Expert: Josh - 8/28/2007

Question
Dear Josh,

I am in my forties and working to sit the GMAT.  I've managed to work all sorts of questions out but am floundering on what is obviously seen as very simple.  The format goes like this:

If x/ y = 199 what percentage of  x is x-y?

Or If x/4 +y/4 = 10 What percentage of x is 80 - 2y

I thought it might be something to do with fractions but have failed completely.  Please advise.

Yours Fiona

Answer
Dear Fiona,

To express "x-y" as a percentage of "x", we consider the ratio 100*(x-y)/x. The problem here is not knowing "y".

However, from the equation x/y=199, y is related to x by y=x/199.

Substituting this into (x-y)/x, we obtain [x-(x/199)]/x
=[(199x-x)/199]/x which may be factorized as
=(1/199)(198x/x)
=198/199
We multiply this by 100 to convert it into a percentage.
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Same approach for the second question.
The ratio of interest is (80-2y)/x....[#1]
Need to express y in terms of x.
From x/4+y/4=10, y=40-x. We put this into [#1] and simplify to obtain the answer.

Regards
Josh