2011 AMC 10A Problem 4

Problem 4 of 25EasierAlgebra

Let

X

and

Y

be the following sums of arithmetic sequences:

\begin{aligned} X &= 10+12+14+\cdots+100,\\ Y &= 12+14+16+\cdots+102. \end{aligned}

What is the value of

Y - X?

Show solution

Solution

Note that the terms

12

through

100

are common to both sums. When we subtract, all these terms cancel out. This means that

Y - X = 102 - 10 = 92.

Thus, A is the correct answer.

Concepts: arithmetic sequence · summation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.