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Bunuel
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­A certain number of people were polled to determine which of three 04 Aug 2026, 19:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

78% (01:35) correct 22% (02:15) wrong based on 92 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.


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C
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laborumquibusdam
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­A certain number of people were polled to determine which of three 04 Aug 2026, 20:31
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Answer is C because we can take all of together as a fraction of 1
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dhart
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­A certain number of people were polled to determine which of three 04 Aug 2026, 22:15
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applying sets forumla , option C must work
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odionam
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­A certain number of people were polled to determine which of three 04 Aug 2026, 23:10
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From 1 we can calculate exactly one and extra including twice of exactly two and thrice of exactly 3 as it given in fraction we can assume total unit but here we can't get separate exactly 2 so we need another statement which is given by exactly 3 now from combing together we can find exactly two
Bunuel
­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.


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­A certain number of people were polled to determine which of three 05 Aug 2026, 02:18
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Statement 1 is telling us about the fractions of apple pie, cupcakes and ice cream sundaes but they are not sufficient to answer the question.
Statement 2 is telling us about the fraction of all 3 desserts. Not sufficient again

Statement 1 plus Statement 2 is giving us the over all picture and together they are sufficient to answer this question.

Hence option C is the answer.
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­A certain number of people were polled to determine which of three 05 Aug 2026, 05:15
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Answer is C.

Set Total People = 12 (LCM of denominators 3, 2, and 4) to convert fractions into whole people.

Cupcakes: \(\frac{1}{3} \times 12 = 4\)
Pie: \(\frac{1}{2} \times 12 = 6\)
Sundaes: \(\frac{3}{4} \times 12 = 9\)

Sum of individual counts = \(4 + 6 + 9 = 19\text{ total votes}\).
Since there are only 12 people in the room, there are \(19 - 12 = 7\text{ extra votes}\).
Extra votes happen because people liking multiple desserts get counted on multiple lists:
  • Person in 1 group: Counted 1 time \(\rightarrow\) 0 extra votes
  • Person in 2 groups: Counted 2 times \(\rightarrow\) 1 extra vote
  • Person in 3 groups: Counted 3 times \(\rightarrow\) 2 extra votes
\(\text{Extra Votes } (7) = (\text{Exactly 2}) + 2 \times (\text{All 3})\)

Statement Analysis
  • Statement (1): Gives us \(7 = (\text{Exactly 2}) + 2 \times (\text{All 3})\). One equation, two variables. Insufficient.
  • Statement (2): All 3 = \(\frac{1}{4} \times 12 = 3\text{ people}\). Gives no information about the total votes or the "Exactly 2" group. Insufficient.
  • Together: Plug 3 into our overlap equation: \(7 = (\text{Exactly 2}) + 2(3)\) \(\text{Exactly 2} = 1\text{ person}\) Fraction = \(\frac{1}{12}\). Sufficient.

    Hence, Correct Answer: C
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