2023/24 AHSMC Part 1 Problem 3

Problem 3 of 16

In the table, $a$ , $b$ , $c$ , $d$ and $e$ are integers such that every row and column has the same sum. $\begin{array}{|c|c|c|} \hline a & b & c \\ \hline d & -1 & 2 \\ \hline 4 & e & 3 \\ \hline \end{array}$ The value of $a$ is

Show solution

Solution

Since the sum of the second row equals the sum of the first column we must have $d - 1 + 2 = a + d + 4$ . Hence $a = -3$ . The answer is (A).

(If $r$ is the common row/column sum then $a = -3$ , $b = 8$ , $c = r-5$ , $d = r-1$ and $e = r-7$ .)

University of Alberta

Answer choices

Solution