# Difference between revisions of "1994 AHSME Problems/Problem 5"

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

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

--Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] |

## Revision as of 14:17, 28 June 2014

## Problem

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

## Solution

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

Now, we multiply by to get . Finally, . Since , our answer is .

--Solution by TheMaskedMagician