1992 AJHSME Problems/Problem 3

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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 \[12-(-16)=28\rightarrow \boxed{\text{D}}.\]

See Also

1992 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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

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