A club has 256 members of whom 144 can play football, 123 can play ten

Question

A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

A. 45
B. 43
C. 38
D. 33
E. 32

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Official Answer

B

A. 45
B. 43
C. 38
D. 33
E. 32

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Accepted Answer

Total Players = Football only + Tennis only + Cricket only - (students playing min two games) + Students playing all three games + players of no game

256 = 144+123+132 - (58+25+63) + Playing all three games

Playing all three games = 3

Only tennis = Tennis players - Tennis with one other game + all three games

Only tennis = 123 - (58+25) + 3 = 43

Answer:Option B

https://www.youtube.com/watch?v=G9h4hT5Uj8A

GMATWhizTeam · Answer

Solution 
 • Let us assume that f, t, and c denote the number of members who can play only football, only tennis, and only cricket, respectively.
 o So, we need to find the value of t. 
• Now, let us draw a Venn- Diagram, as given below:
 https://www.dropbox.com/s/v3ktz9a2istvulc/3_sets.png?dl=1 
• So, based on the information given in the question and the above Venn-diagram, we can write:
 o Total number of members  = f+t+c+w+x+y+z =256…………..Eq(i) 
o The number of members who can play football  = f+w+x+z = 144 
  Subtracting the above equation from equation(i), we get,
  t+c+y = 112…………..Eq.(ii)  
o The number of people who can play cricket  = c+x+y+z = 132……….Eq.(iii) 
o We know that the number of people who plays both football and cricket  =x+z= 63 
  Substituting the above value in Eq.(iii), we get,
  c + y = 132 – 63 =69 
 • Now, Substituting the above value of c+y in Eq.(ii), we get,
•  t+69 = 112⟹t = 43     
Thus, the correct answer is   Option B.

sambitspm · Answer

It's much more difficult to solve with the whiteboard.
Answer B

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A club has 256 members of whom 144 can play football, 123 can play ten

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A club has 256 members of whom 144 can play football, 123 can play ten

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