Of the 31 students in a 4th grade class, 21 can swim, 24 can ride a bike, and 19 can ice skate. For a competition, students are needed who can
a) swim and ride a bike,
b) swim and ice skate,
c) ride a bike and ice skate,
d) swim and ride a bike and ice skate.
How many students from the class are available for a), b), c), and d) at a minimum, and how many at a maximum?
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Official solution
Maximal available
a) 21, as there are only 21 swimmers, b) 19, as there are only 19 skaters, c) 19, as there are only 19 skaters, d) 19, as there are only 19 skaters.
Minimal available a) 14 because 24+21−31=14, b) 9 because 21+19−31=9, c) 12 because 24+19−31=12, d) 2 because 24+21+19−31−31=2.
Source: NuminaMath-1.5,
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