1991 AJHSME Problems/Problem 6

Problem

Which number in the array below is both the largest in its column and the smallest in its row? (Columns go up and down, rows go right and left.) \[\begin{tabular}[t]{ccccc} 10 & 6 & 4 & 3 & 2 \\ 11 & 7 & 14 & 10 & 8 \\ 8 & 3 & 4 & 5 & 9 \\ 13 & 4 & 15 & 12 & 1 \\ 8 & 2 & 5 & 9 & 3 \end{tabular}\]

$\text{(A)}\ 1 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 15$

Solution

The largest numbers in the first, second, third, fourth and fifth columns are $13,7,15,12,9$ respectively. Of these, only $7$ is the smallest in its row $\rightarrow \boxed{\text{C}}$.

See Also

1991 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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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