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

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.

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

Hi Bunuel / Experts

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

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

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

Any comments please?

Hahahaha... if not an expert den "expert in making" for sure
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...

Please have a look below:

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

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

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..

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

A= only suites.
C= only blue
B= both

So X=A+B and Y=B+C

A+B+C=100

B=100-A-C = 100-(X-B)-(Y-B)

= 100-X+B-Y+B

Rearranging:

2B-B=X+Y-100= B

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