GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Sep 2018, 21:56

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

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

Author Message
TAGS:

Hide Tags

CEO
Joined: 12 Sep 2015
Posts: 2906
From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

Show Tags

04 Apr 2017, 08:35
Top Contributor
6
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:31) correct 48% (01:42) wrong based on 204 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

_________________

Brent Hanneson – GMATPrepNow.com

Math Expert
Joined: 02 Aug 2009
Posts: 6810
Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

Show Tags

04 Apr 2017, 09:46
1
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

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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Joined: 19 Apr 2016
Posts: 274
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, 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
Hit Kudos if you liked it
CEO
Joined: 12 Sep 2015
Posts: 2906
Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

Show Tags

05 Apr 2017, 07:56
1
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

RELATED VIDEOS

_________________

Brent Hanneson – GMATPrepNow.com

Intern
Joined: 05 Sep 2016
Posts: 20
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, 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.

Sent from my Redmi 4 using GMAT Club Forum mobile app
Manager
Joined: 10 Apr 2015
Posts: 195
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, 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).
_________________

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

Non-Human User
Joined: 09 Sep 2013
Posts: 8195
Re: From a group of 6 employees, k employees are chosen to be on the party  [#permalink]

Show Tags

12 Jun 2018, 05:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: From a group of 6 employees, k employees are chosen to be on the party &nbs [#permalink] 12 Jun 2018, 05:36
Display posts from previous: Sort by

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

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.