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In a marketing survey, 60 people were asked to rank three flavors of i

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In a marketing survey, 60 people were asked to rank three flavors of i  [#permalink]

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New post 18 Dec 2018, 10:50
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Simple Solution:

Total = Vanilla before Chocolate + Vanilla before Strawberry - Vanilla before Both + Vanilla before neither
1 = 1/10 + 1/3 - Vanilla before Both + 3/5
1 - 3/5 = 13/30 - Vanilla before Both
2/3 = 13/30 - Vanilla before Both
Vanilla before Both = 1/30.

1/30 of 60 = 2.
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Re: In a marketing survey, 60 people were asked to rank three flavors of i  [#permalink]

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New post 18 Dec 2018, 22:18
The sum of the number of people who ranked vanilla should be 60.
Here, 36(third) + 6(before chocolate) + 20(before strawberry) = 62.
The extra count is the number of people who rated vanilla before both chocolate and strawberry i.e. who ranked vanilla first.
This means, that 62 – 60 = 2 people ranked vanilla first.
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Re: In a marketing survey, 60 people were asked to rank three flavors of i  [#permalink]

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New post 29 Jan 2019, 08:07
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johng2016 wrote:
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


Let C represent chocolate, V represent vanilla, and C represent strawberry

Let a = the number of people who ranked the flavors (from best to worst) as V-C-S
Let b = the number of people who ranked the flavors (from best to worst) as V-S-C
Let c = the number of people who ranked the flavors (from best to worst) as C-S-V
Let d = the number of people who ranked the flavors (from best to worst) as C-V-S
Let e = the number of people who ranked the flavors (from best to worst) as S-C-V
Let f = the number of people who ranked the flavors (from best to worst) as S-V-C

We know that a + b + c + d + e + f = 60 [since there are 60 people in the survey]

3/5 of the people ranked vanilla last
This refers to people who had any of the following rankings: C-S-V (c) or S-C-V (e)
3/5 of 60 = 36
So, we can write: c + e = 36

1/10 of the people ranked vanilla before chocolate
This refers to people who had any of the following rankings: V-C-S (a), V-S-C (b) or S-V-C (f)
1/10 of 60 = 6
So, we can write: a + b + f = 6

1/3 of the people ranked vanilla before strawberry
This refers to people who had any of the following rankings: V-C-S (a), V-S-C (b) or C-V-S (d)
1/3 of 60 = 20
So, we can write: a + b + d = 20

How many people ranked vanilla first?
This refers to people who had any of the following rankings: V-C-S (a) or V-S-C (b)
So, our GOAL is to find the value of a + b

So, we have the following equations:
c + e = 36
a + b + f = 6
a + b + d = 20
ADD them all to get: 2a + 2b + c + d + e + f = 62
We also know that a + b + c + d + e + f = 60

If we SUBTRACT the bottom equation from the top equation, we get: a + b = 2
Answer: A

Cheers,
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In a marketing survey, 60 people were asked to rank three flavors of i  [#permalink]

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New post 13 Feb 2019, 20:03
"1/10 of them ranked vanilla before chocolate"

so 9/10 of then ranked vanilla AFTER chocolate. SO 54 ranked vanilla AFTER chocolate. 6 of them have vanilla before chocolate, but we don't know if vanilla is 1st or second for now. We can deduce the answer has to be 6 or 2.

36 ranked vanilla last so these are part of the 54 who ranked vanilla after chocolate. There must be 54-36 who ranked vanilla after chocolate but did not rank it last. So the order must be c,v,s....There are 1-(1/3) or 40 who ranked vanilla after strawberry. These are part of the 36 who ranked vanilla last so 4 must rank vanilla after strawberry but must not have it be last. The order must be s,v,c. So 36+18+4=58 DO NOT RANK VANILLA FIRST. The remaining 2 people must rank vanilla first.
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In a marketing survey, 60 people were asked to rank three flavors of i  [#permalink]

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New post 30 Apr 2019, 14:54
Hi,

If we read the entire question all its asking is in how many ways can we Write V first

So either its VSC or VCS

Or think of it like this
So we have 3 Slots where First Slot is Selected in 1 way ( we can select only Vanilla)

First Slot can be filled 1 Way
Second Slot we can Select i out of 2 so 2 ways
Third slot can be Selected in 1 way after the second slot is filled


So we have 1 * 2 *1 = 2 Ways

So we can have vanilla 2 ways in first place .
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In a marketing survey, 60 people were asked to rank three flavors of i  [#permalink]

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New post 20 Sep 2019, 23:04
johng2016 wrote:
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


Given:
1. In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference.
2. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed.

Asked: 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?
Q. V1S2C3 + V1C2S3 = ?

Let chocolate, vanilla, and strawberry be denoted by C, V & S respectively
And 1, 2 & 3 denote the first, second and third preference respectively

V3 = 3/5 * 60 = 36 = C1S2V3 + S1C2V3 = 36
V1C2S3+V1S2C3 + S1V2C3 = 1/10*60 = 6
V1S2C3 + V1C2S3 + C1V2S3 = 1/3 *60 = 20

Total there are 6 possibilities
(C1V2S3, C1S2V3, V1C2S3, V1S2C3, S1C2V3, S1V2C3)

C1V2S3+V1C2S3+V1S2C3+C1S2V3+V1C2S3+V1S2C3+S1C2V3+S1V2C3 = 60 + V1C2S3+V1S2C3
36 + 6 + 20 = 60 + V1C2S3+V1S2C3
V1C2S3+V1S2C3 = 2

IMO A
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In a marketing survey, 60 people were asked to rank three flavors of i   [#permalink] 20 Sep 2019, 23:04

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