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# Each correctional facility in a certain state has the same

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

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05 Dec 2007, 10:00
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Each correctional facility in a certain state has the same number of interns. If Lockwood Correctional 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 21% of the state's male interns.
(2) Lockwood has more female interns than does any other facility in the state.
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06 Dec 2007, 09:22
I feel that (1) alone is not sufficient.
With (2) alone
Name f(i), m(i) the number of female and male in facility i
We have n facilities and Lockwood has f(1) and m(1)
f(1) > f(2),..,f(n)
=> n>=5 (bcz f(1)= 22% (f(1) + f(2) + ... + f(n) )
and m(1) < m(2), ... , m(n) (bcz all facilities have the same number of interns)
=> m(1) < 1/5 ( m(1) + m(2) + ... + m(n) )
It means that from (2), we can conclude that Lockwood has less than 20% of total male interns.
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06 Dec 2007, 09:33
Can you explain it very slowly, step by step?
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06 Dec 2007, 12:44
kevincan wrote:
Each correctional facility in a certain state has the same number of interns. If Lockwood Correctional 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 21% of the state's male interns.
(2) Lockwood has more female interns than does any other facility in the state.

I think it's B (though I spent more than 2 min. to figure it out)

ok, st.1 definitely says nothing.

now, st2. I used numbers. Let's say there are total of 1000 inters in all state's correctional facility. Let's say there 500 males and 500 females. These people should be evenly distributed among at least 5 facilities (incl. Lockwood). Why "at least 5"? Well, st.2 says that Lockwood has more female interns than does any other facility in the state. Which is 22% from the question stem. So, it means that 78% remained females should be distributed in such a manner that no one facility has more that 22%. It could be only if you put this 78% in at least 4 facilities.

So, we have 1000 inters and 5 facilities. Since "each facility has the same number of interns", each facility has 200 people. Now we know that Lockwood has 22% of 500 females, which is 110. It means that there are 90 males in Lockwood (add up to 200). 90 out of 500 is 18% which is less than 20%. you can play with numbers, but I guess the outcome will be the same.

hope I didn't mess up:)
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06 Dec 2007, 19:52
elgo wrote:
kevincan wrote:
Each correctional facility in a certain state has the same number of interns. If Lockwood Correctional 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 21% of the state's male interns.
(2) Lockwood has more female interns than does any other facility in the state.

I think it's B (though I spent more than 2 min. to figure it out)

ok, st.1 definitely says nothing.

now, st2. I used numbers. Let's say there are total of 1000 inters in all state's correctional facility. Let's say there 500 males and 500 females. These people should be evenly distributed among at least 5 facilities (incl. Lockwood). Why "at least 5"? Well, st.2 says that Lockwood has more female interns than does any other facility in the state. Which is 22% from the question stem. So, it means that 78% remained females should be distributed in such a manner that no one facility has more that 22%. It could be only if you put this 78% in at least 4 facilities.

So, we have 1000 inters and 5 facilities. Since "each facility has the same number of interns", each facility has 200 people. Now we know that Lockwood has 22% of 500 females, which is 110. It means that there are 90 males in Lockwood (add up to 200). 90 out of 500 is 18% which is less than 20%. you can play with numbers, but I guess the outcome will be the same.

hope I didn't mess up:)

you can't assume there are an equal number of male and female interns in the state though. There may be 200 female interns and 1,500 male interns for all we know.

I'm not even sure it can be figured out using both 1 and 2, but I'd love to find out
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06 Dec 2007, 20:26
I am getting B
assume for instance that there are 100 female studensts and 100 male students
lockwood has 22 females

then others might have 21, 20, 19 and 18 female interns

assume that if 21 guys are in lockwood then there is no way 21+22=43 total student population, is going to be the same for other schools can have the same number of students if lockwood were to have more than 20 male students..try it..
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06 Dec 2007, 20:48
fresinha12 wrote:
I am getting B
assume for instance that there are 100 female studensts and 100 male students
lockwood has 22 females

then others might have 21, 20, 19 and 18 female interns

assume that if 21 guys are in lockwood then there is no way 21+22=43 total student population, is going to be the same for other schools can have the same number of students if lockwood were to have more than 20 male students..try it..

but if we're just going off of the information in B, how can we assume there are an equal number of male and female students?

why couldn't there be 100 prisons and only 5 of them have female students at all? and the other 95 have all male guards, so that the percent at Lockwood is < 1%?

you could have 22% of the females at lockwood and only 5% of the males and still have the same number of students at each facility.
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07 Dec 2007, 01:00
eschn3am wrote:
elgo wrote:
kevincan wrote:
Each correctional facility in a certain state has the same number of interns. If Lockwood Correctional 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 21% of the state's male interns.
(2) Lockwood has more female interns than does any other facility in the state.

I think it's B (though I spent more than 2 min. to figure it out)

ok, st.1 definitely says nothing.

now, st2. I used numbers. Let's say there are total of 1000 inters in all state's correctional facility. Let's say there 500 males and 500 females. These people should be evenly distributed among at least 5 facilities (incl. Lockwood). Why "at least 5"? Well, st.2 says that Lockwood has more female interns than does any other facility in the state. Which is 22% from the question stem. So, it means that 78% remained females should be distributed in such a manner that no one facility has more that 22%. It could be only if you put this 78% in at least 4 facilities.

So, we have 1000 inters and 5 facilities. Since "each facility has the same number of interns", each facility has 200 people. Now we know that Lockwood has 22% of 500 females, which is 110. It means that there are 90 males in Lockwood (add up to 200). 90 out of 500 is 18% which is less than 20%. you can play with numbers, but I guess the outcome will be the same.

hope I didn't mess up:)

you can't assume there are an equal number of male and female interns in the state though. There may be 200 female interns and 1,500 male interns for all we know.

I'm not even sure it can be figured out using both 1 and 2, but I'd love to find out

you don't have assume that there an equal number of males and females (I just used it b/c it's easier to calculate:)

total of 1700 people, who are evenly distributed among 5 facilities=> 340 interns in each. Then, 22% of 200 females, which is 44, is in Lockwood. It means that there are 340-44= 296 males. Finally, 296/1500=19.7%<20%.
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07 Dec 2007, 01:24
this one is killing me.

all I know is that 1 puts a limit on how small the number of men can be. Picking numbers like 22 women vs 4 men is too disparate. What's the limit?

To test 2, you should use that lower limit number from 1.

But I still dont know if this is sufficient, together. and It took me more than 5 minutes to get no answer
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07 Dec 2007, 01:37
WIth at least 5 facilities and 22% of the women in the first one, the % of men can only approach 20% (as the total number of men approaches infinity).

To go to an extreme, imagine we've got 100 women and 1000000000 men to work with. That's 200000020 people per facility. 22% of the women is 22 women, leaving 199999998 men, or 19.9999998%

Imagine we kept the same 5 facilities and employed only 20% of the female interns in the first one. To have an equal number of total employees in each facility, 20% of the males would also have to be employed there too. But if we increase the % of women, we must decrease the % of men to keep things even.
07 Dec 2007, 01:37
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# Each correctional facility in a certain state has the same

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