MathDB

1

Part of 2015 AIME Problems

Problems(2)

Positive Difference Between A and B

Source: 2015 AIME I Problem 1

3/20/2015
The expressions A=1×2+3×4+5×6+⋯+37×38+39A=1\times2+3\times4+5\times6+\cdots+37\times38+39 and B=1+2×3+4×5+⋯+36×37+38×39B=1+2\times3+4\times5+\cdots+36\times37+38\times39 are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers AA and BB.
AMCAIMEAIME I
Smallest Integer 22% Less Than and 16% Greater Than Integer

Source: 2015 AIME 2 Problem 1

3/26/2015
Let NN be the least positive integer that is both 2222 percent less than one integer and 1616 percent greater than another integer. Find the remainder when NN is divided by 10001000.