2006 AMC 10B Problem 11 — Solution | LIVE by Po-Shen Loh

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2006 AMC 10B Problem 11

Attempt Problem 11 of the 2006 AMC 10B 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 2006 AMC 10B solutions, or check the answer key.

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

11.

What is the tens digit in the sum $7! + 8! + 9! + \cdots + 2006!\,?$

$1$

$3$

$4$

$6$

$9$

Answer: C

Concepts:factorial modular arithmetic digits

Difficulty rating: 1280

Solution:

For $n\ge 10,$ $n!$ is divisible by $100,$ so it does not affect the last two digits.

The tens digit comes from $7!+8!+9!$ $=5040+40320+362880$ $=408240,$ whose tens digit is $4.$

Thus, the correct answer is C.

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Problem 11 in Other Years

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