ExplanationYou should Plug In on this question. Variables a and b can be consecutive numbers such as 6 and 12. Plug in consecutive multiples of 8 for x and y, such as 8 and 16. Finding the ratio of the averages is easy now; the averages of each pair of numbers will be the halfway point between the two numbers. For 6 and 12, the average is 9. For 8 and 16, the average is 12.
The ratio of these averages is \(\frac{3}{4}\). Now, plug your original numbers into the answer choices and
look for the one that equals \(\frac{3}{4}\). Choice (A) gives you \(\frac{4}{3}\), which is the reciprocal of what you want. Cross it off. Choice (B) gives you \(\frac{3}{4}\)which is what you’re looking for. But don’t stop yet—keep checking all of the answers. Choice (D) also works with these numbers. No harm done, just try a different set of numbers and check the two remaining choices.
Plug in some really unusual numbers, like 24 and 30 for a and b, and 80 and 88 for x and y. Now you are looking for an answer to give you \(\frac{9}{28}\) Choice (B) no longer works, so choice (D) is your answer.
Hence
option D is the only correct option.
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