p%)j => (1+p%)(2000+j)= 2400+(1+p%)j
i.e. (1+p%)2000 = 2400 u get P

this is a nice solution, short as it may be in the annotation department.

here's a brief explanation:
the poster has defined 'k' to be karen's 1995 salary, and 'j' to be jason's 1995 salary.

each of the statements alone is insufficient, because the first statement provides no information about the 'after' condition and the second statement provides no information about the 'before' condition. you need the 'before' AND the 'after' to figure out anything involving percentage changes.

you can write the '98 salaries as (1 + p%)k and (1 + p%)j, as the original poster has done, or you can write them as (1 + p/100)k and (1 + p/100)j. it's immaterial; either approach is fine.

then write the equation, in pretty much exactly the same way as in the above post.

the important realization at this step is that there's no reason to solve the resulting equation all the way; it's sufficient to stop at the point where the j's cancel, whereupon 'p' is the only variable left in play. at that point, you have a linear equation in one variable, which can therefore be solved. that's sufficient - no need to actually solve.

[Anon]

Hi Ron,

cant we assume that the difference also would have gained by P% ...


as in 2000.... 2400 ... therefore... 400/2000 is the % ??

[RonPurewal]

Hi Ron,

cant we assume that the difference also would have gained by P% ...


as in 2000.... 2400 ... therefore... 400/2000 is the % ??

that is correct, although i don't like one word you used in there: 'assume'. it's always dangerous to assume things - especially things about which you apparently aren't sure!

here's one way of explaining why this 'assumption' happens to work in this particular case:
* imagine the original salaries on a number line
* now multiply the salaries by the same fixed constant (equivalent to increasing them by the fixed percentage p cited in the problem - remember that percentage increases/decreases can be accomplished by multiplying by appropriate constants)
* in this case, the gap between the points representing the two salaries will grow by the same factor as do the salaries themselves (because everything on the number line grows by that same factor).
* therefore, your approach is valid.

--

still, even though you may not even have meant the word 'assume' literally, i feel as though i should comment on that (sorry if i'm being repetitive). you should never assume the truth of any shortcut that you don't absolutely KNOW to be valid, because the entire crux of the data sufficiency problem will boil down to whether the shortcut is valid in the first place.

[parakh.rahul]

I was approaching the problem like this:

J98/J95 = K98/K95
=> [J95(1+p%)]/J95 = [K95(1+p%)]/K95
=> [J95(1+p%)]/J95 = [(J95)(1+p%) + 240]/[J95 +2000]

I just completely lost myself after this..where did I go wrong? And is this equation solvable?

I would guess yes, but I have faced situations where its not necessary that a equation with just one variable has to solve, because the above eq might lead to a quadratic equation format..

I need an explanation as to whether the above approach is correct and appropriate to use. If not, then why?

Thanks,
Rahul

[RonPurewal]

parakh,

that's not the most efficient way in the world to set up this problem, but the important part is that it will work.

[quote="parakh.rahul"]=> [J95(1+p%)]/J95 = [(J95)(1+p%) + 240]/[J95 +2000]

at this point, you can cancel out the blue j95's. (in fact, you could cancel them at any point, or even work the entire problem without ever including them in the first place, since this fraction is just the overall percentage factor.)
once you cancel those out, you can cross-multiply the resulting stuff and get...
(1 + p%)(j + 2000) = (1 + p%)(j) + 2400).
note: in the above, i have just written "j" rather than "j95", for ease of reading.
in this equation, the terms (1 + p%)(j) will go away, leaving a linear equation that you can solve for p.