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

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bhanu29

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17 Dec 2025, 20:13

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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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To find B last = ?

A first people = 36

B first people = 44

C first people = 120 -(44+36) = 40

Among A first 24 ranked B second, So B last = 12 (no ties and all ranked)

Among B first (none last)

Among C first, 30 ranked B second, So B last = 10 (no ties and all ranked)

So total B last = 12 + 10 = 22

Correct Answer: D

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17 Dec 2025, 21:27

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120 ppl
3/10 -> 36 ranked A 1st, 11/30 -> 44 ranked B 1st, remaining 120-36-44 = 40 would have ranked C 1st
2/3 of A 1st ranked B 2nd + 3/4 of C 1st ranked B 2nd => 24 + 30
B -> hz 3rd would have ranked 120 - 44 - 54 = 22

A 36 ? ?
B 44 54 22
C 40 ? ?

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17 Dec 2025, 21:31

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Bunuel

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total = 120

A1st = (3/10) * 120 = 36
B1st = (11/30) * 120 = 44
this implies the rest should be C1st = 40

People who voted A1st:
- B2nd = (2/3) * 36 = 24
- the rest should have voted B3rd = 36 - 24 = 12. Because there are two cases here ABC and ACB, people who voted B2nd have to vote C3rd which the the rest 12 votes B3rd

Similarly, for people who voted C1st:
- B2nd = (3/4) * 40 = 30
- rest voted for B3rd = 40 - 30 = 10

=> total who voted for B3rd are 12 + 10 = 22

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17 Dec 2025, 21:44

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Let us consider the given information
36((3/10)*120) people ranked A first
44((11/30)*120) people ranked B first
So, 120 - (36+44) = 40 people ranked C first

24((2/3)*36) people ranked B second
In addition, 30 ((3/4)*40) also ranked B second
In total, 54 people ranked B second

Number of people who ranked B third = (120 - 44 - 54) = 120 - 98 = 22

Bunuel

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TrinhNguyen157

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17 Dec 2025, 22:01

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We have: 3/10 ranked A first=> in 120 people, total rank A first is 120*3/10=36. among these people, 2/3 (24 ppls) ranked B second=> so 12 people rank B last
11/30 ranked B first=> in 120 people, total ranked B first is 120*11/30=44.
people rank C first is 120-44-36=40. among these people, 3/4 ranked B second, so 40*1/4=10 people rank B last.
Total people ranked B last is 10+12=22

Bunuel

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ledzep10

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17 Dec 2025, 23:10

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Total = 120
First rank: A = 3/10 = 9/30, B = 11/30 C = 1 - (9+11)/30 = 10/30
Second rank for B: From those who ranked A first: 2/3*3/10 = 1/5, From those who ranked B First = 0, From those who ranked C first: 3/4 * 10/30 = 1/4
Those who ranked B second = 1/4 + 1/5 = 9/20
Those who did not rank B third = Those who ranked B first and those who ranked B second = 11/30 +9/20 = 49/60
Those who ranked B third = 1-49/60 = 11/60 => 11/60 * 120 = 22

Answer D

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17 Dec 2025, 23:15

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Each column, row has to to be 120.

=> First : 36+44+x = 120 => x = 40 (C - first)

B second = 24 + 3*40/4 = 54

B Total = 120 = 44 + 54 + B last
=> B last = 22 (D)

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17 Dec 2025, 23:28

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Here it is given that A is ranked first by 3/10 of total population (120) which is 36; and out of that 36, 2/3rd rank B as 2nd which means 24; so we can tell by this that 12 rank B as 3rd.

B is ranked first by 11/30 of 120 which is 44; So C is ranked first by 120 - 44 - 36 = 40 people. Question says that 3/4th of 40, which is 30, ranks B second. so 10 people rank B as third.

Total = 12 + 10 = 22

So D is the answer

remdelectus

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17 Dec 2025, 23:32

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Total s=120
A first=3/10x120=36
B =11/30x120=44
C Rem=120-(36+44)=40

2/3 ranked B sec
2/3x36=24 A>B>C
36-24=12 A>C>B
So B is last for the 12

3/4 ranked B sec
3/4x40=30 C>B>A
40-30=10 C>A>B
So B is last for the 10

A first=12
C first=10
total 12+10=22

jai169

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18 Dec 2025, 00:03

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so let just make table

people who ranked A as 1=3/10*120=36 among those who rank A first, 2/3rd ranked b second= 2/3*36= 24 so remaining who ranked a as1 Rank C as third= 12
people who ranked B as 1= 11/30*120=44
Remaining people ranked c as first=120-36-44=40 among those who ranked c first 0.75(3/4) ranked B second=30 so remaining who ranked c as 1 ranked a as 3=10
so we got total people who ranked b as 2nd= 24+30=54

each row and column should summed to 120 as each of 120 people is ranking each A, B, and C

	1	2	3
a	36		10
b	44	54	22
c	40

So total 22 people ranked b as 3rd ans is option D 22

Bunuel

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KannikaSahni

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18 Dec 2025, 00:59

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Answer: D

People who ranked B first= 11/30*120 = 44
People who ranked A first= 3/10*120 = 36
Thus, people who ranked C first = 120 - (36 + 44) = 40

People who ranked B second = (36*2/3) + (3/4*40) = 24 + 30 =54

Therefore, people who ranked B last = 120 - (44 + 54) = 22

Bunuel

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msignatius

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18 Dec 2025, 01:06

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I'd definitely recommend creating a table for this. The text editor here has a nifty tool for that, so I will proceed to use it.

