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

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Joined: 12 Sep 2015
Posts: 4226
From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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04 Apr 2017, 08:35
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Difficulty:

65% (hard)

Question Stats:

51% (01:32) correct 49% (01:40) wrong based on 259 sessions

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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.

*kudos for all correct solutions

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Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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04 Apr 2017, 09:46
1
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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.

*kudos for all correct solutions

6 employees and k are choosen...
k is POSITIVE integer, so $$k\neq{0}$$...

Let's see the statements..
1) k is prime.
k can be 2,3,5
Insufficient

2)15 different ways to select k..
Easy to believe that we will get an answer ..
But there will be two values which will give us same answer..
6Ck=15..
$$\frac{6!}{(6-k)!k!}=15$$
k can be 4 or 2..
Insufficient

Combined
Only 2 is left
Sufficient

C
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Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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04 Apr 2017, 09:47
2
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.

*kudos for all correct solutions

St I
k is a prime number
k can be 2,3 or 5 -----------Insufficient

St II
6Ck = 15
k can take values from 1,2,3,4,5,6

out of all the above 6 values only 2,4 satisfies 6Ck = 15 since 6C2 = 6C4 =15 ----------Insufficient

Combining St I and II we have
k can be 2 or 4 and k is prime
so k = 2 -----------Sufficient

Hence option C is correct
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Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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05 Apr 2017, 07:56
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Top Contributor
2
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 the video below)
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

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Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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05 Apr 2017, 09:12
1
1. k is a prime number between 1 and 6 inclusive. k could be 2,3,5. Insuff.
2. The number of ways to create the committe is 6!/(k!(6-k)!).
This is equal to 15 in case k is 2 or 4. Insuff.
Combined: combining the statments we get that k must be 2. Suff.

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Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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05 Apr 2017, 09:52
1
2,3,5 0- multiple possibilities.
A,D eliminated.

The concept is 6C2 = 6C4.
which eliminates (ii)

B eliminated.

Combined, only 2.

(C).
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Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

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12 Jun 2018, 05:36
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Re: From a group of 6 employees, k employees are chosen to be on the party   [#permalink] 12 Jun 2018, 05:36
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