The following question is accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. In a company there are total 360 employees in the office. Number of employees who plays cricket is 288. Find the number of employees who doesn’t play any game. (Assume cricket and pool are the only two games they play) I. 216 employees play only cricket but not pool. II. The total numbers of employees who play either cricket or pool or both is 216 more than the number of employees who does not play any game.
The following question is accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. In a company there are total 360 employees in the office. Number of employees who plays cricket is 288. Find the number of employees who doesn’t play any game. (Assume cricket and pool are the only two games they play) I. 216 employees play only cricket but not pool. II. The total numbers of employees who play either cricket or pool or both is 216 more than the number of employees who does not play any game. Correct Answer Statement II along is sufficient, but statement I alone is not sufficient.
Lets number of employees who plays cricket is F1,
Number of employees who play pool is F2,
Number of employees who play both cricket and pool is G and
Number of employees who doesn’t play any game is H.
Total employees = F1 + F2 – G + H = 360 ----(1)
F1 = 288
From I:
Employees who plays only chess = F1 – G = 216
G = 288-216 = 72
But, we cannot find the value of H.
So. I alone is not sufficient.
From II:
Number of employees who play either cricket or pool or both = (F1 + F2 - G)
Number of employees who does not play any game = H = (F1 + F2 - G) – 216
⇒ (F1 + F2 – G) = H + 216 ----(2)
From equation (1) and (2)
⇒ H + 216 + H = 360
⇒ 2H = 144
⇒ H = 72
Hence, total employes who doesn’t play any game is 72.
So, II alone is sufficient.
