1987 AMC 8 Problem 3 — Solution | LIVE by Po-Shen Loh

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1987 AMC 8 Problem 3

Below is the professionally curated solution for Problem 3 of the 1987 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1987 AMC 8 solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:arithmetic sequence whole number operations

Difficulty rating: 660

3.

What is the value of

$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)?$

$1600$

$1650$

$1700$

$1750$

$1800$

Solution:

The ten evenly spaced numbers have average $90,$ so their sum is $10 \times 90 = 900.$

Doubling gives $2 \times 900 = 1800.$

Thus, the correct answer is E .

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Problem 3 in Other Years

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