Statement 1 ensures that a_1 and c_2 are both 11. If each number (3, 5 and 11) needed to occur exactly once in a row and in a column, this would be sufficient, since it would force d_2 to be 11. But we're allowed to have two fives in a row or column. So another possibility is that d_2 = 3, and all of the remaining letters are 5's. So Statement 1 is not sufficient.
Statement 2 tells us the product of the four numbers which share a row or column with d_2, the number we're interested in. We know that product is 375 = (3)(5^3). So the four numbers in a row or column with d_2 are 3, 5, 5, and 5. So either the row or the column must contain two 5s already, and d_2 cannot be 5, and then the column or row contains 3 and 5, so d_2 cannot be 3 either. So d_2 must be 11, and statement 2 is sufficient. The answer is B.
It's a very good question on a conceptual level, but I can't understand why the unknowns are written using unnecessary subscripts (instead of just using a, b, c, d, e, f, g, h, and then "x" for the letter we're asked to find) - a test taker could reasonably wonder why there is both an a_1 and an a_2 in the grid, for example, and might wonder if those two letters must both equal 5 based on the constraints mentioned in the problem (since there is no other obvious reason to have two "a" letters in the grid). What is the source?
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