Explanation

You 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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sandy could you define this approach? how can we be sure that substitution method is to be applied for this question and not solving it through algebraic method?

Algebraic method takes time. And time is something you will not have on the GRE. So substitution is the best option in this case.
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I could not understand your post sandy.Please explain.

Put value 6 and 12 for \(a\) and \(b\); and 8 and 16 for \(x\) and \(y\). See which options hold.

Then put value 30 and 36 for \(a\) and \(b\); and 40 and 48 for \(x\) and \(y\). To validate your answer.
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i think you are wrong, answer is B, I plug number you provide B is answer

You are correct! Answer is B and the official explanation is super wrong!

Fixed it! Thanks
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Yeah i got B too

What is the final correct ans ? B or D?

It is B
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