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23 Mar 2014, 01:40
Kudos
Bookmarks
C
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Difficulty:
35%
(medium)
Question Stats:
71% (01:47) correct
29%
(01:47)
wrong
based on 610
sessions
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Not Attempted Yet
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
A. 10 to 20
B. 10 to 40
C. 30 to 40
D. 30 to 70
E. 40 to 70
23 Mar 2014, 05:33
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Mountain14
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.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 70 - {both} + {neither}
{both} = {neither} + 10.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+10=30. Eliminate A and B.
Answer: C.
25 Jul 2014, 02:49
Kudos
Bookmarks
Refer diagram below
We require to find the shaded region
Setting up the equation
40 + 70-x + 20 = 100
x = 30
For defence = 40; the maximum value for which x can reach is also 40
Range = 30 to 40
Answer = C
We require to find the shaded region
Setting up the equation
40 + 70-x + 20 = 100
x = 30
For defence = 40; the maximum value for which x can reach is also 40
Range = 30 to 40
Answer = C
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