1991 AJHSME Problems/Problem 11

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Problem

There are several sets of three different numbers whose sum is $15$ which can be chosen from $\{ 1,2,3,4,5,6,7,8,9 \}$. How many of these sets contain a $5$?

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 7$

Solution

Let the three-element set be $\{ a,b,c \}$ and suppose that $a=5$.

We need $b+c=10$ and $b\neq c$. This gives us four solutions, so there are $4$ sets with a $5$ also with the desired properties $\rightarrow \boxed{\text{B}}$.

See Also

1991 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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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