Salary :D

codesnooker · Posted: Wed Jul 09, 2008 1:52 am Post subject: Salary :D

How to solve this question?

olika · Posted: Wed Jul 09, 2008 7:38 am Post subject: Re: Salary :D

Is the answer "C"?

I would solve it in this way.

Lets label 'K'- Karen's salary in '95 and 'J' - Jason's salary in '95.
In 1995, the difference between Karen's salary and Jason's salary was 2,000 (K-J=2,000).
In 1998, the gap between their salaries increased by 400, which represents "p" percent. So, we have 2,000 is 100% and 400 is p%. Solving this, we get p=20%.

The answer is C. We need both statements.

ksh · Posted: Thu Jul 10, 2008 3:56 am Post subject: Re: Salary :D

olika · Posted: Thu Jul 10, 2008 7:15 am Post subject: Re: Salary :D

lunarpower · Posted: Thu Jul 10, 2008 10:21 pm Post subject:

remember that you can think of percentage increases in the same way in which you'd think of just multiplying by a constant - because that's all that percentage increases really are, after all.*

simpler analogy:
let's say you multiply a series of numbers x, y, and z by some unknown constant. now let's say i tell you that the gaps between the numbers are 3 times as big as they used to be.
what does this mean?
it means that we must have tripled the numbers, because the size of the gaps increases proportionally with the size of the numbers themselves.

this means that, if we know the number by which the gaps between the numbers have been multiplied (which is the same as knowing the % change in those gaps), we'll also know the multiplier / % change for the numbers themselves.

in this problem, if we take the 2 statements together, we know that the gap between the salaries has increased by a factor of 2440/2000 = 1.22; this means a percentage increase of 22%. (note that you don't really care about the specific percentages, since this is data sufficiency; all that matters is that you can find them.)
therefore, the salaries themselves have increased by 22 percent.
that means both statements together are sufficient.

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note that none of the above reasoning is valid if the quantities increase by different percentages.

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*as a side note, it's extremely useful to be able to use percentage multipliers for percent increases. some examples:
to increase a quantity by 14%, multiply by 1.14
to increase a quantity by 70%, multiply by 1.7
to decrease a quantity by 14%, multiply by 0.86
to decrease a quantity by 70%, multiply by 0.3
etc.