Difference between revisions of "2018 AMC 10A Problems/Problem 7"

Revision as of 13:02, 2 July 2020

Problem

For how many (not necessarily positive) integer values of $n$ is the value of $4000\cdot \left(\tfrac{2}{5}\right)^n$ an integer?

$\textbf{(A) }3 \qquad \textbf{(B) }4 \qquad \textbf{(C) }6 \qquad \textbf{(D) }8 \qquad \textbf{(E) }9 \qquad$

Solution

The prime factorization of $4000$ is $2^{5}\cdot5^{3}$ . Therefore, the maximum number for $n$ is $3$ , and the minimum number for $n$ is $-5$ . Then we must find the range from $-5$ to $3$ , which is $3-(-5) + 1 = 8 + 1 = \fbox{\textbf{(E) }9}$ .

Video Solution

https://youtu.be/ZiZVIMmo260

https://youtu.be/2vz_CnxsGMA

~savannahsolver

2018 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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All AMC 10 Problems and Solutions

2018 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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All AMC 12 Problems and Solutions

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Difference between revisions of "2018 AMC 10A Problems/Problem 7"

Revision as of 13:02, 2 July 2020

Contents

Problem

Solution

Video Solution

See Also

@@ Line 16: / Line 16: @@
 ==Video Solution==
 https://youtu.be/ZiZVIMmo260
+https://youtu.be/2vz_CnxsGMA
+~savannahsolver
 == See Also ==