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

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Math Expert
Joined: 02 Sep 2009
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A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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26 Aug 2015, 00:19
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:15) correct 21% (00:44) wrong based on 136 sessions

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A bicycle rider rides four stages of a race in 2 hours and 45 minutes. The four stages are named with four different colors: blue, yellow, red, and white. What is the rider’s average speed for the whole race?

(1) The red and blue stages combined are 55 miles long.
(2) The blue and yellow stages combined are 42 miles long.

Kudos for a correct solution.

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Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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26 Aug 2015, 04:11
Bunuel wrote:
A bicycle rider rides four stages of a race in 2 hours and 45 minutes. The four stages are named with four different colors: blue, yellow, red, and white. What is the rider’s average speed for the whole race?

(1) The red and blue stages combined are 55 miles long.
(2) The blue and yellow stages combined are 42 miles long.

Kudos for a correct solution.

Let b,y,r,w stand for 4 stages of the race.

Total time = 2 h 45 m

Average speed = Total distance / Total time

Clearly statements 1 and 2 on their own are not sufficient as total distance is still not provided.

Even after combining them, we will not be getting total distance. Thus, E is the correct answer.
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Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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26 Aug 2015, 10:24
Bunuel wrote:
A bicycle rider rides four stages of a race in 2 hours and 45 minutes. The four stages are named with four different colors: blue, yellow, red, and white. What is the rider’s average speed for the whole race?

(1) The red and blue stages combined are 55 miles long.
(2) The blue and yellow stages combined are 42 miles long.

Kudos for a correct solution.

IMO : E

$$Avg Speed = \frac{Total Distance Traveled}{Total Time Taken}$$
Total Time is given = 2hr 45 min.

St 1: The red and blue stages combined are 55 miles long.

Only two stages distances are given.
Hence not suff

St 2: The blue and yellow stages combined are 42 miles long.

Only two stages distances are given.
Hence not suff

Combined:

Only three stages distances are given.
Hence not suff
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Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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26 Aug 2015, 19:00
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

Math Expert
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Posts: 50001
Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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30 Aug 2015, 09:15
Bunuel wrote:
A bicycle rider rides four stages of a race in 2 hours and 45 minutes. The four stages are named with four different colors: blue, yellow, red, and white. What is the rider’s average speed for the whole race?

(1) The red and blue stages combined are 55 miles long.
(2) The blue and yellow stages combined are 42 miles long.

Kudos for a correct solution.

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).
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Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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31 Aug 2015, 19:54
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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Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes.  [#permalink]

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04 May 2017, 16:06
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Re: A bicycle rider rides four stages of a race in 2 hours and 45 minutes. &nbs [#permalink] 04 May 2017, 16:06
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