1992 AJHSME Problems/Problem 3

Problem

What is the largest difference that can be formed by subtracting two numbers chosen from the set $\{ -16,-4,0,2,4,12 \}$ ?

$\text{(A)}\ 10 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 28 \qquad \text{(E)}\ 48$

Solution

To maximize anything of the form $a-b$ , we maximize $a$ and minimize $b$ . The maximal element of the set is $12$ and the minimal element is $-16$ , so the maximal difference is $12-(-16)=28\rightarrow \boxed{\text{D}}.$

1992 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AJHSME/AMC 8 Problems and Solutions

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1992 AJHSME Problems/Problem 3

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