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In a class of 100 students, 70 play basketball. How many students in the class play volleyball but not basketball?
(1) 60 students in the class do not play volleyball.
(2) The number of students playing both basketball and volleyball is twice the number of students playing neither.
(1) 60 students in the class do not play volleyball.
(2) The number of students playing both basketball and volleyball is twice the number of students playing neither.
29 Dec 2025, 09:12
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Given 100 students in class and 70 play basketball
To find no of students who play volleyball alone
Hence total = n(B) + n(V) - n(B&V) + neither
From (1) we can get no of students that play volley ball to be 40 as 60 don't play volley ball. Still both is unknown
From (2) number of people who play both is twice who play neither. Still not sufficient
Using (1) and (2) we can get no. of people who play both and therefore who play volleyball alone. Option C
To find no of students who play volleyball alone
Hence total = n(B) + n(V) - n(B&V) + neither
From (1) we can get no of students that play volley ball to be 40 as 60 don't play volley ball. Still both is unknown
From (2) number of people who play both is twice who play neither. Still not sufficient
Using (1) and (2) we can get no. of people who play both and therefore who play volleyball alone. Option C
29 Dec 2025, 10:10
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ExpertsGlobal5
Let us use the following letters to denote the two set Venn diagram.
Let a denote the set containing Basketball only.
Let c denote the set containing Volleyball only.
Let b denote the set containing both volley ball and basket ball.
Let d denote the neither of the sets.
Given that: Volleyball = a+b = 70
c = ?
Statement 1:
60 students in the class do not play volleyball.
So, a+d = 60
we cannot find C.
Hence, Insufficient.
Statement 2:
The number of students playing both basketball and volleyball is twice the number of students playing neither.
b = 2*d
a + b+ c + d =100
a+ c + 3d = 100
Hence, Insufficient.
combining both statements 1 and 2, we get
a+ b = 70 = a+ 2d
a+d = 60
solving we get d = 10, then a= 50, b=20
thus c=20
Hence, Sufficient .
Option C
