In the grid shown the three non-zero numbers in each row, each column and each diagonal multiply to give the same product.
What is the value of x?
A. 36 B. 18 C. 12 D. 9 E. 4
A. 36
From the bottom row we see that the common value of the products is2 × x × 3 = 6x.
Let the numbers in the cells in the top row be r, s and t from left to right.
Then the product of the numbers in the diagonal from top-left to bottom-right is r × 6 × 3 = 18r.
It follows that 18r = 6x. Hencer = x/3.The product of the numbers in the middle column is s × 6 × x = 6sx.
It follows that 6sx = 6x.Hence, as x , 0, s = 1.
The product of the numbers in the diagonal from top-right to bottom-left is t × 6 × 2 = 12t.
It follows that 12t = 6x. Hence t = x/2.The product of the numbers in the top row is x/3 × 1 × x/2 = x2/6. It follows that x2/6 = 6x.
Hence, as x , 0, we can deduce that x/6 = 6. Therefore x = 36.
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