A poll of 40 gymnastics club members were asked where they should focus their tr
ID: 3142274 • Letter: A
Question
A poll of 40 gymnastics club members were asked where they should focus their training: routine, fundamental skills, or conditioning. The responses were 21 for routines, 18 for skills, 16 for conditioning, 10 for routines and skills, 8 for skills and conditioning, 7 for routines and conditioning, and 4 for all three. How many members thought that the priorities should be routines or skills, but not both? How many members thought that the priority should be skills and conditioning, but not routines? How many members thought that the priority should be something other than these three issues?Explanation / Answer
Let A: People who focus on routines B: People who focus on skills C: People who focus on conditioning
Total number of members |AUBUC| = 40
|A| = 21 |B| = 18 |C| = 16 |AB| = 10 |BC| = 8 |AC| = 7 |ABC| = 4
a) Number of members who thought that the priorities should be routines and skills but not both
= |AUB| - |AB|
= |A| + |B| - |AB| -|AB|
= 21 + 18 - 10 - 10
= 19
b) Number of members who thought that the priorities should be skills and conditioning but not both
= |BUC| - |BC|
= |B| + |C| - |BC| - |BC|
= 18 + 16 - 8 - 8
= 18
c) We have the formula |AUBUC| = |A| + |B| + |C| - |AUB| - |BUC| - |AUC| + |ABC|
=> |AUBUC| = 21 + 18 + 16 - 10 - 8 - 7 + 4
=> |AUBUC| = 34
Thus the number of members who thought that the priority should be something else
= 40 - 34 = 6