A certain club has 20 members. What is the ratio of the member of 5-member

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:14 am

A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

Answer: C
Source: GMATPrep test

Ratio of the member of 5-member committees to the number of 4-member committees

= 20C5 / 20C4 = [(20.19.18.17.16)/(1.2.3.4.5) / (20.19.18.17)/(1.2.3.4)] = 16/5

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review

Locations: Manhattan Review Chennai | GMAT Prep Himayatnagar | GRE Prep Hyderabad | Bangalore GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:14 am

A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

Answer: C
Source: GMATPrep test

The ratio is the following:

(20C5) / (20C4) = [(20 x 19 x 18 x 17 x 16) / 5!] / [(20 x 19 x 18 x 17) / 4!]

= [(20 x 19 x 18 x 17 x 16) / 5!] x [4! / (20 x 19 x 18 x 17)]

= 16/5

Answer: C

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:14 am

A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

Answer: C
Source: GMATPrep test

5-member committees
Since the order in which we select the committee members does not matter, we can use COMBINATIONS
We can select 5 people from 20 people in 20C5 ways
20C5 = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)

4-member committees
Since the order in which we select the committee members does not matter, we can use COMBINATIONS
We can select 4 people from 20 people in 20C4 ways
20C4 = (20)(19)(18)(17)/(4)(3)(2)(1)

The RATIO = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)]/[(20)(19)(18)(17)/(4)(3)(2)(1)]
= (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)][(4)(3)(2)(1)/(20)(19)(18)(17)]
=(20)(19)(18)(17)(16)(4)(3)(2)(1)/(20)(19)(18)(17)(5)(4)(3)(2)(1)
=(20)(19)(18)(17)(16)(4)(3)(2)(1)/(20)(19)(18)(17)(5)(4)(3)(2)(1)
=16/5

Answer: C

Cheers,
Brent