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X percents of the rooms are suits, Y percent of the rooms

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Director
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X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 17 Oct 2007, 23:24
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A
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D
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  65% (hard)

Question Stats:

62% (02:09) correct 38% (02:21) wrong based on 551 sessions

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X percents of the rooms are suits, Y percent 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
Director
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New post 18 Oct 2007, 10:50
Isn't this just a union/venn diagram?
If we let LS = light blue suites we get

x + y - LS is less than or equal to 100, so
LS >= x + y - 100

Now let's try x = 50% and y = 50%, there's no guarantee that there is an overlap. If we plug in we get B >= 0
But if we try x = 75%, y = 75%, there is bound to be overlap and we get B >= 50% (50% or more rooms are guaranteed to be light blue suites).
Not sure though.
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Pained rooms  [#permalink]

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New post 06 Jul 2010, 00:11
2
1
123. X percents of the rooms are suits, Y percent of the rooms are painted
light blue. Which of the following best represents the least percentage of
the light blue painted suits?
1) X-Y
2)Y-X +100
3)100X-Y
4)X+Y-100
e)100-XY

Please explain your method. Also please help me know in case the questions was as below then how we can solve that:
123. X percents of the rooms are suits, Y percent of the rooms are painted
light blue. Which of the following best represents the MAX percentage of
the light blue painted suits?
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Re: Pained rooms  [#permalink]

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New post 06 Jul 2010, 03:46
1
rohitgoel15 wrote:
123. X percents of the rooms are suits, Y percent of the rooms are painted
light blue. Which of the following best represents the least percentage of
the light blue painted suits?
1) X-Y
2)Y-X +100
3)100X-Y
4)X+Y-100
e)100-XY

Please explain your method. Also please help me know in case the questions was as below then how we can solve that:
123. X percents of the rooms are suits, Y percent of the rooms are painted
light blue. Which of the following best represents the MAX percentage of
the light blue painted suits?



Answer is going to be the same whether its MAX or MIN percentage.

Using the simple formula

100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour

So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values.

Hence Answer D

Hope this helps.
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Re:  [#permalink]

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New post 25 Apr 2014, 21:25
2
1
sonibubu wrote:
Isn't this just a union/venn diagram?
If we let LS = light blue suites we get

x + y - LS is less than or equal to 100, so
LS >= x + y - 100

Now let's try x = 50% and y = 50%, there's no guarantee that there is an overlap. If we plug in we get B >= 0
But if we try x = 75%, y = 75%, there is bound to be overlap and we get B >= 50% (50% or more rooms are guaranteed to be light blue suites).
Not sure though.


I agree with you:
% suited + %light - % suited and light + % no suited or light = 100 %
Because % of no suited or light >= 0
==> x + y - % suited light <= 100
--> % suited & light >= x + y - 100
--> min SL = x+y - 100 :D
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 16 Jul 2014, 04:16
Hi Bunuel,

Although I got the right answer. Could you please provide your comments on this.

I did it in a following way

Lets total are 100 rooms. so x%of 100 = x.
and Y %of 100 = y

100 = x+y-both +neither

both = x+y-100. Assuming neither = 0


I am not sure this is the right way.

Please provide your comments on this

Thanks
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X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 17 Jul 2014, 15:56
Hi Bunuel / Experts

Can you please explain me the question with the help of 2-D matrix. I am terribly stuck :cry:
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 17 Jul 2014, 20:28
2
maggie27 wrote:
Hi Bunuel / Experts

Can you please explain me the question with the help of 2-D matrix. I am terribly stuck :cry:


Not an expert, but lets try :)

Refer Diagram below:

To maximize the value "a" (Overlap), 100-(x+y) should be zero

100 = x-a + y-a + a + 100 - (x+y)

100 = x+y-a

a = x+ y - 100

Answer = D
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overl.png [ 6.97 KiB | Viewed 6241 times ]


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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 17 Jul 2014, 20:31
Himalayan wrote:
X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the followingbest 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


Bunuel, looking at the answer, I doubt the highlighted portion of the wording.

