1992 AMC 8 Problem 6

Below is the professionally curated solution for Problem 6 of the 1992 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.

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Concepts:custom operation

Difficulty rating: 820

6.

Define an operation on three numbers—a top number, a lower-left number, and a lower-right number—whose value is (top number) ++ (lower-left number) - (lower-right number). For example, top 55, lower-left 44, lower-right 66 gives 5+46=3.5 + 4 - 6 = 3. What is the sum of the operation applied to top 11, lower-left 33, lower-right 44 and the operation applied to top 22, lower-left 55, lower-right 6?6?

2-2

1-1

00

11

22

Solution:

The first triple gives 1+34=0,1 + 3 - 4 = 0, and the second gives 2+56=1.2 + 5 - 6 = 1.

Their sum is 0+1=1.0 + 1 = 1.

Thus, the correct answer is D .

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