2003 AMC 10A Problem 1

Attempt Problem 1 of the 2003 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

What is the difference between the sum of the first

2003

even counting numbers and the sum of the first

2003

odd counting numbers?

0

1

2

2003

4006

Pair each even number with the odd number just below it

Each of the

2003

pairs contributes a difference of

1

The

k

th even number

2k

is exactly

1

more than the

k

th odd number

2k-1.

Summing this difference over all

2003

pairs gives

2003 \cdot 1 = 2003.

Thus, the correct answer is D.

Problem 1 in other years