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Difference between revisions of "1998 AJHSME Problems/Problem 2"

(Created page with "== Problem 2 == 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}{...")
 
(→‎Problem)
 
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== Problem 2 ==
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== 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
  
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<math>a=3</math>
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<math>a=3</math>,
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<math>b=4</math>
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<math>b=4</math>,
−
<math>c=1</math>
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<math>c=1</math>,
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<math>d=2</math>
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<math>d=2</math>,
  
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<math>a\timesd=3\times2=6</math>
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<math>a\times d=3\times2=6</math>
  
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<math>b\timesc=4\times1=4</math>
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<math>b\times c=4\times1=4</math>
  
 
<math>6-4=2</math>
 
<math>6-4=2</math>
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== See also ==
 
== See also ==
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{{AJHSME box|year=1998|before=[[1997 AJHSME Problems|1997 AJHSME]]|after=[[1999 AMC 8 Problems|1999 AMC 8]]}}
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{{AJHSME box|year=1998|num-b=1|num-a=3}}
 
* [[AJHSME]]
 
* [[AJHSME]]
 
* [[AJHSME Problems and Solutions]]
 
* [[AJHSME Problems and Solutions]]
 
* [[Mathematics competition resources]]
 
* [[Mathematics competition resources]]
 +
{{MAA Notice}}

Latest revision as of 14:40, 20 October 2016

Problem

If $\begin{tabular}{r|l}a&b \\ \hline c&d\end{tabular} = \text{a}\cdot \text{d} - \text{b}\cdot \text{c}$, what is the value of $\begin{tabular}{r|l}3&4 \\ \hline 1&2\end{tabular}$?

$\text{(A)}\ -2 \qquad \text{(B)}\ -1 \qquad \text{(C)}\ 0 \qquad \text{(D)}\ 1 \qquad \text{(E)}\ 2$

Solution

Plugging in values for $a$, $b$, $c$, and $d$, we get

$a=3$, $b=4$, $c=1$, $d=2$,

$a\times d=3\times2=6$

$b\times c=4\times1=4$

$6-4=2$

$\boxed{E}$

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. AMC logo.png

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