A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. Can you explain this answer?

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A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?

(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5

(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5

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 'D'. Can you explain this answer?

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A playgroup is made up entirely of n pairs of siblings, including the ...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Playgroup has n sibling pairs
- So, Total members = 2n
Adam-Josh are a sibling pair
4 members selected from the group
- Number of ways in which 4 members can be selected from 2n members = ²ⁿC₄

To find: n = ?

Step 3: Analyze Statement 1 independently

The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5

Let’s first find out the expression for the Probability that Adam and Josh are among the 4 members chosen. Then, we’ll equate this expression to 25
Calculating the number of ways in which the favorable event can happen
- Adam and Josh are definitely there among the 4 representatives
- So, when choosing the 4 representatives, our task simplifies to choosing 2 representatives out of the 2n-2 members that remain after Adam and Josh are taken out
- The number of ways in which we can chose 2 representatives out of 2n – 2 members =
Calculating the number of total outcomes possible
Total number of members = 2n
Number of representatives to be chosen = 4
The number of ways in which 4 representatives can be chosen out of 2n members =

Calculating the Probability that the favorable event will happen

⇒n=3 (rejecting the negative value since number of people cannot be negative)

Thus, Statement 1 alone is sufficient to arrive at a unique value of n.

Step 4: Analyze Statement 2 independently

The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5
Let’s first find out the expression for the Probability that 2 sibling pairs are chosen to represent the playgroup. Then, we’ll equate this expression to 1/5
Calculating the number of ways in which the favorable event can happen
- Total number of sibling pairs = n
- Number of sibling pairs to be chosen = 2
- The number of ways in which 2 pairs can be chosen out of n pairs =
Calculating the number of total outcomes possible
- Total number of members = 2n
- Number of representatives to be chosen = 4
- The number of ways in which 4 representatives can be chosen out of 2n members =
Calculating the Probability that the favorable event will happen

⇒n=3

(rejecting the negative value since number of people cannot be negative)

Thus, Statement 2 alone is sufficient to arrive at a unique value of n.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not required

Answer: Option D

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A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. Can you explain this answer?

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A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. 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 A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. Can you explain this answer?.

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What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. 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What is the value of n?(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5a)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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.

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