Difference between revisions of "1998 AJHSME Problems/Problem 2"
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| − | == Problem | + | == Problem == |
If <math>\begin{tabular}{r|l}a&b \\ \hline c&d\end{tabular} = \text{a}\cdot \text{d} - \text{b}\cdot \text{c}</math>, what is the value of <math>\begin{tabular}{r|l}3&4 \\ \hline 1&2\end{tabular}</math>? | If <math>\begin{tabular}{r|l}a&b \\ \hline c&d\end{tabular} = \text{a}\cdot \text{d} - \text{b}\cdot \text{c}</math>, what is the value of <math>\begin{tabular}{r|l}3&4 \\ \hline 1&2\end{tabular}</math>? | ||
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Plugging in values for <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math>, we get | Plugging in values for <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math>, we get | ||
| − | <math>a=3</math> | + | <math>a=3</math>, |
| − | <math>b=4</math> | + | <math>b=4</math>, |
| − | <math>c=1</math> | + | <math>c=1</math>, |
| − | <math>d=2</math> | + | <math>d=2</math>, |
| − | <math>a\ | + | <math>a\times d=3\times2=6</math> |
| − | <math>b\ | + | <math>b\times c=4\times1=4</math> |
<math>6-4=2</math> | <math>6-4=2</math> | ||
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* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 15:40, 20 October 2016
Problem
If 
, what is the value of 
?
Solution
Plugging in values for 
, 
, 
, and 
, we get
,
,
,
,
See also
| 1998 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
