A bicycle rider rides four stages of a race in 2 hours and 45 minutes.

4 stages: blue, yellow, red, white. we re not given the distance of the stages. we need to find the distance of each stage in order to have enough info to find the average speed.


(1) The red and blue stages combined are 55 miles long.
no info on the distances of yellow or white
insufficient

(2) The blue and yellow stages combined are 42 miles long.
no info on the distances of red or white
insufficient

combined, there is still no info on the distance of white
Insufficient

Answer: E

PRINCETON REVIEW OFFICIAL SOLUTION:

Before looking closely at the statements, we should consider the question and determine what we’re looking for. The question asks for an average speed, so this is a question about rates and we should write down the rate formula: Rate = Distance / Time. The time is given to us, so the only thing we need to know in order to find the rate is the distance. That’s the missing piece of this puzzle. This means that when we turn to the statements we’re no longer thinking about rate, we’re thinking about distance. If the statement allows us to find the total distance of the race then it is sufficient. If not, it’s insufficient.

Statement 1 tells us the combined distance of two of the stages, but that isn’t enough to know the distance of the whole race. Thus Statement 1 is insufficient.

Statement 2 also tells us the combined distance of only two stages, and is therefore insufficient for the same reason as Statement 1.

When we combine the statements we have to be a bit careful. It may seem that now we have all four stages, but in fact the blue stage was mentioned twice, and nowhere do we have any information about the white stage.

There is no way to know the total distance of the race, and the answer is (E).

To get the average speed you need to know (Db + Dy + Dr + Dw) / 2h 45m.

(1) Dr + Db = 55. Insufficient.
(2) Db + Dy = 42. Insufficient.

(1) and (2) Insufficient. We cannot know about Db + Dy + Dr + Dw

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