X percents of the rooms are suits, and Y Percents of the : PS Archive
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# X percents of the rooms are suits, and Y Percents of the

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Manager
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X percents of the rooms are suits, and Y Percents of the [#permalink]

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01 Sep 2004, 09:01
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23. X percents of the rooms are suits, and Y Percents of the rooms are painted light blue?
Which of the following best represents the least Percentage of the light blue painted suits?

(a) X-Y.
(b) Y-X + 100.
(c) 100X-Y.
(d) X+Y-100.
(e) 100-XY.

I dont find any of the answer choices to be apt. I dont know if i am missing something or if the questions are of poor quality.
But unfortunately these questions are from real test questions web site and so i am unable to neglect them.
Can anyone explain why one of the answer choices mentioned above is correct.

Thanks.
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01 Sep 2004, 10:01

draw two cirlces, one to represent suites, one to represent light blue. Let the suites that are light blue be n, then suite wiill be x-n and light blue y-n.

So x-n+n+y-n = 100 and you will get x+y-100.

I can't seem to be able to upload a picture, otherwise it will be very clear.
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01 Sep 2004, 10:14
I chose 50 and 10 as the number and got X + Y - 100 as the asnwer.
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01 Sep 2004, 10:38
ywilfred,
Aren't you assuming here that the two sets x and y represent the entire sample space (ie they both equal 100 and that there is no other data that represents none of the two ).
It could be possible that there is another entity - z percent of the rooms are painted red.

In that case will x + y -100 not be negative.

Please correct me if i am wrong.

Thanks.
Director
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01 Sep 2004, 11:58
To make sense this question should assume that x+y>100 to guarantee an overlap between the two groups.
I do not understand how you can have a least number with for instance 10% and 50%, you can then have 0 light blue suits...

Do you agree ?
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Re: PS - set theory [#permalink]

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01 Sep 2004, 12:10
anuramm wrote:
23. X percents of the rooms are suits, and Y Percents of the rooms are painted light blue?
Which of the following best represents the least Percentage of the light blue painted suits?

(a) X-Y.
(b) Y-X + 100.
(c) 100X-Y.
(d) X+Y-100.
(e) 100-XY.

I think the Q is poorly framed.
There is a possibility that "the least Percentage of the light blue painted suits" = 0
If we donot assume the above then D is the answer
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01 Sep 2004, 19:16
Yes, i assume the suits and blue rooms represent the entire sample space. there's no other way to solve it unless you made this assumption.
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01 Sep 2004, 19:18
In fact, the question does imply that there are only three types of rooms, suites, and blue rooms, or blue suites. If there was to be a neither, it would probably say "Z percent are neither"
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01 Sep 2004, 20:20
I think it is X + Y -100

Let A be the no of suite room with blue color.
Let D be the no of Non suite room with non blue color.

Then,
E = n(A) + n(B) - n(A n B) + n(A U B)'
100 = X + Y - A + D
A = X + Y - 100 + D

X and Y are fixed and given already; 100 is a constant. Only variable is D.
For A to be minimum D tends to 0. And the least value of A = X + Y - 100
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01 Sep 2004, 22:44
now i understand why D is the answer. thanks hardworker_indian and everyone.
01 Sep 2004, 22:44
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# X percents of the rooms are suits, and Y Percents of the

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