Each correctional facility in a certain state has the same number of

Question

Each correctional facility in a certain state has the same number of interns, and each facility has interns of each sex. If Lockwood Correctional Facility has 22% of the female interns in the state, does it have less than 20% of the male interns?

(1) Lockwood has between 18% and 22% of the state's male interns.
(2) Lockwood has more female interns than does any other facility in the state.

Saloni9453 · Answer

Please if someone can explain how 1 is sufficient and why not B is the answer

ruis · Answer

Suppose that there are n facilities. Each facility has 100/n % of the interns.

(1) As Lockwood has between 18% and 22%the male interns and 22% of the female interns, it has between 18% and 22% of all residents. Therefore 18 < 100/n < 22, and since n is an integer, n=5.
Suppose there are m male interns and f female interns in the state system.
20% are in Lockwood, so if p% of the males are in Lockwood,
0.2(m+f) =pm/100 + 0.22f
0.02f=0.2m –pm/100= m(0.2 –p/100)
As 0.02f > 0 and m>0, 0.2 – p/100 > 0 and p < 20
SUFFICIENT

(2) On average, the facilities have 100/n % of the female interns, and so 100/n < 22. Thus n is at least 5,and each facility has an average of at most 20% of the male interns. As Lockwood has a higher than average number of female interns, it must have a less than average of male interns, as each resident has the same number of interns. Thus Lockwood has less than 20% of the male interns.
SUFFICIENT

missionmba2025 · Answer

Could you share the source of this question  ruis

KarishmaB  - Request your help in this question. Can you share if there is a more intutive approach to solving such questions ?

KarishmaB · Answer

This question is based on the iconic piglet feed official question discussed here: https://gmatclub.com/forum/each-piglet- ... 82321.html You need a sound understanding of weighted averages to solve this intuitively within a minute - no calculations required. "Each correctional facility in a certain state has the same number of interns" Number of facilities will obviously be an integer so 2 or 3 or 4 or 5 or 6 etc. Since each has same number of interns, it means each has 1/2 (50%) or 1/3rd (33.33%) or 1/4th (25%) or 1/5th (20%) or 1/6th (16.66%) of the total interns respectively. L has 22% of the female interns. (1) Lockwood has between 18% and 22% of the state's male interns. If L has 18 to 22% of the male interns and 22% of the female interns, it will have total interns lying between 18% and 22%. Only one value lies between 18% and 22% and that is 20%. So there must be 5 facilities and each facility must have 20% of total interns. If L has 22% female interns and 20% total interns, then it must have less than 20% male interns (only then can the average be 20%). Sufficient alone. (2) Lockwood has more female interns than does any other facility in the state. Each facility has female and male interns. If L has max female interns, everyone else will have less than 22% female interns. Since total interns is the same in each facility, L will have less than 22% male interns. This means that L will have either 20% of the total interns or 16.66% of total interns etc. Then, number of male interns must certainly be less than 20% to bring the average to 20% or to 16.66% etc. Sufficient alone. Answer (D) Check out this video on weighted averages: https://www.youtube.com/watch?v=_GOAU7moZ2Q Or you can freely check out the complete weighted average video and module tomorrow through Super Sunday on my platform. Details in my signature and here: https://youtu.be/gN_vlDpUflo

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Each correctional facility in a certain state has the same number of

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