Difference between revisions of "2008 AMC 8 Problems/Problem 22"

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\textbf{(D)}\ 33\qquad
 
\textbf{(D)}\ 33\qquad
 
\textbf{(E)}\ 34</math>
 
\textbf{(E)}\ 34</math>
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==Solution==
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If <math>\frac{n}{3}</math> is a three digit whole number, <math>n</math> must be divisible by 3 and be <math>\ge 100*3=300</math>. If <math>3n</math> is three digits, n must be <math>\le \frac{999}{3}=333</math> So it must be divisible by three and between 300 and 333. There are <math>12</math> A such numbers, which you can find by direct counting.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2008|num-b=21|num-a=23}}
 
{{AMC8 box|year=2008|num-b=21|num-a=23}}

Revision as of 13:42, 11 December 2012

Problem

For how many positive integer values of $n$ are both $\frac{n}{3}$ and $3n$ three-digit whole numbers?

$\textbf{(A)}\ 12\qquad \textbf{(B)}\ 21\qquad \textbf{(C)}\ 27\qquad \textbf{(D)}\ 33\qquad \textbf{(E)}\ 34$

Solution

If $\frac{n}{3}$ is a three digit whole number, $n$ must be divisible by 3 and be $\ge 100*3=300$. If $3n$ is three digits, n must be $\le \frac{999}{3}=333$ So it must be divisible by three and between 300 and 333. There are $12$ A such numbers, which you can find by direct counting.

See Also

2008 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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