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.
Answer: C
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Difficulty level: 650
From a group of 6 employees, k employees are chosen
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Brent@GMATPrepNow wrote: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.
Target question: What is the value of k?
Given: From a group of 6 employees, k employees are chosen to be on the party-planning committee.
So, k can equal 1, 2, 3, 4, 5, or 6
Since the order of the selected employees does not matter, we can use combinations.
We can choose k employees from 6 employees in 6Ck ways.
Let's take a moment to calculate the combinations (which we can do quickly in our head - see how: https://www.gmatprepnow.com/module/gmat ... /video/789)
6C1 = 6
6C2 = 15
6C3 = 20
6C4 = 15
6C5 = 6
6C6 = 1
Statement 1: k is a prime number
So, k can equal 2, 3, or 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: There are 15 different ways to create the party-planning committee consisting of k employees.
We already saw that 6C2 = 15 AND 6C4 = 15
This means k = 2 OR k = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that k = 2 OR k = 3 OR k = 5
Statement 2 tells us that k = 2 OR k = 4
Since both statements must be true, and since k = 2 is the ONLY k-value that is shared by both statements, we can conclude that k = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C