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# If a runner in a marathon had the 37th fastest time and the 50th slowe

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Math Expert
Joined: 02 Sep 2009
Posts: 55718
If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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26 Dec 2014, 08:32
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Tough and Tricky questions: Word Problems.

If a runner in a marathon had the 37th fastest time and the 50th slowest time, how many runners finished the marathon?

A. 83
B. 84
C. 85
D. 86
E. 87

Kudos for a correct solution.

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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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26 Dec 2014, 09:55
1
If the runner finished 37th, there are 36 runners faster than him. If he has the 50th slowest slowest time, there must be 49 runners slower than him.

We can therefore conclude that there are 86 runners in the marathon: 36 faster runners + 49 slower runners + 1 the runner we are asked about.

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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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26 Dec 2014, 17:31
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If a runner in a marathon had the 37th fastest time and the 50th slowest time, how many runners finished the marathon?

A. 83
B. 84
C. 85
D. 86
E. 87

Kudos for a correct solution.

# of runners faster than runner x = 36
# of runners slower than runner x = 49

Total runners = 36+49+1(Runner x) = 86
Ans D
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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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27 Dec 2014, 01:04
Lets imagine a marathon race. As per question since he is 37th fastest then he has 36 runners ahead of him. Since he is 50th slowest that means 49 runners are behind him.

Total runners=37+50=87. But since the same runner is counted twice we need to subtract 1. hence total runners =87-1=86.

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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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27 Dec 2014, 04:07
1
Imagine at the end of the race all the contestants are made to stand in a line as per the time taken to complete the race, fastest being the first and slowest as the last. Then if we count from first he is at 37 position ie he sees 36 ppl in front of him. and if counted from the last he is at 50th position including him. now to this 50 from the last till him we add the other 36 in front of him. hence 50 + 36 = 86
hence D
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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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02 Jan 2015, 01:53

37 + 50 - 1 = 86

Refer diagram below (Conceptual)

Attachment:

pos.png [ 5.01 KiB | Viewed 1609 times ]

Addition of forward & reverse position would always given 1 more than the actual quantity
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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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08 Jan 2015, 09:31
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If a runner in a marathon had the 37th fastest time and the 50th slowest time, how many runners finished the marathon?

A. 83
B. 84
C. 85
D. 86
E. 87

Kudos for a correct solution.

OFFICIAL SOLUTION:

(D) If the runner had the 37th fastest time that means 36 runners finished before the runner. If the runner had the 50th slowest time that means 49 runners finished after the runner. The total number of runners who finished the marathon is 36 + 1 + 49 = 86.

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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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09 Apr 2016, 14:29
36 runners before him_______the runner himself______ 49 runners after him
So total number of runners in the race is 36+1+49 = 86
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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe  [#permalink]

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29 Dec 2017, 08:17
Top Contributor
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If a runner in a marathon had the 37th fastest time and the 50th slowest time, how many runners finished the marathon?

A. 83
B. 84
C. 85
D. 86
E. 87

Kudos for a correct solution.

Runner had the 37th fastest time...
So, there are 36 people IN FRONT of the runner

Runner had the 50th slowest time...
So, there are 49 people BEHIND the runner

How many runners finished the marathon?
We have:
- - - - - 49 people-----the runner--------36 people------
So, the TOTAL number of runners = 49 + 1 + 36 = 86

Cheers,
Brent
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Re: If a runner in a marathon had the 37th fastest time and the 50th slowe   [#permalink] 29 Dec 2017, 08:17
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