1994 AHSME Problems/Problem 5

Revision as of 14:17, 28 June 2014 by TheMaskedMagician (talk | contribs) (Solution)

Problem

Pat intended to multiply a number by $6$ but instead divided by $6$. Pat then meant to add $14$ but instead subtracted $14$. After these mistakes, the result was $16$. If the correct operations had been used, the value produced would have been

$\textbf{(A)}\ \text{less than 400} \qquad\textbf{(B)}\ \text{between 400 and 600} \qquad\textbf{(C)}\ \text{between 600 and 800} \\ \textbf{(D)}\ \text{between 800 and 1000} \qquad\textbf{(E)}\ \text{greater than 1000}$

Solution

We reverse the operations that he did and then use the correct operations. His end result is $16$. Before that, he subtracted $14$ which means that his number after the first operation was $30$. He divided by $6$ so his number was $180$.

Now, we multiply $180$ by $6$ to get $1080$. Finally, $1080+14=1094$. Since $1094>1000$, our answer is $\boxed{\textbf{(E)}\ \text{greater than 1000}}$.

--Solution by TheMaskedMagician

Invalid username
Login to AoPS