Difference between revisions of "2006 AMC 10B Problems/Problem 11"

Revision as of 21:26, 3 August 2006

Problem

What is the tens digit in the sum $7!+8!+9!+...+2006!$

$\mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 3\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } 6\qquad \mathrm{(E) \ } 9$

Solution

Since $10!$ is divisible by $100$ , any factorial greater than $10!$ is also divisible by $100$ . The last two digits of all factorials greater than $10!$ are $00$ , so the last two digits of $10!+11!+...+2006!$ is $00$ .

So all that is needed is the tens digit of the sum $7!+8!+9!$

$7!+8!+9!=5040+40320+362880=408240$

So the tens digit is $4 \Rightarrow C$

Revision as of 14:59, 2 August 2006 (view source) Xantos C. Guin (talk \| contribs) m (added link to previous and next problem) ← Older edit		Revision as of 21:26, 3 August 2006 (view source) Xantos C. Guin (talk \| contribs) m (added category) Newer edit →
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Difference between revisions of "2006 AMC 10B Problems/Problem 11"

Revision as of 21:26, 3 August 2006

Problem

Solution

See Also