12 Days of Christmas GMAT Competition 2025 - Day 3: In a marketing

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Bunuel

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17 Dec 2025, 10:00

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Bunuel

GMAT Club Official Explanation:

Total people: 120

A first: 3/10 of 120 = 36
B first: 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.

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17 Dec 2025, 09:06

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A first = 3/10 of 120 = 36
B first = 11/30 of 120 = 44
C first = 120-36-44 = 40
Among A first, B second = 2/3 of 36 = 24 & B last = 12
Among C first, B second = 3/4 of 40 = 30 & B last = 10
People who rank B first cant rank B last
Total B last = 12+10 = 22
Hence, D

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17 Dec 2025, 09:24

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Ranked A first
3/10 * 120 = 36
Ranked A>B = 2/3 * 36 = 24
Ranked A>C>B (B last) = 36-24 = 12

Ranked B first
11/30 * 120 = 44
Ranked B last = 0

Ranked C first
120 - 36 - 44 = 40
Ranked C>B = 3/4 * 40 = 30
Ranked C>A>B (B last) = 40-30 = 10

B last total = 12+ 0 + 10 = 22

Answer D

Bunuel

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17 Dec 2025, 09:25

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Bunuel

Deconstructing the Question
Total people: 120.
We need to find the number of people who ranked B last (Position 3).
The possible rankings where B is last are:
1. $A \rightarrow C \rightarrow B$
2. $C \rightarrow A \rightarrow B$

Step 1: Analyze Group "A First"
Size of group: $\frac{3}{10} \times 120 = 36$ people.
Within this group, the possible rankings are ABC (B is 2nd) and ACB (B is 3rd/Last).

Condition: "Two-thirds ranked B second" (ABC).
Implies: One-third ranked B last (ACB).
Count (B Last): $\frac{1}{3} \times 36 = 12$.

Step 2: Analyze Group "B First"
Size of group: $\frac{11}{30} \times 120 = 44$ people.
Since B is ranked 1st, B cannot be last. Count (B Last): 0.

Step 3: Analyze Group "C First"
Size of group: Total - (A First + B First). $120 - (36 + 44) = 120 - 80 = 40$ people.
Within this group, the possible rankings are CBA (B is 2nd) and CAB (B is 3rd/Last).
Condition: "Three-quarters ranked B second" (CBA).
Implies: One-quarter ranked B last (CAB). Count (B Last): $\frac{1}{4} \times 40 = 10$.

Step 4: Total Sum Total people ranking B last = (From A First) + (From C First) Total = $12 + 10 = 22$.
Answer: D

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17 Dec 2025, 09:25

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lets create a table for a,b,c and rank from 1,2,3
1st
120*3/10=36 a
11/30*120=44 b
120-36-44=40(for c)
2nd
2/3*36=24 b
3/4*40=30 b
120-44-54=22

a. b. c.
1)36, 44, 40
2). 54,
3) 22
as the sum of b 1st 2nd and 3rd should be 120 as each voted for one with no draw.
therefore 22

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17 Dec 2025, 09:40

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36 people (3/10 * 120) rank A first.
-> 2/3 * 36 = 24 rank B second
-> 36-24= 12 rank B last

44 people (11/30 * 120) rank B first.
(obv none of them ranks B last)

40 people (120 - 36 - 44) rank C first.
-> 3/4 * 40=30 rank B second
-> 40-30 =10 rank B last

10+12 = 22
D

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17 Dec 2025, 09:41

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from 120 people
There are
(3/10)*120 = 36 rank A first => 36*(1-2/3) = 12 rank B last
(10/30)*120 rank B first
(1-3/10-10/30)*120 = 40 rank C first => 40*(1-3/4)= 10 rank B last

=> Total people rank B last: 12+10=22 people

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17 Dec 2025, 09:46

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In 120 people:
- 3/10*120 = 36 ranked A first, 2/3*36 = 24 ranked B second => 12 ranked B last
- 11/30*120 = 44 ranked B first
- (120-36-44)= 40 ranked C first, 3/4*40 = 30 ranked B second => 10 ranked B last
Total ranked B last = 12+10 = 22

Answer: D

Bunuel

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17 Dec 2025, 09:50

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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, 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

total people 120
ranked A 1st = 120* 3/10 ; 36
ranked B 1st = 120* 11/30 ; 44
ranked C 1st = remaining people i.e. 40

for group A

36 * 2/3 = 24 ranked B 2nd
36-24 =12 ranked C 2nd

group B no one ranked it 2nd

for group C
3/4 * 40 = 30 ranked B second
remaining 10 people ranked A second

total people who ranked B 2nd are 10+12 ; 22
OPTION D , 22

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17 Dec 2025, 09:53

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Quote:

As everyone gave their rankings of all 3 designs. The number of people ranked B last = 120 - the number of people ranked B in either first or second.
The number of people who ranked B first: 120*11/30=44

The number of people who ranked A first: 120*3/10=36. Among them, 2/3 = 24 ranked B second.

