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Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink]

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23 Mar 2014, 01:40

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Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between

A. 10 to 20 B. 10 to 40 C. 30 to 40 D. 30 to 70 E. 40 to 70

Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between

A. 10 to 20 B. 10 to 40 C. 30 to 40 D. 30 to 70 E. 40 to 70

First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40. Eliminate D and E.

Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink]

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09 Sep 2015, 08:05

Hello from the GMAT Club BumpBot!

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Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink]

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12 Sep 2015, 00:34

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Mountain14 wrote:

Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between

A. 10 to 20 B. 10 to 40 C. 30 to 40 D. 30 to 70 E. 40 to 70

Fill the attached table and ull get the answer in less than a min

Since max number of athletes who can play defense s only 40, after filling the table u can conclude that the (c) 30 to 40 is the answer

Attachments

Screenshot_2015-09-12-13-01-11.png [ 72.94 KiB | Viewed 1092 times ]

Re: Of the 100 athletes at a soccer club, 40 play defense and 70 [#permalink]

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09 Aug 2017, 04:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between

A. 10 to 20 B. 10 to 40 C. 30 to 40 D. 30 to 70 E. 40 to 70

Here is how you can think about it:

We are given the minimum value of "Neither" and we need to find the minimum and maximum value of "Both".

Total = A + B - Both + Neither

Both = 40 + 70 - 100 + Neither

Both = 10 + Neither

Minimum value of Neither is 20.

Maximum value of Neither will be obtained when "defense" circle in inside the "midfield" circle. So 100 - 70 = 30 would be Neither.

So minimum value of Both is 10+20 = 30 and maximum value is 10+30 = 40.

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