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21 Feb 2024, 02:30
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C
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Difficulty:
25%
(medium)
Question Stats:
81% (01:43) correct
19%
(02:03)
wrong
based on 98
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.
(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.
21 Feb 2024, 03:42
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IMO (C)
Since we are dealing with fraction, we can write
1= C+A+I+Two desert-All three desert
(1) 1/3 of the people polled enjoyed cupcakes, 1/2 enjoyed apple pie, and 3/4 enjoyed ice cream sundaes.
We don't know about exactly three desert. Hence Insufficient.
(2) 1/4 of the people polled enjoyed all three desserts.
We don't know about C+A+I. Hence insufficient
(1)+(2), Sufficient to know value of both
Since we are dealing with fraction, we can write
1= C+A+I+Two desert-All three desert
(1) 1/3 of the people polled enjoyed cupcakes, 1/2 enjoyed apple pie, and 3/4 enjoyed ice cream sundaes.
We don't know about exactly three desert. Hence Insufficient.
(2) 1/4 of the people polled enjoyed all three desserts.
We don't know about C+A+I. Hence insufficient
(1)+(2), Sufficient to know value of both
21 Feb 2024, 12:45
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Option C seems correct.
Looking at the denominators of the fractions given in the options, we calculate their LCM(2,3,4) = 12 and say that the total number of people shoulkd be a multiple of 12.
We take a value = 120
So,
From Statement 1:
For total 120 people :
So, total = A+B+C = 190
We know 120 = 190 - people who like exactly 2 + people who liked all 3
=> people who liked exactly 2 = 70 + people who liked all 3
We don't know how many people liked all 3.
Hence, Insufficient.
From Statement 2:
For total 120 people :
1/4 of the people polled enjoyed all three desserts. So
people who liked all 3 = 30
people who liked exactly 2 = A+B+C - 120 + 30 = A+B+C-90
Don't know values of A,B,C
Insufficient.
If we club both together we get A+B+C= 190
And A+B+C-90 = 100
So, both statements together are sufficient.
Hence, option C
Looking at the denominators of the fractions given in the options, we calculate their LCM(2,3,4) = 12 and say that the total number of people shoulkd be a multiple of 12.
We take a value = 120
So,
From Statement 1:
For total 120 people :
| category | fraction | Count |
|---|---|---|
| cupcakes (A) | 1/3 | 40 |
| apple pie (B) | 1/2 | 60 |
| ice cream (C) | 3/4 | 90 |
So, total = A+B+C = 190
We know 120 = 190 - people who like exactly 2 + people who liked all 3
=> people who liked exactly 2 = 70 + people who liked all 3
We don't know how many people liked all 3.
Hence, Insufficient.
From Statement 2:
For total 120 people :
1/4 of the people polled enjoyed all three desserts. So
people who liked all 3 = 30
people who liked exactly 2 = A+B+C - 120 + 30 = A+B+C-90
Don't know values of A,B,C
Insufficient.
If we club both together we get A+B+C= 190
And A+B+C-90 = 100
So, both statements together are sufficient.
Hence, option C