Design	Rank 1	Rank 2	Rank 3
A
B
C

First thing first, we see the overall conditions:

1. 120 people were asked to rank.
2. Each person gave a complete ranking with no ties.

Now, to fill in the table.

Of the 120, 3/10 ranked A as first. That's 120 / 10 * 3 = 36.

11 / 30 ranked B as first. That's 120 / 30 * 11 = 44.

What does that imply? As everyone is ranking everyone as either first, second, or third, each will add to 120.

So, to find how many ranked C as first, we get 120 - 36 - 44 = 40.

This is our table now:

Design	Rank 1	Rank 2	Rank 3
A	36
B	44
C	40

Next, we get, "among those who rank A first, 2/3rds rank B second" (that's 24 people ranking B second, until now)

"Among those who rank C first, three-quarters rank B second" (that's 30 people ranking B second, until now)

That's a total of 54 marking B second.

Which means how many will people rank B third? That's, again, the difference between 120, Rank 1 and Rank 2. 120 - 54 - 44 = 22 is the answer, D.

Here's how the completed table will look:

Design	Rank 1	Rank 2	Rank 3
A	36
B	44	54	98
C	40

Bunuel

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asperioresfacere

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Total people = 120
First Choice options ;
A first : 3/10 x120 = 36
B first : 11/30 x 120 = 44
C first : 120-36 = 40
Second Rank :
Among A First (36)
2/3 x 36 = 24 ranked B second
Among C first (40)
3/2 x 40 = 30 Ranked B second
Total B second = 24+30 = 54

Total B positions ;
First :44
Second : 54
Last : ?
B last = 120-(44+54)= 22 , Correct option D ✅

tanvi0915

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Out of 120 people
120*3/10 =36 people put A first
32 * 2/3 = 24 people put B second
Therefore 12 people put B last

120 * 11/30 = 44 people put B first
Therefore 120 - (36 +54) = 40 people put C first
40 * 3/4 = 30 people put B second
Thus 10 people put B last

10 + 12 = 22 Answer is D

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The number of people who ranks B third shall be 1/3rd of those who ranked A first and 1/4th of those who ranked C first
The number of people who ranked C first can be found by using the data from question which says no tie in rankings

As 36 ranked A 1st and 44 ranked B 1st and 40 will be the people who ranked C 1st

From this we get 22 are those who ranked B 3rd

Bunuel

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18 Dec 2025, 02:10

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total 120
A first = 36
B First= 44
C First= 120-80 = 40

24 people from A first Selected B second
30 people from C first selected B second

36-24 =12 B last from set A
40-30 =10 B last from set C
total B last= 22
IMO D

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18 Dec 2025, 02:24

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From 120 interviewees, $3/10 = 36$ ranked A first, $11/30=44$ ranked B first and, accordingly, $120-44-36=40$ ranked C first.

From 36 A-lovers, $2/3=24 $ ranked B second => this means the remaining $36-24=12$ ranked B last.

From 40 C-lovers, $ 3/4=30$ ranked B second => this means the remaining $40-30=10$ ranked B last.

Therefore, the total number of respondents ranking B last was $10+12=22.$ The right answer is D.

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18 Dec 2025, 03:11

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Multiplying the fractions by 120 we get from the data:

36 ranked A first (of which 24 B second) ----> 12 B last
44 ranked B first -----> 0 B last
120 - 36 - 44 = 40 ranked C first (of which 30 B second) ----> 10 B last

Hence 12 + 10 = 22 B last

IMO D!

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18 Dec 2025, 03:32

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Given in the question are the Total number of people which is equal to 120

A first: (3/10) × 120 = 36
B first: (11/30) × 120 = 44
C first: 120 − 36 − 44 = 40

Among A-first (36):
(2/3) rank B second = 24
Remaining = 36 − 24 = 12 (B last)

Among C-first (40):
(3/4) rank B second = 30
Remaining = 40 − 30 = 10 (B last)

Total ranking B last = 12 + 10 = 22

Therefore the answer is option D

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18 Dec 2025, 03:33

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Bunuel

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Total people N=120, Need to find no. who ranked B last i.e. CAB or ACB.
For A(1st) = 3/10 of N = 36. For these 36 people, given that 2/3 ranked B(2nd) i.e. 1/3 gave C(2nd) i.e. 12 gave C(2nd) i.e. 12 gave B(3rd).
For B (1st) = 11/30 of N = 44.
Thus C(1st) given by 120-A(1st)-B(1st) = 40. Out of these 40, 3/4 gave B(2nd) i.e. 1/4 gave B(3rd) => 10 gave B(3rd).
Thus total = 12+10=22.