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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2.

If  abcd=a⋅d−b⋅c,~\begin{array}{r|l}a&b \\ \hline c&d\end{array} = a\cdot d-b\cdot c, what is the value of  3412 ?~\begin{array}{r|l}3&4 \\ \hline 1&2\end{array}~?
−2-2
−1-1
00
11
22
Answer: E
Concepts:custom operation
Small hint:
Match a,a, b,b, c,c, and dd to the four entries.
Big hint:
Compute 3⋅2−4⋅1.3\cdot 2-4\cdot 1.
Solution:
Substituting into the definition gives 3⋅2−4⋅1=2.3\cdot 2-4\cdot 1=2.
Thus, the correct answer is E .
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