Difference between revisions of "1994 AHSME Problems/Problem 5"
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\textbf{(D)}\ \text{between 800 and 1000} \qquad\textbf{(E)}\ \text{greater than 1000}</math> | \textbf{(D)}\ \text{between 800 and 1000} \qquad\textbf{(E)}\ \text{greater than 1000}</math> | ||
==Solution== | ==Solution== | ||
| + | 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>. | ||
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| + | 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>. | ||
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| + | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | ||
Revision as of 15:15, 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
