Ratio GRE question?

Question

> Cashews cost 4.75 per pound and hazelnuts cost 4.50 per pound. What is > larger, the number of pounds of cashews in a mixture of cashews and > hazelnuts that costs $5.50 per pound, or 1.25? Alternatively, are they > equal, or is it impossible to calculate? My answer: I believe that 1.25 is larger. I conclude this because even if a 1.25lb mix were entirely composed of cashews, it would be more costly than $5.50/lb. Therefore, the mixture must have fewer than 1.25lbs of cashews, and 1.25 is greater. The supposed answer: "There is no way to calculate the number of pounds of either nut in the mixture. We can calculate the ratio of the number of pounds of cashews to the number of pounds of hazelnuts required of the mixture to cost $5.50 per pound, but without knowing how many total pounds the mixture is, we cannot calculate the number of pounds of either component." Please let me know if I'm wrong, but if I'm not, I think I need to email them.

Answer 1

The question is nothing more than a red herring, meant to get you, the unwitting test-taker, to chase a rate (i.e. per pound) when the question is asking about the number of pounds of cashews in some unspecified amount of the mixture, not the relative weight of cashews in the per-pound mixture. I will admit that I had to read the setup twice to see through the trap, as the phrasing of the question is ambiguous. I am curious about the source of the question. If it comes from an ETS publication, then so be it: just learn to be skeptical of your assumptions. If, on the other hand, this question comes from some other source, then it might be a case in which the question-writer went a little too far in hoping to mimic an official question.

Good luck with your studies.

Andrew