2013 AMC 8 Problems/Problem 1

Problem

Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the greatest number of additional cars she must buy in order to be able to arrange all her cars this way?

$\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 533$

Solution 1

The least multiple of 6 greater than 23 is 24. So she will need to add $24-23=\boxed{\textbf{(A)}\ 51}$ more model car. ~avamarora

Solution 2

$23\equiv5\equiv-1\pmod6$ For the number of cars to be a multiple of $6$ , we have to increase the number of cars by $\boxed{\textbf{(A)}~1}$ .

~megaboy6679

Video Solution

https://youtu.be/HcWVIEnH0vs ~savannahsolver

2013 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

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2013 AMC 8 Problems/Problem 1

Contents

Problem

Solution 1

Solution 2

Video Solution

See Also