2013 CEMC Gauss (Grade 8) Problems/Problem 5

Problem

Jarek multiplies a number by $3$ and gets an answer of $90$ . If instead, he divides the number by $3$ , what answer does he get?

$\textbf{(A)}\ 5 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 30 \qquad\textbf{(D)}\ 60 \qquad\textbf{(E)}\ 270$

Let $x$ be the number that Jarek multiplied by $3$ . Using the first sentence, we have:

$3x = 90$

$x = 30$

We are then looking for $x \div 3$ , which is $30 \div 3 = \boxed {\textbf {(B) } 10}$

~anabel.disher

Without finding the number that Jarek multiplied by $3$ , we can note that $x \div 3 = 3x \div 9$ . Thus, we can divide the product by $9$ :

$90 \div 9 = \boxed {\textbf {(B) } 10}$

~anabel.disher