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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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Question Stats:

81% (01:35) correct 19% (01:49) wrong based on 253 sessions

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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
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 26 Aug 2018, 13:22
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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Re: A certain number of people were polled to determine which of three des &nbs [#permalink] 26 Aug 2018, 13:22
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