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Three of the events at a track meet were the 100 m dash

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Three of the events at a track meet were the 100 m dash  [#permalink]

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New post 19 Mar 2019, 04:12
3
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A
B
C
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E

Difficulty:

  55% (hard)

Question Stats:

53% (03:51) correct 47% (03:18) wrong based on 15 sessions

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Three of the events at a track meet were the 100 m dash, the 200 m dash, and the 100 m hurdles. Sixteen runners qualified for and competed in each event. Six competed only in the 100 m dash, 7 only in the 200 m dash, and 9 only in the 100 m hurdles. Additionally, 5 competed in both dashes, 3 competed in both 100 m events, and 2 competed in the 200 m dash and 100 m hurdles. How many competitors participated in all three events?

A) 0
B) 2
C) 3
D) 6
E) 12
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Re: Three of the events at a track meet were the 100 m dash  [#permalink]

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New post 19 Mar 2019, 07:27
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Tabouray wrote:
Three of the events at a track meet were the 100 m dash, the 200 m dash, and the 100 m hurdles. Sixteen runners qualified for and competed in each event. Six competed only in the 100 m dash, 7 only in the 200 m dash, and 9 only in the 100 m hurdles. Additionally, 5 competed in both dashes, 3 competed in both 100 m events, and 2 competed in the 200 m dash and 100 m hurdles. How many competitors participated in all three events?

A) 0
B) 2
C) 3
D) 6
E) 12


From the question, we know in each of the three events we had 16 participants each.

For 100 m dash
16 = (Only in 100m dash) + (100m dash + 200m dash) + (100m dash + 100m hurdle) + (all three)
16 = 6 + 5 + 3 + x
=> x = 2

Hence B is the correct answer.

We can also the above for the remaining two events to check our answer.

For 200 m dash
16 = (Only in 200m dash) + (100m dash + 200m dash) + (200m dash + 100m hurdle) + (all three)
16 = 7 + 5 + 2 + x
=> x = 2

For 100 m hurdle
16 = (Only in 100m hurdle) + (100m hurdle + 200m dash) + (100m dash + 100m hurdle) + (all three)
16 = 9 + 3 + 2 + x
=> x = 2
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Re: Three of the events at a track meet were the 100 m dash  [#permalink]

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New post 19 Mar 2019, 09:33
Hi Tabouray
Can you provide official OE of this question
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Three of the events at a track meet were the 100 m dash  [#permalink]

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New post 19 Mar 2019, 10:23
Tabouray wrote:
Three of the events at a track meet were the 100 m dash, the 200 m dash, and the 100 m hurdles. Sixteen runners qualified for and competed in each event. Six competed only in the 100 m dash, 7 only in the 200 m dash, and 9 only in the 100 m hurdles. Additionally, 5 competed in both dashes, 3 competed in both 100 m events, and 2 competed in the 200 m dash and 100 m hurdles. How many competitors participated in all three events?

The answer should be 2,
but I think the wording of the problem is poor, and that's why it seems misleadingly difficult.
while the problem explicitly said that: Six competed "ONLY" in the 100 m dash, it failed to clarify that in further givens.

if we dealt with the 16 competitors in 100 m dash as it is:
Six competed only in the 100 m dash ------> which is clearly in area A.
5 competed in both dashes ---------> there is no "ONLY", so the sum of area C + D = 5
3 competed in both 100 m events ------> there is no "ONLY", so the sum of are B + D = 3

the 16 competitors = A + B + C + D
16 = A + (C+D) + (B+D) - D
16 = 6 + 5 + 3 - D
and end up with D = -2 which is invalid.

while the problem intended to say:
"5 competed in both dashes" .... not in hurdle" ---> so Area C only
"3 competed in both 100 m events ... not in 200 m" ----> so Area B only
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Three of the events at a track meet were the 100 m dash   [#permalink] 19 Mar 2019, 10:23
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