1

Part of 2008 AIME Problems

Problems(2)

Source: AIME 2008II Problem 1

Let N\equal{}100^2\plus{}99^2\minus{}98^2\minus{}97^2\plus{}96^2\plus{}\cdots\plus{}4^2\plus{}3^2\minus{}2^2\minus{}1^2, where the additions and subtractions alternate in pairs. Find the remainder when

N

1000

AMCAIMEalgebradifference of squaresspecial factorizationsarithmetic series

Boys and Girls at a Party

Source: AIME 2008I Problem 1

Of the students attending a school party,

60\%

of the students are girls, and

40\%

of the students like to dance. After these students are joined by

20

more boy students, all of whom like to dance, the party is now

58\%

girls. How many students now at the party like to dance?