Discussion

Explanation:

From (2): The number of students who belong to A, B and C is 8.

From (1): The number of students who belong to only A is twice the number of students who belong to B and C.
Let the number of students belonging to only B and C is x.
⇒ Number of students belonging to B and C = x + 8
∴ Number of students belonging to only A = 2x + 16

From (5): Number of students belonging to only A and C = (2x + 16) + 8 = 2x + 24
Also, number of students belonging to only B = (2x + 24) + 16 = 2x + 40

From (4): Number of students belonging to only A and B = Number of students belonging to only A and C + 8
⇒ Number of students belonging to only A and B = 2x + 24 + 8 = 2x + 32
[Since 8 is common to both regions mentioned in the point, we have ignored it.]

From (3): Number of students belonging to B = 8 + 2x + 32 + x + 2x + 40
Number of students belonging to C = 8 + x + 2x + 24 + only C
⇒ 8 + x + 2x + 24 + only C = 8 + 2x + 32 + x + 2x + 40
⇒ only C = 2x + 48

​​​​​​​

Now, total number of students is 300.
⇒ (2x + 16) + (2x + 32) + (2x + 40) + 8 + (2x + 24) + x + (2x + 48) = 300
⇒ 11x + 168 = 300
⇒ x = 12

∴ Number of students in A but not B = 2x + 16 + 2x + 24 = 4x + 40 = 88

Hence, 88.

» Your doubt will be displayed only after approval.