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

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17 Oct 2007, 23:24

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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?

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.

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?

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.

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

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

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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.

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

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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

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 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...

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

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17 Jul 2014, 22:42

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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

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 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...

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

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23 Apr 2016, 11:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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
_________________

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

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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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28 Aug 2017, 09:53

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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