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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.
ReplyDeleteWhen 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 = 1
B = 3/4
A is greater than B.
For the second pair:
A = 1
B = 3/4
A is greater than B.
For the third pair:
A = -1
B = -3/4
B is greater than A.
For the fourth pair:
A = -1
B = -3/4
B 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.