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#people ranked A first = (3/10) * 120 = 36
Out of 36, #people ranked B second = (2/3) * 36 = 24
=> 12 people ranked B as last.

#people ranked B first = (11/30) * 120 = 44

#people ranked C first = 120 - 36 - 44 = 40
Out of 40, #people ranked B second = (3/4) * 40 = 30
=> 10 people ranked B as last.

Thus, 22 people ranked B as last.
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The answer is 22 (d)
Solution : Use the fractions to calculate - now 3/10 of 120 ranked A FIRST - that is 36, therefore 84 ranked B & C as second or third (we don't know). Next 11/30 ranked B first which is 44 people, so 76 ranked A & C as second or third we don't know the order. Of those who ranked A FIRST (2/3 ranked B second) meaning 24 ranked B second and of those who ranked C first which would be 3/10+11/30 = 20/30, 1-2/3 = 1/3 of 120 = 40 ranked C first 3/4th 40 = 30 ranked B SECOND. B SECOND TALLY is 30 + 24 = 54, B FIRST TALLY IS 44, add the two to get 98, subtract this from 120 to get 22.
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We can see that 36 picked A as first choice, 44 for B. This would mean that the rest from 120 i.e. 40 would have definitely chosen C as first choice.
Also, we are given that 24 from A chose B as 2nd option and 30 from C chose B as 2nd option.

If 44 people chose B as 1st option, 24+30=54 as 2nd option, then the rest from 120 ie. 22 people chose B as third option.

Therefore, Option D
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Bunuel
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, 3/10 ranked design A first and 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

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Let the three advertisements designs A,B and C be arranged in 3! = 6 ways.

The possible combinations are :

A First:(followed by sequence)

A B C

A C B

B First:

B A C

B C A

C First:

C A B

C B A

There are 120 persons included among this 6 groups.

(3/10)*120 = 36 ranked A first.

(11/30)*120 = 44 ranked B First.

So, the number of people who ranked C first = 120 - (36+44) = 40

Among those who have ranked A First. This means among 36 who have ranked A First.

(2/3) of 36 = 24 ranked B as second.

A FIRST: (total 36)

A B C - this combination is 24

A C B - this combination = (36-24) = 12.

Among those who ranked C First , which is 40 in total.

Three quarters ranked B second. (3/4)*40 = 30 = C B A

Thus, C A B = 40-30 = 10.

How many ranked B last ?

ACB + CAB = 12+10 = 22

Option D
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A first = (3/10)*120=36 & B second = (2/3)*36=24
B first = (11/30)*120=44
C first=40 & B second =(3/4)*40=30

So, A,C,B =(36-24)=12
&, C,A,B = (40-30)=10

total B =12+10 =22

Ans 22
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A 1st = 3/10x120= 36
B 1st = 11/30x120 = 44
C 1st = 120-44-36 = 40

B second from A 2/3x36 =24 meaning the rest 36-24 =12 ranked B last
B second from C 3/4X40 = 30 meaning the rest 40-30=10 ranked B last too
So total is 12+10 = 22
Bunuel
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, 3/10 ranked design A first and 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

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Total people = 120

A as first is for 3/10 of total cases = 3/10 of 120 = 36

- B as second is for 2/3 of 36 = 2/3 of 36 = 24.
- C will be second for remaining (36-24) = 12 people. Here B will be third.

B as first is for 11/30 of 120 = 44

C will be first for remaining (120-36-44) = 40 people

- B as second is for 3/4 cases = 3/4 of 40 = 30
- A will be second for remaining (40 - 30) = 10 people. B will be third here too.

So, the total cases with B as last = 10 +12 = 22

(D) is the answer
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Total 120. 1st place A=36, B=44 and C= 120-36-44=40
2nd place B= 2/3 of 36 + 3/4 of 40 = 24+30 =54
(1st + 2nd) of B = 54+44 =98.
120-98=22
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Bunuel
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, 3/10 ranked design A first and 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

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Let's calculate how many people ranked each design first, second, and last in each subgroup, then add it up to get the number of people who ranked B last.

Ranked A First:

\(\frac{3}{10}*120= 36\)

2/3 ranked B second, thus 1/3 of this ranked B last.

\(\frac{1}{3}*36=12\)

Ranked B First:
We only need this number to see how many ranked C first. No one in this group would have ranked B last because, well, they all ranked B first.

