1994 AHSME Problems/Problem 5

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

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1994 AHSME Problems/Problem 5

Problem

Solution