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Each correctional facility in a certain state has the same [#permalink]

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20 Jul 2008, 10:06

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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.

Please explain your answer

Last edited by tarek99 on 20 Jul 2008, 11:16, edited 1 time in total.

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.

St1: is clearly insuff. (EDITED LATER: how wrong I was... See the later post).

St2: First, we can conclude than each of the other facilities has less than 22% female interns in the state… Which means that there must be at least 5 facilities (including Lockwood one). Also, since the number of interns is the same for all facilities and Lockwood has more females than does any other one => Lockwood has less males than any other one => the Lockwood male interns should constitute less than 100%/5 = 20% of the male interns in the state (because if we assume they constitute 20% or more, it would mean that each of the other facilities would constitute more, and, in order not to exceed 100%, we would have to conclude that there’re less than 5 facilities =>contradiction). Sufficient.

What is the OA?

Last edited by greenoak on 20 Jul 2008, 18:33, edited 1 time in total.

For statement 1: Let m and f be the quantities of interns of the corresponding sex in state, and let’s calculate the minimum possible number of facilities. Minimum possible number of facilities corresponds to maximum possible number of interns in each facility.

The greatest percentage of males that Lockwood could contribute is 22% => The maximum number of interns in Lockwood (and thus, in each facility) is 0.22f+0.22m = 0.22(f+m) which means that the minimum number of facilities is no less than 1/0.22, or, in other words, no less than 5 (because the number of facilities should be an integer).

Now, if we assume that Lockwood contributes 20% or more to the number of males it would mean that it contributes at least 0.22f+0.2m>0.2(f+m) people – i.e., strictly greater than one/fifth. But, since the number of interns is the same it would mean that all other facilities would contribute more than 1/5 =>it is possible only if we have less than five facilities =>contradiction.

For statement 1: Let m and f be the quantities of interns of the corresponding sex in state, and let’s calculate the minimum possible number of facilities. Minimum possible number of facilities corresponds to maximum possible number of interns in each facility.

The greatest percentage of males that Lockwood could contribute is 22% => The maximum number of interns in Lockwood (and thus, in each facility) is 0.22f+0.22m = 0.22(f+m) which means that the minimum number of facilities is no less than 1/0.22, or, in other words, no less than 5 (because the number of facilities should be an integer).

Now, if we assume that Lockwood contributes 20% or more to the number of males it would mean that it contributes at least 0.22f+0.2m>0.2(f+m) people – i.e., strictly greater than one/fifth. But, since the number of interns is the same it would mean that all other facilities would contribute more than 1/5 =>it is possible only if we have less than five facilities =>contradiction.