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14 Jul 2023, 01:30
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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)!
Difficulty:
25%
(medium)
Question Stats:
78% (01:40) correct
22%
(01:57)
wrong
based on 160
sessions
History
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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.
(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.
14 Jul 2023, 01:45
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Assume number of people = 12.
Stmt (1): 1/3 (=4) of the people polled enjoyed cupcakes, 1/2 (=6) enjoyed apple pie, and 3/4 (=9) enjoyed ice cream sundaes.
We can't find exactly 2 from this information. INSUFFICIENT
Stmt (2): 1/4 (=3) of the people polled enjoyed all three desserts.
We can't find exactly 2 from this information. INSUFFICIENT
Stmt (1) and Stmt (2): Apply following formula, CC = cupcakes, AP = apple pies, ICS = ice cream sundaes
Total = CC + AP + ICS - (Exactly 2 groups) - 2 (Exactly 3 groups) + None
Since none = 0, We have only one unknown and hence solvable. SUFFICIENT
Therefore C is the answer.
Hope it helped.
Stmt (1): 1/3 (=4) of the people polled enjoyed cupcakes, 1/2 (=6) enjoyed apple pie, and 3/4 (=9) enjoyed ice cream sundaes.
We can't find exactly 2 from this information. INSUFFICIENT
Stmt (2): 1/4 (=3) of the people polled enjoyed all three desserts.
We can't find exactly 2 from this information. INSUFFICIENT
Stmt (1) and Stmt (2): Apply following formula, CC = cupcakes, AP = apple pies, ICS = ice cream sundaes
Total = CC + AP + ICS - (Exactly 2 groups) - 2 (Exactly 3 groups) + None
Since none = 0, We have only one unknown and hence solvable. SUFFICIENT
Therefore C is the answer.
Hope it helped.
Bunuel
14 Jul 2023, 02:13
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(1) Only
Supposing there are a total of 12 people
4 enjoyed cupcakes
6 enjoyed apple pie
9 enjoyed ice cream sundaes
It is possible that 4 people enjoyed all three
Then nobody enjoys cupcakes only, or both cupcakes and apple pie, or both cupcakes and ice cream sundaes.
Even in this rather extreme case, the number of people who enjoy both pie and ice cream sundaes can be 0, 1, or 2.
Not sufficient
(2) Only
Evidently insufficient.
(1)(2) Together
fraction of the people polled enjoyed exactly two desserts
= 1/3 + 1/2 + 3/4 - 2*(1/4) - 1
Sufficient
The answer is thus (C).
Supposing there are a total of 12 people
4 enjoyed cupcakes
6 enjoyed apple pie
9 enjoyed ice cream sundaes
It is possible that 4 people enjoyed all three
Then nobody enjoys cupcakes only, or both cupcakes and apple pie, or both cupcakes and ice cream sundaes.
Even in this rather extreme case, the number of people who enjoy both pie and ice cream sundaes can be 0, 1, or 2.
Not sufficient
(2) Only
Evidently insufficient.
(1)(2) Together
fraction of the people polled enjoyed exactly two desserts
= 1/3 + 1/2 + 3/4 - 2*(1/4) - 1
Sufficient
The answer is thus (C).
