2014 CEMC Gauss (Grade 7) Problems/Problem 7

Problem

How many positive two-digit whole numbers are divisible by $7$ ?

$\textbf{(A)}\ 11 \qquad\textbf{(B)}\ 9 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 13$

We can simply list all of the numbers and then count how many there are. $7$ is too small and $105$ is too large. We have:

$14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98$

We see that there are $\boxed {\textbf {(E) } 13}$ numbers in the list.

~anabel.disher

We can see that $14 = 2 \times 7$ and $98 = 14 \times 7$ are the smallest and largest numbers possible, respectively.

Thus, there are $14 - 2 + 1 = \boxed {\textbf {(E) } 13}$ positive two-digit multiples of $7$ .

~anabel.disher

2014 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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CEMC Gauss (Grade 7)