It is currently 25 Feb 2018, 11:54

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

SVP
Joined: 11 Sep 2015
Posts: 2071
From a group of 6 employees, k employees are chosen to be on the party [#permalink]

### Show Tags

04 Apr 2017, 07:35
Expert's post
Top Contributor
2
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

52% (02:03) correct 48% (01:10) wrong based on 148 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Founder of gmatprepnow.com

Math Expert
Joined: 02 Aug 2009
Posts: 5663
Re: From a group of 6 employees, k employees are chosen to be on the party [#permalink]

### Show Tags

04 Apr 2017, 08:46
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Senior Manager
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: From a group of 6 employees, k employees are chosen to be on the party [#permalink]

### Show Tags

04 Apr 2017, 08:47
2
KUDOS
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
Hit Kudos if you liked it
SVP
Joined: 11 Sep 2015
Posts: 2071
Re: From a group of 6 employees, k employees are chosen to be on the party [#permalink]

### Show Tags

05 Apr 2017, 06:56
1
KUDOS
Expert's post
Top Contributor
2
This post was
BOOKMARKED
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

[Reveal] Spoiler:
C

RELATED VIDEOS

_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 05 Sep 2016
Posts: 21
Location: Israel
Concentration: Economics, Technology
WE: Engineering (Telecommunications)
Re: From a group of 6 employees, k employees are chosen to be on the party [#permalink]

### Show Tags

05 Apr 2017, 08:12
1
KUDOS
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.

Sent from my Redmi 4 using GMAT Club Forum mobile app
Manager
Joined: 10 Apr 2015
Posts: 204
GPA: 3.31
Re: From a group of 6 employees, k employees are chosen to be on the party [#permalink]

### Show Tags

05 Apr 2017, 08:52
1
KUDOS
2,3,5 0- multiple possibilities.
A,D eliminated.

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

B eliminated.

Combined, only 2.

(C).
_________________

In case you find my posts helpful, give me Kudos. Thank you.

Re: From a group of 6 employees, k employees are chosen to be on the party   [#permalink] 05 Apr 2017, 08:52
Display posts from previous: Sort by