120 people responded to a survey asking which type of vacation they

Question

120 people responded to a survey asking which type of vacation they prefer: city visits, ski trips, or beach holidays. No two trips were ranked equally by any of the respondents. If 55% of the respondents ranked beach holidays first, 25% ranked ski trips ahead of beach holidays, and 30% ranked city visits ahead of beach holidays, how many ranked beach holidays last?

(A) 6
(B) 12
(C) 24
(D) 30
(E) 54

(A) 6
(B) 12
(C) 24
(D) 30
(E) 54

demawtf · Accepted Answer

Total who did not rank beach holidays first=People who ranked ski trips ahead of beach holidays+People who ranked city visits ahead of beach holidays−People who ranked both higher.

54 = 30 + 36 - x

x=12

55%*120 =66 --> (120 - 66 = 54 )

MoshiSenpai · Answer

GMATNinja  I apologize beforehand if this question was not intended to be shared from the youtube video.

I had trouble with the explanation provided by Charles in the youtube video and was amazed to find that this question hasn't been posted on gmat club.

Charles mentions an alternative solution which mentions intuition to determine the entity being double counted and arrives at 10% of total people somehow. I was unable to understand the logic behind that conclusion and would really appreciate a detailed explanation behind the same.

vinhtc · Answer

55% put the beach at the top => 45% left 
there are 3 cases in 45% is the beach in the middle and the beach at the end
25%+30% =55% => 55%-45% =10% => there is 10% beach at the end => there are 120 people => 12 people

ThatDudeKnows · Answer

See attached.

55% ranked B first. That's 66 people. That leaves 54 people who ranked B either second or third. Since we are asked for the number who ranked B third, let's make B3 = x. That means B2 = 54-x.

What does B2 mean? It means that that number of people ranked exactly one of either C or S ahead of B. So 54-x rankings had exactly one of C or S ahead of B.
What does B3 mean? It means that that number of people ranked both C and S ahead of B. If x people ranked both C and S ahead of B, 2x rankings were ahead of B.

25% ranked S>B. That's 30 rankings. 30% ranked C>B. That's 36 rankings.

54-x+2x = 30+36
54+x = 66
x = 12

Answer choice B.

maximilius491 · Answer

Total respondents: 120.
55% ranked beach holidays (B) first.

Calculate the number of people who ranked B first:
0.55×120=66
Therefore, 66 people ranked B first.

Remaining Respondents: 
The remaining respondents did not rank B first:
120−66=54
These 54 people ranked B either second or third.

Define Variables:
Let B3=x represent the number of people who ranked B third.

Consequently, 
B2=54−x represents the number of people who ranked B second.
Interpretation of B2 and B3:
B2 means these people ranked exactly one of either city visits (C) or ski trips (S) ahead of B.
B3 means these people ranked both C and S ahead of B. Hence, if x people ranked B third, 2x rankings were ahead of B (one for C and one for S).
Given Percentages:

25% ranked S ahead of B:
0.25×120=30
30% ranked C ahead of B:
0.30×120=36
Formulating the Equation:
Combine the rankings for S and C ahead of B:
30+36=66
Now, the number of people who ranked B second plus twice the number of people who ranked B third should equal 66 (total number of rankings ahead of B):
B2+2x=66
Substitute B2 54−x:
54−𝑥+2𝑥=66
54−x+2x=66
Simplify the equation:
54+x=66
x=66−54
x=12

​

madkilla07 · Answer

55% have ranked ski holidays first. So 45% have it ranked 2nd or third.
If people lave ranked ski holidays over beach it can be S,B,C or C,S,B or S,C,B.
If people lave ranked City hikes over beach it can be C,B,S or C,S,B or S,C,B.

Now we can see we have over counted for people ranking beach last as it occurs in the last 2 cases where beach is ranked last. Therefore the extra 10% or 12 people.

Marcelo7 · Answer

How I approched:

C = city visits
S = ski trips
B = beach holidays

25% ranked S ahead B: SBC or SCB or CSB

30% ranked C ahead B: CBS or CSB or SCB

Note that there is a overlap there when B is the last.

Now we do START WITH B + S BEFORE B + C BEFORE B - B LAST = 100% (you can check that this are all the possible answer to the survey: (BCS + BSC) + (SBC + SCB + CSB) + (CBS + CSB + SCB) - (SCB + CSB) = BCS + BSC + SBC + CSB + SCB + CSB )

Then: 55% + 25% + 30% - B LAST = 100% -> B LAST = 10%

10%*120 = 12!

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=88442 --- Harsha GMAT-Club-Forum-408j0dgc.png

120 people responded to a survey asking which type of vacation they

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