The product of two positive numbers is 1,800. One number is twice the other number. The equation to determine the two numbers, with x representing the value of the lesser number, is x(2x) = 1,800.

Since the lesser number is x and the greater is 2x, the equation is x(2x) = 1,800. Thus 2x² = 1,800, so x² = 900 and the positive solution is x = 30. The lesser number is 30, choice B.

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