1995 AHSME Problem 16

Anita attends a baseball game in Atlanta and estimates that there are 50,000 fans in attendance. Bob attends a baseball game in Boston and estimates that there are 60,000 fans in attendance. A league official who knows the actual numbers attending the two games notes that:

i. The actual attendance in Atlanta is within 10 \% of Anita's estimate. ii. Bob's estimate is within 10 \% of the actual attendance in Boston.

To the nearest 1,000, the largest possible difference between the numbers attending the two games is

\mathrm{(A) \ 10000 } \qquad \mathrm{(B) \ 11000 } \qquad \mathrm{(C) \ 20000 } \qquad \mathrm{(D) \ 21000 } \qquad \mathrm{(E) \ 22000 }

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.