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

Question

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

nhanqtvn · Accepted Answer

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

sonibubu · Answer

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.

rohitgoel15 · Answer

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?

cipher · Answer

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.

PathFinder007 · Answer

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

maggie27 · Answer

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

PareshGmat · Answer

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

PareshGmat · Answer

Bunuel, looking at the answer, I doubt the highlighted portion of the wording. Any comments please?

maggie27 · Answer

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...

PareshGmat · Answer

Please have a look below:

usre123 · Answer

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

MorningRunner · Answer

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?

chetan2u · Answer

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

ScottTargetTestPrep · Answer

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

Regor60 · Answer

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

Posted from my mobile device

saubhikbhaumik · Answer

Let us consider total rooms to be 100.

Light blue 
 Not light blue 
 
  Suits 
  a  
  b  
 X 
 
  Not suits

100 - X 
 
  Total 
 Y 
 100-Y 
 100

What we have to find is the minimum value of 'a'.

a + b = X

To minimize a we have to maximize b.

Max value possible for b = 100 - Y

Therefore, a = X - 100 + Y

KarishmaB · Answer

The question is flawed as given. It must mention that there is no room which is neither. So Neither = 0. Else values such as X = 10% and Y = 20% which are definitely possible give negative answers.

Total = X + Y - Both
Both = X + Y - 100

Answer (D)

Overlapping sets video:  https://youtu.be/HRnuURqGhmg

Taidaishar · Answer

Elegant solution.

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

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	Light blue	Not light blue
Suits	a	b	X
Not suits			100 - X
Total	Y	100-Y	100

GMAT Problem Solving (PS) Questions

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

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