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

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

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.

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.