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12 Jan 2026, 06:41
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In a marketing survey, 120 people were asked to rank three new advertisement designs A, B, and C from most favorite to least favorite. Each person gave a complete ranking with no ties. Of these people, \(\frac{3}{10}\) ranked design A first and \(\frac{11}{30}\) ranked design B first. Among those who ranked A first, two-thirds ranked B second. Among those who ranked C first, three-quarters ranked B second. How many people ranked B last?
A. 16
B. 18
C. 20
D. 22
E. 24
A. 16
B. 18
C. 20
D. 22
E. 24
12 Jan 2026, 06:41
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Official Solution:
In a marketing survey, 120 people were asked to rank three new advertisement designs A, B, and C from most favorite to least favorite. Each person gave a complete ranking with no ties. Of these people, \(\frac{3}{10}\) ranked design A first and \(\frac{11}{30}\) ranked design B first. Among those who ranked A first, two-thirds ranked B second. Among those who ranked C first, three-quarters ranked B second. How many people ranked B last?
A. 16
B. 18
C. 20
D. 22
E. 24
Total people: 120
A first: \(\frac{3}{10}\) of 120 = 36
B first: \(\frac{11}{30}\) of 120 = 44
C first: 120 - 36 - 44 = 40
Among A-first (36), two-thirds rank B second, so B last there: 36 - 24 = 12.
Among C-first (40), three-quarters rank B second, so B last there: 40 - 30 = 10.
Total ranking B last = 12 + 10 = 22.
Answer: D
In a marketing survey, 120 people were asked to rank three new advertisement designs A, B, and C from most favorite to least favorite. Each person gave a complete ranking with no ties. Of these people, \(\frac{3}{10}\) ranked design A first and \(\frac{11}{30}\) ranked design B first. Among those who ranked A first, two-thirds ranked B second. Among those who ranked C first, three-quarters ranked B second. How many people ranked B last?
A. 16
B. 18
C. 20
D. 22
E. 24
Total people: 120
A first: \(\frac{3}{10}\) of 120 = 36
B first: \(\frac{11}{30}\) of 120 = 44
C first: 120 - 36 - 44 = 40
Among A-first (36), two-thirds rank B second, so B last there: 36 - 24 = 12.
Among C-first (40), three-quarters rank B second, so B last there: 40 - 30 = 10.
Total ranking B last = 12 + 10 = 22.
Answer: D
18 Jun 2026, 01:47
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I don’t quite agree with the solution. How can we say that "Among those who ranked A first, two-thirds ranked B second", so B is the last?
If A is first and B is second, C is last.
As per the given explanation => Among A-first (36), two-thirds rank B second, so: 36 - 24 = 12
These "12" may also include those who ranked "C" as last. While the question talks about "2/3rds have ranked B as second", and does not mention anything about C, we can't just simply assume that it does not include people who ranked C as last...
Am I missing something here?
If A is first and B is second, C is last.
As per the given explanation => Among A-first (36), two-thirds rank B second, so: 36 - 24 = 12
These "12" may also include those who ranked "C" as last. While the question talks about "2/3rds have ranked B as second", and does not mention anything about C, we can't just simply assume that it does not include people who ranked C as last...
Am I missing something here?
