Bunuel wrote:
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 total area of the countertop is 9 to 16, which of the following could be the width, in inches, of the strip?
I. 3
II. 5
III. 6
A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III
Let uniform width be "x"
Let side of the square countertop be equal to "a"
So,
total area of countertop = \(a^2\)
total area of tiled part = \((a-2x)^2\)
Now as per question,
\(\frac{total area of tiled part }{ total area of countertop}\) = \(\frac{(a-2x)^2}{a^2}\) = \(\frac{9}{16}\)
=> \(\frac{(a-2x)}{a}\) = \(\frac{3}{4}\)
=> \(4a - 8x = 3a\)
=> \(a = 8x\)
=> \(x = \frac{a}{8}\)
So as we need to find "x", we see that it is dependent on the value of "a" and hence can be anything as we have no restriction for value of "a"
Hence any real number will be possible as value of "x"
Hence E _________________
Regards,
AD
----------------
An admiration by anybody is an explanation understood by somebody !!! Happy GMATing... Go Nuts