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what fraction of the people enjoyed exactly two desserts?

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by himu » Sat Mar 30, 2013 9:09 pm
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?

1/3 of the people polled enjoyed cupcakes, 1/2 enjoyed apple pie, and 3/4 enjoyed ice cream sundaes.
1/4 of the people polled enjoyed all three desserts.
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Source: — Data Sufficiency |

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by Anju@Gurome » Sat Mar 30, 2013 10:05 pm
himu wrote: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?

1/3 of the people polled enjoyed cupcakes, 1/2 enjoyed apple pie, and 3/4 enjoyed ice cream sundaes.
1/4 of the people polled enjoyed all three desserts.
For three overlapping sets A, B, and C :
  • Total = (Total in A) + (Total in B) + (Total in C) - (Total in exactly two) - 2*(total in all three) + (total in none of them)
In this case, total in none of them = 0
We need to determine the total in exactly two.
Which is only possible if we know what fraction of people enjoyed each of the three desserts separately as well as all of them.

Therefore, we need both the statements.

The correct answer is C.
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