Each correctional facility in a certain

netcaesar wrote:Each correctional facility in a certain state has the same number of interns, and each facility has interns of each GMAT. 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.

OA is D

One of the more interesting official questions - certainly 800-level. The question is essentially based on weighted average principles, and the key idea is this: if Lockwood has 22% of female interns, and 20% of all interns, then Lockwood must have less than 20% of all male interns. On to the solution:

Note first that each facility has the same number of interns, so if there are n facilities, each has 1/n of the total number of interns. Using Statement 1, we know that Lockwood has 22% of female interns, and between 18% and 22% of male interns. This is a weighted average; in total, Lockwood must therefore have between 18% and 22% of all interns (the total percentage must lie somewhere between the percentage of male interns and the percentage of female interns). So 0.18 <= 1/n <= 0.22, and since n is an integer, n must be 5. So there are 5 facilities in total, and each has 20% of all interns. If Lockwood has 22% of female interns, Lockwood must therefore have less than 20% of all male interns.

Using Statement 2, since Lockwood has more female interns than any other facility, then no other facility has more than 22% of the female interns. If there were 4 or fewer facilities, one facility would need to have at least 25% of all female interns. Since we know that not to be the case, there must be at least 5 facilities. Thus Lockwood has no more than 1/5 of all interns, and again since Lockwood has 22% of female interns, Lockwood must have less than 20% of all male interns.