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27 Mar 2024, 10:19
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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.
(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.
27 Mar 2024, 22:39
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Please if someone can explain how 1 is sufficient and why not B is the answer
28 Mar 2024, 00:36
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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
(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
