Skip to main content

2014 AMC 12A Problem 9

Problem 9 of 25EasierAlgebraProbability & Statistics

Five positive consecutive integers starting with aa have average b.b. What is the average of 55 consecutive integers that start with b?b?

Answer choices

Show solution

Solution

The integers a,a+1,a+2,a+3,a+4a,a+1,a+2,a+3,a+4 have average a+2,a+2, so b=a+2.b=a+2. The integers starting at bb have average b+2=(a+2)+2=a+4.b+2=(a+2)+2=a+4. Thus, the correct answer is B.
AoPS wiki

Tagged: mean · arithmetic sequence

More practice