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A certain number of people were polled to determine which of three des

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A certain number of people were polled to determine which of three des  [#permalink]

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New post Updated on: 16 Feb 2016, 01:13
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A certain number of people were polled to determine which of three desserts they enjoyed: cupcakes, apple pie, and ice cream sundaes. If everyone polled enjoyed at least one of the three desserts, what fraction of the people polled enjoyed exactly two desserts?

(1) 1/3 of the people polled enjoyed cupcakes, 1/2 enjoyed apple pie, and 3/4 enjoyed ice cream sundaes.
(2) 1/4 of the people polled enjoyed all three desserts.

Originally posted by Ekland on 16 Feb 2016, 01:11.
Last edited by Bunuel on 16 Feb 2016, 01:13, edited 1 time in total.
Edited the question.
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Re: A certain number of people were polled to determine which of three des  [#permalink]

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New post 22 May 2017, 05:40
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TheMastermind wrote:
Any other way to do this besides the formula?


Hi TheMastermind ,

This question can be solved as follows:

All you need to know is the formula for three items :

Total - Neither = A+ B + C - (Exactlly two) - 2(Exactly three);

Looking at Statement 1, I can say we should take some total value in such a way that 1/3 or 1/2 or 3/4 always give an integer value. I can take the value as 60.

So, total we are taking = 60. We are also given that Neither = 0 (everyone takes atleast 1)

Suppose,
A : cupcakes
B: apple pie
C: ice cream sundaes

Statement 1:
A = 20
B = 30
C = 45.

Or substituting the value in the formula, we have

60 - 0 = 20+ 30 + 45 - (Exactly two) - 2(Exactly three)

In order to find out Exactly two, we need exactly 3 in the above equation. Since we dont have that value, we can say Statement 1 is insufficient.

Statement 2: We have exactly 3 here but not any other thing. Hence, insufficient.

Combining, We know exactly 3 now, we can substitute this value in Equation above and get exactly 2. Hence, sufficient.

I hope that makes sense.

Feel free to reach out in case of any concern. :)
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Re: A certain number of people were polled to determine which of three des  [#permalink]

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New post 16 Feb 2016, 05:34
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1
if we have fractions in overlapping sets try to take arbitrary number

take a lcm of numerators .

from statement 1
1/3 cupcakes,1/2 apple pie and 3/4 ice creams

so lcm is 12. take a total number of people as 12.

cupcakes is 4, apple pie is 6 and ice creams is 9.

if three sets are there, formula is a+b+c+2(d+e+f)+3g.=19-1
here a =only cupcakes. b= only apple pie, c= ice cream.

d+e+f is people take exactly two items.

g= people take all three items.

total number = a+b+c+d+e+f+g=12 -2
substitute 1-2= d+e+f+g=9 from option 1

from statement 2
not sufficient.

put statment2 in statment 1=1/4 like all=3.

so we can find exactly two people like. so option C is correct.
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Re: A certain number of people were polled to determine which of three des  [#permalink]

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New post 13 May 2017, 11:34
Any other way to do this besides the formula?
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Re: A certain number of people were polled to determine which of three des  [#permalink]

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New post 20 Dec 2018, 04:02
I was confused here. Please enlighten me guys. If I know statement 1, I only get total values for how many people liked e.g. sundaes. I dont know how many of these people liked ONLY sundaes or maybe applepie, too. How is that enough information? Its not the exact value that we can yield here, but the value of the twice overlapping sets with the case of (like exactly one).
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Re: A certain number of people were polled to determine which of three des   [#permalink] 20 Dec 2018, 04:02
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