udaymathapati wrote:

A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12

B. 2/5

C. 1/2

D. 3/4

E. 5/6

Simplified the numbers as below:

Req fraction is (3.14 * 10 * 10)/(24 * 24)

Cancel 10 and 24 by 2: (3.14 * 5 * 5)/(12 * 12)

Cancel 5*5=25 in numerator with 12 in denominator: (3.14 * 2.something)/(1 * 12) = 6.something / 12 =~1/2. (Here it is important to note that 2.something and 6.something are in the lower end, i.e., much lesser than 2.5 and 6.5.)

Bunuel has given a standard way to deal with fraction comparison in the previous posts. In some cases, the above sort of simplifications might help in getting a fraction with realtively smaller numerator and denominators.