\(\frac{11}{30}*120=44\)

Ranked C First:

\(120-36-44=40\)

Of these, 3/4 ranked B second, thus 1/4 ranked B last.

\(\frac{1}{4}*40=10\)

Total:
\(10+12=22\)

Thus answer is D.
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To calculate who ranked B last, we need to eliminate the people who ranked B first & second.

People who ranked B first = 11/30 * 120 = 44
People who ranked B second =

1. People who ranked A first and B second = 3/10 *2/3 * 120 = 24
2. People who ranked C first and B second = 10/30 (star) * 3/4 * 120 = 30

star - to calculate who ranked C first = 1 - 3/10 - 11/30 = 10/30

Hence, people who ranked B last = 120 - 44 - 24 - 30 = 22 = Final Answer

Bunuel
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, 3/10 ranked design A first and 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

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Ranked A first=3/10 x 120= 36
B first= 11/30 x 120= 44
B last is 2/3 of A first so
2/3 x36= 24
Correct answer is E
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total 120 people.
A first 36, B first 44, C first 40
now from 36 2/3 says B second that means 1/3 says B last that is 12 people.
now from c=40, 3/4 says b second that means 1/4 says B last that is 10
so total 22 people
Bunuel
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, 3/10 ranked design A first and 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

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1. 120 people in total.
2. 3/10 = 36 people; ranked A 1st. Of those, 2/3 = 24 ranked B 2nd; so, 12 ranked B last.
3. 11/30 = 44 people; ranked B 1st.
4. 120 - 36 - 44 = 40 people left.
5. From the remaining 40 people, 3/4 = 30 ranked B 1st. So, 10 ranked B last.
6. Add 12 and 10 to get 22. D is your answer.
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Bunuel
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, 3/10 ranked design A first and 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

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ABC
1364440
224 + 30
3150 - B1 -B2


hence answer is 22
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Tree like structure representation helps best here where we start with top level as A, B, C and then start branching based on what the potential 2nd and 3rd options could be.

In simplified form, we want total number of people who picked B last (3rd).

The cases are A,C,B + C,A,B

Firstly, \(\frac{3}{10} = \frac{9}{30}\) marked A, \(\frac{11}{30}\) marked B, so the rest \(\frac{10}{30}\) marked C as first.

Case A,C,B:

\(\frac{2}{3}\) of those who ranked A first, ranked B as 2nd. which means \(\frac{1}{3}\) ranked C as second.

\(\frac{1}{3} * \frac{9}{30} =\frac{3}{30}\)

Naturally, all of those \(\frac{3}{30}\) ranked B as third in this case. Because there is no other option left after marking C as second for them.

Case C,A,B:

\(\frac{3}{4}\) of those who ranked C first, ranked B as 2nd which means \(\frac{1}{4}\) ranked A as 2nd

\(\frac{1}{4} * \frac{10}{30} = \frac{10}{120}\)

Here also, all of those \(\frac{10}{120}\) ranked B as third in this case too since no other option is left after marking A as 2nd.

Total = \(\frac{3}{30} + \frac{10}{120 }\)
= \(\frac{12}{120} + \frac{10}{120} \)
= \(\frac{22}{120 }\)

There are total of 120 students \( * \frac{22}{120}\) of them = 22

Ans: Option D
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No of people who ranked A first is (3/10)*120 = 36. No of people who ranked B first is (11/30)*120 = 44. Since each person gave a complete ranking with no ties and there are total 120 people surveyed, no. of people who ranked C first is 120-44-36 = 40 . Now of those who ranked A first , no of people who ranked B last is (1/3)*36 = 12. Among people who ranked C first , no of people who ranked B last is 0.25*40 =10 . So , total no. of people who ranked B last is 22.
Bunuel
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, 3/10 ranked design A first and 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

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Let there are three rankings 1,2,3

3/10 of 120=36 ranked A as 1
11/30 of 120=44 ranked B as 1

so remaining will rank C as 1 i.e 120-36-44=40

2/3of 36=24 ranked B as 2
3/4 of 40=30 ranked B as 2

B is ranked 2 by 54 people

so B is ranked 1 by 44 people, 2 by 54 people, then it must be ranked 3 by remaining people because it has been given that there is no ties in ranking, so answer is 120-54-44=22 option D
Bunuel
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, 3/10 ranked design A first and 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

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