There are k-2 members in a certain band, including Jim...

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

There are k-2 members in a certain band, including Jim...

by swerve » Tue Jan 30, 2018 5:38 am

There are k-2 members in a certain band, including Jim and Allan. Two members are to be selected to attend the Grammy awards ceremony. If there are 10 possible combinations in which Jim and Allan are not selected, what is the value of k?

A. 5
B. 9
C. 15
D. 18
E. 25

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Quote

Source: Beat The GMAT — Problem Solving | Tue Jan 30, 2018 5:38 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

There are k-2 members in a certain band, including Jim...

by regor60 » Tue Jan 30, 2018 6:29 am

swerve wrote:There are k-2 members in a certain band, including Jim and Allan. Two members are to be selected to attend the Grammy awards ceremony. If there are 10 possible combinations in which Jim and Allan are not selected, what is the value of k?

A. 5
B. 9
C. 15
D. 18
E. 25

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

If you find the combination formula confusing in this context, try using slots.

There are two slots available. Since you want to pick from the group excluding Jim and Allan, there are K-4 members to choose from.

Number of choices to fill the first slot is K-4. Therefore, the number of choices to fill the second slot is K-5.

Therefore, there are (K-4)*(K-5) groups of two, BUT this treats a group AB and BA as separate groups, which they are not, so need to divide by 2.

So, there are (K-4)*(K-5)/2 choices. The problem indicates that there are 10 combinations, therefore:

(K-4)*(K-5)/2 = 10 > K^2 - 9K + 20 =20

K^2 = 9K, therefore K=9, B

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jan 31, 2018 4:18 pm

swerve wrote:There are k-2 members in a certain band, including Jim and Allan. Two members are to be selected to attend the Grammy awards ceremony. If there are 10 possible combinations in which Jim and Allan are not selected, what is the value of k?

A. 5
B. 9
C. 15
D. 18
E. 25

We are given that there are k - 2 members in a band, including Jim and Allan. We are also given that 2 members are selected to attend the Grammy awards, not including Jim or Allan. We need to determine the value of k.

Since there are k - 2 members, if Jim and Allan are not selected, we have k - 2 - 2 = k - 4 members from which we can select. We can create the following equation to determine k:

(k - 4)C2 = 10

(k - 4)!/[2!(k - 4 - 2)!] = 10

(k - 4)!/[2!(k - 6)!] = 10

(k - 4)(k - 5)(k - 6)!/[2!(k - 6)!]

[(k - 4)(k - 5)]/2! = 10

k^2 - 9k + 20 = 20

k^2 - 9k = 0

k(k - 9) = 0

k = 0 or k = 9

Since k cannot be zero, k = 9.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]