From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?(1) k is a prime number(2) There are 15 different ways to create the party-planning committee consisting of k employees.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?

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From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?

(1) k is a prime number
(2) There are 15 different ways to create the party-planning committee consisting of k employees.

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
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 are needed

Correct answer is option 'C'. Can you explain this answer?

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From a group of 6 employees, k employees are chosen to be on the party...

Given:
From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, we need to find the value of k.

We have two statements to consider:

Statement (1): k is a prime number.
Statement (2): There are 15 different ways to create the party-planning committee consisting of k employees.

Let's analyze each statement separately:

Statement (1) alone:
If k is a prime number, we know it is greater than 1 and can only be divided evenly by 1 and itself. However, this information does not provide any direct information about the value of k. It could be any prime number greater than 1. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) alone:
Statement (2) tells us that there are 15 different ways to create the party-planning committee consisting of k employees. We know that the total number of employees is 6, and we are selecting k employees. Since there are 15 different ways to create the committee, we can set up an equation to solve for k:

C(6, k) = 15

Here, C(n, r) represents the combination function, which calculates the number of ways to choose r items from a set of n items.

Unfortunately, this equation is not enough to determine the value of k uniquely. We need additional information to solve it. Therefore, statement (2) alone is not sufficient to answer the question.

Considering both statements together:
When we combine the information from both statements, we have some constraints. We know that k must be a prime number and that there are 15 different ways to create the committee. By combining these constraints, we can determine the possible values of k.

If we list the prime numbers greater than 1 up to 6, we have: 2, 3, 5.

Now, we can calculate C(6, k) for each of these values:

C(6, 2) = 15
C(6, 3) = 20
C(6, 5) = 6

From these calculations, we see that only C(6, 2) = 15, satisfies the condition stated in statement (2). Therefore, the value of k is 2.

Hence, both statements together are sufficient to answer the question, but neither statement alone is sufficient.

Therefore, the answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Answered by Talent Skill Learning · View profile

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From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?(1) k is a prime number(2) There are 15 different ways to create the party-planning committee consisting of k employees.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?

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From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?(1) k is a prime number(2) There are 15 different ways to create the party-planning committee consisting of k employees.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect 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 From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?(1) k is a prime number(2) There are 15 different ways to create the party-planning committee consisting of k employees.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect 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 From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?(1) k is a prime number(2) There are 15 different ways to create the party-planning committee consisting of k employees.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?.

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