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The host of a television debate show has to select a 4-member discussion panel out of a list of 22 willing candidates that includes 5 politicians and 6 businessmen. If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted? 
(1)  The list includes 5 journalists and 2 authors
(2)  The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
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The host of a television debate show has to select a 4-member discussi...
Steps 1 & 2: Understand Question and Draw Inferences
Given:
  • Total number of candidates on the list = 22
    • Let number of politicians and businessmen be P and B respectively
    • P = 5
    • B = 6
    • So, candidates in other professions = 22 – 5 – 6 = 11
 
  • Total number of professions in the list is greater than or equal to 4
    • We already know 2 professions – Politics and Business
    • This means, there are at least 2 other professions in the list
    • The maximum number of other professions can be 11 (this will happen in the case where each of the 11 candidates in other professions has a distinct profession)
    • So, the number of other professions lies between 2 and 11, inclusive
To find: Number of ways to constitute a 4 – member panel, such that all members have different professions
  • If the total number of professions = 4
    • This means, there are 2 other professions. Let’s label these as P1 and P2
    • So, the distribution of the 22 candidates among these 4 professions will be as under:
      • Politics = 5
      • Business = 6
      • P1 = x (assuming this number)
      • P2 = 11 – x
    • So, the tasks involved in fulfilling the objective will be:
      • Task 1 – Select 1 out of 5 politicians AND
      • Task 2 – Select 1 out of 6 businessmen AND
      • Task 3 – Select 1 out of x P1 people AND
      • Task 4 – Select 1 out of 11 – x P2 people
    • So, the objective equation will be:
(RequiredNumberofways)=
  • Thus, to answer this question, we need to know the value of x
  • If the total number of professions > 4
    • So, the total number of professions is 5 or more
    • This means, there are 3 or more other professions. Let’s label these as P1, P2, P3 etc.
    • So, the distribution of the 22 candidates among these 4 professions will be as under:
      • Politics = 5
      • Business = 6
      • P1 = x (assuming this number)
      • P2 = y (assuming this number)
      • P3 = z (assuming this number)
      • And so on, where x + y + z + .  . . = 11
 
  • So, here the objective consists of 2 events:
    • Event 1 - Determine which 4 professions should be represented on the panel
      • If the total number of professions is N, then the number of ways in which Event 1 can happen = N4C
        • Depends on the value of N
 
  • Event 2 - Determine the number of ways in which candidates from each of the 4 chosen professions can be represented. The computation for this event will be done using the same process as shown above in the case where the number of professions was 4
    • This calculation will depend on the number of candidates in each profession
 
  • So, in this case, we need to know the number of professions and the number of candidates in each profession
 
  • Thus, we observe that in order to answer the question, we need to know:
 
  • the number of professions and
  • the number of candidates in each profession
 
Step 3: Analyze Statement 1 independently
  • The list includes 5 journalists and 2 authors
    • Let number of journalists and authors be J and A respectively
    • J = 5
    • A = 6
  • So, candidates in still unknown professions (apart from Business, Politics, Journalism and Authorship) = 11- 5 - 2 = 4
    • There may be 1 unknown profession with 4 candidates in it (so, total number of professions = 5)
    • Or, there may be 2 unknown professions, with 2 candidates each in it (thus, total number of professions = 6)
    • Or, 3 unknown professions with 1, 1 and 2 candidates in each (thus, total number of professions = 7)
    • Or 4 unknown professions with 1 candidate each (thus, total number of professions = 8)
So, since we have not been able to determine a unique number of professions, Statement 1 alone is not sufficient.
 
Step 4: Analyze Statement 2 independently
  • The list includes only 1 profession from which there are fewer than 3 candidates
    • Politics has 5 candidates
    • Business has 6 candidates
    • This means, the profession mentioned in Statement 2 must be one of the ‘other professions’        
      • This particular profession, let’s call it P1 has either 1 or 2 candidates
      • We’ve already calculated in Steps 1 and 2 that Total candidates in ‘other professions’ = 11
    • So, the number of candidates in professions apart from Politics, Business or P1 (let’s call these ‘unknown professions’) is 11 – 1 or 11 – 2, that is, 10 or 9
      • There may be 1 unknown profession with 9 or 10 people in it (thus, total number of professions = 4)
      • Or, there may be 2 unknown professions (thus total number of professions = 5) and the 9 or 10 people may be split between these 2 unknown professions in many possible ways: (1,8) or (2, 7) etc.
      • And so on. .  .
We quickly see that multiple values for the number of professions and for the number of people in each profession are possible here.
So, Statement 2 is not sufficient to answer the question
 
Step 5: Analyze Both Statements Together (if needed)
  • From Statement 1:
    • Number of candidates in still unknown professions = 4
      • Possible split of these 4 candidates among distinct unknown professions = {4, 0}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}
  • From Statement 2:
    • There is only one profession with less than 3 candidates
  • Combining the two statements:
    • The only split of the 4 candidates among distinct unknown professions = {4, 0}
    • Thus, the split of the 22 candidates among different professions is as under:
      • Politics = 5
      • Business = 6
      • Journalism = 5
      • Authorship = 2
      • Unknown Profession 1 = 4
Since we now know the number of professions and the number of candidates in each profession, we will be able to answer the Q.
The 2 statements together are sufficient to answer the question.
 
Answer: Option C
 
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Most Upvoted Answer
The host of a television debate show has to select a 4-member discussi...
Explanation:

Statement 1:
- The statement provides information about additional candidates on the list (journalists and authors), which helps in determining the number of ways to constitute the panel.
- With this information, we can ensure that the panel includes at least 4 different professions.

Statement 2:
- This statement suggests that there is only one profession with fewer than 3 candidates, which is not enough information to determine the composition of the panel.

Combining Both Statements:
- By combining both statements, we know that there are additional candidates from professions other than politicians, businessmen, journalists, and authors, allowing for a diverse panel.
- This information, along with the specific details provided in each statement, is sufficient to determine the number of ways to constitute the panel.
Therefore, both statements together are sufficient to answer the question, making the correct choice (C).
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The host of a television debate show has to select a 4-member discussion panel out of a list of 22 willing candidates that includes 5 politicians and 6 businessmen. If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?(1) The list includes 5 journalists and 2 authors(2) The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askedd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?
Question Description
The host of a television debate show has to select a 4-member discussion panel out of a list of 22 willing candidates that includes 5 politicians and 6 businessmen. If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?(1) The list includes 5 journalists and 2 authors(2) The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askedd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The host of a television debate show has to select a 4-member discussion panel out of a list of 22 willing candidates that includes 5 politicians and 6 businessmen. If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?(1) The list includes 5 journalists and 2 authors(2) The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askedd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The host of a television debate show has to select a 4-member discussion panel out of a list of 22 willing candidates that includes 5 politicians and 6 businessmen. If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?(1) The list includes 5 journalists and 2 authors(2) The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askedd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?.
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If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?(1) The list includes 5 journalists and 2 authors(2) The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askedd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. 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If the list includes candidates from at least 4 professions and no two members of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?(1) The list includes 5 journalists and 2 authors(2) The list includes only 1 profession from which there are fewer than 3 candidatesStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question askedd)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. 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