Given that everyone gives their rankings of all 3 designs, the number of people who ranked C first = 120 - 36 (those ranked A first) - 44 (those ranked B first) = 40. Among them, 3/4 = 30 ranked B second.
=> there are 24+30=54 people ranked B second
The number of people ranked B last = 120 - 44 - 54 = 22

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17 Dec 2025, 09:54

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Bunuel

A first = 3/10 * 120 = 36
B first = 11/30 * 120 = 44
C first = 120 - (36+44) = 40

Among those who ranked A first

B Second = 2/3 * 36 = 24
B Last = 36 - 24 = 12

Among who ranked C first

B Second = 3/4 * 40 = 30
B Last = 1/4 * 40 = 10

Total B Last = 12 + 10 = 22

Option D

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17 Dec 2025, 09:54

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Number of ways to rank 3 new advertisement designs A, B & C = 3! = 6

3/10*120 = 36 people ranked design A first
11/30*120 = 44 people ranked design B first
Remaining 120 - 36 - 44 = 40 people ranked design C first

Among those who ranked A first (36 people), 2/3 ranked B second = 2/3*36 = 24 people
Among those who ranked A first (36 people), remaining 1/3 ranked C second (B last) = 1/3*36 = 12 people

Among those who ranked C first (40 people), 3/4 ranked B second = 3/4*40 = 30 people
Among those who ranked C first (40 people), remaining 1/4 ranked A second = 1/4*40 = 10 people

Sequence of A, B & C	Number of people
ABC	24
ACB	12
BAC	?
BCA	?
CAB	10
CBA	30

The number of people who ranked B last (ACB & CAB) = 12 + 10 = 22 people

IMO D

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17 Dec 2025, 09:58

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Took some careful reading for the question.
Determine the first ranks first from the conditions given in the question:
A 1st: (3/10 of 120) = 36.
B 1st: (11/30 of 120) = 44
Hence C 1st will be 120-26-44 = 40

Now moving on to the Seconds :
There are only 2 sequences possible: ABC or ACB.
The statement said that among who ranked A first, 2/3rds ranked B second.
Hence in 1/3 ranked B 3rd: 1/3 of 36 = 12........(i)

Now Also give the group who ranked the C first 3/4 of them marked B second. Which means 1/4 of them marked B third.
=> 1/4 of 40 = 10.......... (ii)

So adding (i) and (ii) we get total = 22.
Hence D.

Bunuel

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17 Dec 2025, 10:01

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Easy problem. Just make a table in between design and rank.
Enter provided data in table and calculate as shown in image.

Attachments

SolutionPS3.jpg [ 217.04 KiB | Viewed 1275 times ]

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17 Dec 2025, 10:02

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Bunuel

No. of people who ranked 1st A= 36, B=44 , C= 120 -(44+36) = 40

Number of people who ranked A first are 36, 2/3rd of 36 ranked B second ---> 1/3rd of 36 ranked B last = 12

Number of people who ranked C first are 40, 3/4th of 40 ranked B second ----> 1/4 of 40 ranked B last = 10
Total 22 people ranked B last hence D.

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17 Dec 2025, 10:04

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Of 120 people
3/10 ranked A first => 36
- Out of which 2/3rd ranked B as second meaning 1/3rd ranked B as last = 12 people
11/30 ranked B first => 44
Out of 120 people 80 ranked either A or B as first => 40 ranked C as first
Out of 40 who ranked C as first,
3/4 ranked B second => 1/4 ranked B last = 10 people
Total people who ranked B as last = 22

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17 Dec 2025, 10:06

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A1 = 3/10*120=36, out of which B2 = 2/3 *36 = 24, therefore, C2 = 12. In this case, then B3 = 12
( Since A1 = A ranked first and C2 = C ranked second, means B ranked last)

Similarly, B1=11/30*120 = 44
Therefore, C1 = 120-A1-B1 = 120-36-44 = 40
out of these, B2 = 3/4*C1 = 30, then A2 =40-30 = 10
Hence B3 = 10

Total B3 = 12+10 = 22

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17 Dec 2025, 10:07

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People who ranked A first: 36.
Now, out of these 24 ranked B second, which means 12 ranked B last.

People who ranked C first: 40 (36 ranked A first, 44 ranked B first, left 120-80 = 40 ranked C first, these are non-overlapping sets).
Now, out of these, 30 ranked B second, which means 10 ranked B last.

So a total of 12+10=22, ranked B last. Option D.

Bunuel

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17 Dec 2025, 10:24

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Bunuel