If ~\beginarrayr|la&b \ \hline c&d\endarray = a× d - b× c, what is the value of ~\beginarrayr|l3&4 \ \hline 1&2\endarray~?

1998 AMC 8 Problem 2 — Solution

1998 AMC 8 Problem 2

Attempt Problem 2 of the 1998 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 8 solutions, or check the answer key.

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

$-2$

$-1$

$0$

$1$

$2$

Answer: E

Concepts:custom operation

Difficulty rating: 450

Solution:

Plugging into the formula above, we get: $3\cdot 2-1\cdot 4=2.$

Thus, the correct answer is E .

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