No one likes a fraction made out of fractions, so we've got to do something to make the fraction in Quantity B look a little more civilized. The denominators in that fraction are n, 3x, and x, so the least common denominator is 3nx.When I multiply the fraction by (3nx/3nx), I get a simpler-looking fraction:12x/(n + 15n) = (3/4)(x/n)At this point, it's just a matter of plugging in numbers. We know that x and n have to be nonzero quantities, but we're not told whether they might be positive or negative. So let's try some combinations of x and n that cover the major possibilities:x = 1, n = 1 (+/+)x = -1, n = -1 (-/-)x = -1, n = 1 (-/+)x = 1, n = -1 (+/-)For the first pair:A = 1B = 3/4A is greater than B.For the second pair:A = 1B = 3/4A is greater than B.For the third pair:A = -1B = -3/4B is greater than A.For the fourth pair:A = -1B = -3/4B is greater than A.By plugging in simple numbers like 1 and -1, we quickly see that there are times when A is greater, and times when B is greater.The answer is D: The relationship cannot be determined from the information given.Or so I say, anyway. MGRE will publish the official answer next week.
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