Any comments please? :)
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 17 Jul 2014, 20:57
PareshGmat wrote:
maggie27 wrote:
Hi Bunuel / Experts

Can you please explain me the question with the help of 2-D matrix. I am terribly stuck :cry:


Not an expert, but lets try :)

Refer Diagram below:

To maximize the value "a" (Overlap), 100-(x+y) should be zero

100 = x-a + y-a + a + 100 - (x+y)

100 = x+y-a

a = x+ y - 100

Answer = D



Hahahaha... if not an expert den "expert in making" for sure :-D
Thanks for the explanation .However, I was stuck with 2-D matrix for it, with which I started fixing it.
Can u please help me understand the same with the matrix too... :o
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X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 17 Jul 2014, 22:42
2
maggie27 wrote:
PareshGmat wrote:
maggie27 wrote:
Hi Bunuel / Experts

Can you please explain me the question with the help of 2-D matrix. I am terribly stuck :cry:


Not an expert, but lets try :)

Refer Diagram below:

To maximize the value "a" (Overlap), 100-(x+y) should be zero

100 = x-a + y-a + a + 100 - (x+y)

100 = x+y-a

a = x+ y - 100

Answer = D



Hahahaha... if not an expert den "expert in making" for sure :-D
Thanks for the explanation .However, I was stuck with 2-D matrix for it, with which I started fixing it.
Can u please help me understand the same with the matrix too... :o



Please have a look below:
Attachments

ma.png
ma.png [ 6.18 KiB | Viewed 6236 times ]


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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 09 Nov 2014, 12:01
I too did it with the simple formula. But even within set sets have max/ min overlaps. I'm not sure how to apply that to this question though
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 11 May 2016, 08:23
Hi..
Can anyone help me to understand my doubt?
What if x and y are less than 50% ?

If x =20% and y =30% and x and y = 10%
then the expression x+y-100 would result -50% which is nonsense..


Whats wrong with my thinking?
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 11 May 2016, 08:35
2
MorningRunner wrote:
Hi..
Can anyone help me to understand my doubt?
What if x and y are less than 50% ?

If x =20% and y =30% and x and y = 10%
then the expression x+y-100 would result -50% which is nonsense..


Whats wrong with my thinking?


Hi,
you are totally correct with your observation.
The Q is flawed in that it fails to mention clearly that all houses are either suits or painted light blue...

When you take all these house to be atleast ONE of the two groups with few common to the two groups, the Qs will stand, otherwise it will fall apart..

But as the way Q stands, it is FLAWED and you are not likely to see anything of this kind in ACTUALs
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 07 Jul 2016, 20:59
Himalayan wrote:
X percents of the rooms are suits, Y percent 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


The answer is easy..the wording I think..is awkward.. I want Bunuel to respond on this..

The minimum is..0 percent..but if you ask me what is going to be the number of blue painted suits in any case?..I would say (D). But I dont think thats what the question is asking..
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Re: X percents of the rooms are suits, Y percent of the rooms  [#permalink]

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New post 12 Sep 2018, 18:23
Himalayan wrote:
X percents of the rooms are suits, Y percent 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


If we assume there are 100 rooms, we see that x will be the number of suites and y will be the number of rooms that are painted light blue. In order to minimize the number of those that are both suites and painted light blue, we use the formula:

Total = number of suites + number of painted light blue – blue suites + neither blue nor suite

100 = x + y – blue suites + neither blue nor suite

By simple algebra, we have:

Blue suites = x + y + neither – 100

We observe that increasing the number of rooms that are neither light blue nor a suit while keeping everything else the same increases the number of rooms that are both suits and painted light blue. Therefore, to minimize the number of blue suites , we need the number of those that are neither suites nor painted blue to be 0, leaving us with the expression x + y – 100 for the minimum number of rooms that are both suites and painted light blue.

Answer: D
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Re: X percents of the rooms are suits, Y percent of the rooms   [#permalink] 12 Sep 2018, 18:23
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