Problem Solving

A square countertop has a square tile inlay in the center,leaving an untiled strip of uniform width around the tile.If the ratio of the tiled area to the untiled area is 25 to 39,which of the following could be the width in inches of the strip?

I. 1 1/2
II.3
III.4 1/2

A) I only
B) II only
C) I and II only
D) I and III only
E) I,II and III

if we set up the quadratic equation as per the given information all 3 values seem to be possible.so imo e.
whats oa?

yup the OA is E.Could u just explain the reasoning?

if length of square is x an width is y we have x^2 /(x+2y)^2 = 25/36.we need to know y .this gives us 14 x ^ 2 -100 xy -100 y ^2 =0 . you need not really solve this equation but you can see that for every value of y there is a possible value of x(mind x need not be an integer)..
hence answer is e.some other approach/explanation awaited.

It is very easy to waste a lot of time on this type of question, but don't!

Two things that you should spot immediately are:

1) There was no qualifications given for the answer(ie. it doesn't say it has to be an integer)

2) The ratio given isn't very easy to work with algebraically. 25/36 would have been much more friendly.

The only criteria that has to be met is the 25/39 ratio.

(25/39)x , where x>0 satisfies this. (x could be .0000023, .1, 54, 1000, etc.)

With that said, ANY positive number COULD be the width.