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UKMT Senior Mathematical Challenge, 2016

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The digits from 1 to 9 are to be written in the nine cells of the $3 \times 3$ grid shown, one digit in each cell. The product of the three digits in the first row is 12. The product of the three digits in the second row is 112. The product of the three digits in the first column is 216. The product of the three digits in the second column is 12. What is the product of the digits in the shaded cells?

(A) $24$ (B) $30$ (C) $36$ (D) $48$ (E) $140$

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