Difference between revisions of "1991 AJHSME Problems/Problem 13"

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Latest revision as of 23:07, 4 July 2013

Problem

How many zeros are at the end of the product \[25\times 25\times 25\times 25\times 25\times 25\times 25\times 8\times 8\times 8?\]

$\text{(A)}\ 3 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12$

Solution

\begin{align*} (5^2)^7\times (2^3)^3 &=  5^{14}\times 2^{9} \\ &= 5^5\times 10^9  \end{align*} Since $5^5$ doesn't end in a $0$, we can conclude that the product ends in $9$ zeroes $\rightarrow \boxed{\text{C}}$.

See Also

1991 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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