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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
In a marketing survey, 60 people were asked to rank three flavors of
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13 Apr 2022, 09:11
13 Apr 2022, 09:11
Expert Reply
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Question Stats:
60% (02:37) correct
40% (03:36) wrong based on 10 sessions
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In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?
A. 2
B. 6
C. 14
D. 16
E. 24
A. 2
B. 6
C. 14
D. 16
E. 24
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: In a marketing survey, 60 people were asked to rank three flavors of
[#permalink]
17 Apr 2022, 03:14
17 Apr 2022, 03:14
2
Expert Reply
This question can be easily solved by actually arranging the three flavors.
These three flavors can be chosen in
3 2 1 = 6 ways. It would be better to actually write these 6 ways.
So VCS means that Vanilla is most preferred and then Chocolate and then Strawberry
a) VCS
b) VSC
c) SVC
d) SCV
e) CVS
f) CSV
1. (3/5) people ranked vanilla last. SCV+CSV = (3/5)*20 = 36. (d+f= 36)
2. (1/10) ranked vanilla before chocolate. VSC+VCS+SVC = (1/10)*60 = 6. (a+b+c=6)
3. (1/3) of ranked vanilla before strawberry. VCS+VSC+CVS = (1/3) *60 = 20 (a+b+e = 20)
Question Asked: what is (a+b)?
we can write e = 20-(a+b)
Now
(a+b+c)+(d+f) + (20-(a+b)) = 60
6+36+20-(a+b) = 60
a+b = 2
Answer is (A)
These three flavors can be chosen in
3 2 1 = 6 ways. It would be better to actually write these 6 ways.
So VCS means that Vanilla is most preferred and then Chocolate and then Strawberry
a) VCS
b) VSC
c) SVC
d) SCV
e) CVS
f) CSV
1. (3/5) people ranked vanilla last. SCV+CSV = (3/5)*20 = 36. (d+f= 36)
2. (1/10) ranked vanilla before chocolate. VSC+VCS+SVC = (1/10)*60 = 6. (a+b+c=6)
3. (1/3) of ranked vanilla before strawberry. VCS+VSC+CVS = (1/3) *60 = 20 (a+b+e = 20)
Question Asked: what is (a+b)?
we can write e = 20-(a+b)
Now
(a+b+c)+(d+f) + (20-(a+b)) = 60
6+36+20-(a+b) = 60
a+b = 2
Answer is (A)
Re: In a marketing survey, 60 people were asked to rank three flavors of
[#permalink]
05 Mar 2024, 21:20
05 Mar 2024, 21:20
1
It's a good question.
Total 60 people.
"3/5 of the people ranked vanilla last"
For 36 people, Vanilla came last. So 24 people ranked it 1st or 2nd.
"1/10 of them ranked vanilla before chocolate"
For 6 people, vanilla came before chocolate
"and 1/3 of them ranked vanilla before strawberry"
For 20 people, vanilla came before strawberry
Note that this forms a sets question:
6 people ranked vanilla before chocolate, 20 people ranked vanilla before strawberry. There are 24 people who ranked vanilla before chocolate or before strawberry or before both. How many ranked vanilla before both?
24 = 6 + 20 - Both
Both = 2
Total 60 people.
"3/5 of the people ranked vanilla last"
For 36 people, Vanilla came last. So 24 people ranked it 1st or 2nd.
"1/10 of them ranked vanilla before chocolate"
For 6 people, vanilla came before chocolate
"and 1/3 of them ranked vanilla before strawberry"
For 20 people, vanilla came before strawberry
Note that this forms a sets question:
6 people ranked vanilla before chocolate, 20 people ranked vanilla before strawberry. There are 24 people who ranked vanilla before chocolate or before strawberry or before both. How many ranked vanilla before both?
24 = 6 + 20 - Both
Both = 2
