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

1. 45
2. 43
3. 38
4. 33
5. 32

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

Total Players = Football only + Tennis only + Cricket only (students participating in a minimum of two matches) + Students participating in all three matches + Players not participating in any matches
256 is equal to 144 + 123 + 132 - 58 + 25 + 63 + playing all three games.
playing all three games equals three
Tennis players plus all three games plus tennis with one additional game equals only tennis.
Tennis only: 123 - (58 + 25) + 3 = 43

B is the correct answer.

Approach Solution 2:

Assume that f, t, and c represent the proportion of members who can only play cricket, football, or tennis, respectively.

Therefore, we must ascertain t's value.

Let's now create a Venn diagram as shown below:

Therefore, using the data from the question and the Venn diagram above, we may write:

Total members are equal to f + t + c + w + x + y + z = 256. Eq(i)

Football-playing members total 144, or f+w+x+z.
We obtain t+c+y=112 by removing the aforementioned equation from the equation I

Equation (ii) states that c+x+y+z=132 persons can play cricket.
Equation (iii): We know that x+z=63 represents the number of people who play both cricket and football.
Using the above value as a substitute in Eq. (iii), we obtain c+y=132-63=69.
Using the aforementioned value of c+y as a substitute in Eq. (ii), we obtain
t+69=112
t=43.

Therefore, Option B is the right response.

“A club has 256 members of whom 144 can play football, 123 can play ten" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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