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Bunuel
A group of friends went to an ice-cream parlour and ordered only two types of ice-cream - chocolate and strawberry. Of the people in the group, at least one person ate only one type ice-cream, some people ate both types of ice-cream and at least one person did not eat any type of ice-cream. Did more people eat chocolate ice-cream than strawberry ice-cream?

(1) The ratio of the number of people who ate chocolate ice-cream to people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour to the number of people who did not eat any type of ice-cream.

(2) The number of people who ate only one type of ice-cream is greater than the number of people who ate strawberry ice-cream.


T = C + S - B + N, where T equals the total number of people, C is the number who got chocolate only, S is the number who got strawberry only, B is the number who got both, and N is the number who got neither.

S1: In other words, C+B/S+B > T/N. Intuitively, we know that T must be greater than N, so T/N must be greater than 1. Therefore, C + B must be greater than S + B. B cancels out on both sides and you are left with C>S. SUFFICIENT

S2: This can be written as C + S > S + B. S cancels out and we are left with C>B. This does not help us answer the question. NOT SUFFICIENT.

ANSWER: A
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Bunuel
A group of friends went to an ice-cream parlour and ordered only two types of ice-cream - chocolate and strawberry. Of the people in the group, at least one person ate only one type ice-cream, some people ate both types of ice-cream and at least one person did not eat any type of ice-cream. Did more people eat chocolate ice-cream than strawberry ice-cream?

(1) The ratio of the number of people who ate chocolate ice-cream to people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour to the number of people who did not eat any type of ice-cream.

(2) The number of people who ate only one type of ice-cream is greater than the number of people who ate strawberry ice-cream.


You can use 2*2 matrix for such questions.
....................C........nC.........Total
S..................a..........b............a+b
nS................c..........d.............c+d
Total..........a+c.......b+d......a+b+c+d

Given
Quote:
a) at least one person ate only one type ice-cream => \(b+c\geq 1\)
b) some people ate both types of ice-cream => \(a\geq 1\)
c) at least one person did not eat any type of ice-cream => \(d\geq 1\)


We are looking for - Is a+c>a+b ? Or Is c>b?

Statement I
The ratio of the number of people who ate chocolate ice-cream (a+c) to people who ate strawberry ice-cream(a+b) was greater than the ratio of the total number of people who went to ice-cream parlour (Total) to the number of people who did not eat any type of ice-cream (d).
Thus, \(\frac{a+c}{a+b}>\frac{a+b+c+d}{d}= \frac{a+b+c}{d} + \frac{d}{d} = \frac{a+b+c}{d} +1>1\)
So \(\frac{a+c}{a+b}>1.....a+c>a+b\)
Sufficient

Statement II
The number of people who ate only one type of ice-cream (b+c) is greater than the number of people who ate strawberry ice-cream(a+b).
\(b+c>a+b....c>a\)
But we do not know anything about b!
Insufficient

A
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chetan2u
Bunuel
A group of friends went to an ice-cream parlour and ordered only two types of ice-cream - chocolate and strawberry. Of the people in the group, at least one person ate only one type ice-cream, some people ate both types of ice-cream and at least one person did not eat any type of ice-cream. Did more people eat chocolate ice-cream than strawberry ice-cream?

(1) The ratio of the number of people who ate chocolate ice-cream to people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour to the number of people who did not eat any type of ice-cream.

(2) The number of people who ate only one type of ice-cream is greater than the number of people who ate strawberry ice-cream.


You can use 2*2 matrix for such questions.
....................C........nC.........Total
S..................a..........b............a+b
nS................c..........d.............c+d
Total..........a+c.......b+d......a+b+c+d

Given
Quote:
a) at least one person ate only one type ice-cream => \(b+c\geq 1\)
b) some people ate both types of ice-cream => \(a\geq 1\)
c) at least one person did not eat any type of ice-cream => \(d\geq 1\)


We are looking for - Is a+c>a+b ? Or Is c>b?

Statement I
The ratio of the number of people who ate chocolate ice-cream (a+c) to people who ate strawberry ice-cream(a+b) was greater than the ratio of the total number of people who went to ice-cream parlour (Total) to the number of people who did not eat any type of ice-cream (d).
Thus, \(\frac{a+c}{a+b}>\frac{a+b+c+d}{d}=a+b+c>1\)
So \(\frac{a+c}{a+b}>1.....a+c>a+b\)
Sufficient

Statement II
The number of people who ate only one type of ice-cream (b+c) is greater than the number of people who ate strawberry ice-cream(a+b).
\(b+c>a+b....c>a\)
But we do not know anything about b!
Insufficient

A



Hi chetan2u,

Hope you are doing well and many many advance wishes for Diwali.

I have checked all the responses which people have posted for this question and everyone has assumed that (a+b+c+d)/d is greater than one, which is true, and then prove c>b.

I would like to inquire if (a+b+c+d)/d is greater than 1, lets suppose 2 then how can we prove that c>b. Because then the equation will be c>a+2b.

Waiting for your response ahead and Many thanks in advance.
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RahulHGGmat
chetan2u
Bunuel
A group of friends went to an ice-cream parlour and ordered only two types of ice-cream - chocolate and strawberry. Of the people in the group, at least one person ate only one type ice-cream, some people ate both types of ice-cream and at least one person did not eat any type of ice-cream. Did more people eat chocolate ice-cream than strawberry ice-cream?

(1) The ratio of the number of people who ate chocolate ice-cream to people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour to the number of people who did not eat any type of ice-cream.

(2) The number of people who ate only one type of ice-cream is greater than the number of people who ate strawberry ice-cream.


You can use 2*2 matrix for such questions.
....................C........nC.........Total
S..................a..........b............a+b
nS................c..........d.............c+d
Total..........a+c.......b+d......a+b+c+d

Given
Quote:
a) at least one person ate only one type ice-cream => \(b+c\geq 1\)
b) some people ate both types of ice-cream => \(a\geq 1\)
c) at least one person did not eat any type of ice-cream => \(d\geq 1\)


We are looking for - Is a+c>a+b ? Or Is c>b?

Statement I
The ratio of the number of people who ate chocolate ice-cream (a+c) to people who ate strawberry ice-cream(a+b) was greater than the ratio of the total number of people who went to ice-cream parlour (Total) to the number of people who did not eat any type of ice-cream (d).
Thus, \(\frac{a+c}{a+b}>\frac{a+b+c+d}{d}=a+b+c>1\)
So \(\frac{a+c}{a+b}>1.....a+c>a+b\)
Sufficient

Statement II
The number of people who ate only one type of ice-cream (b+c) is greater than the number of people who ate strawberry ice-cream(a+b).
\(b+c>a+b....c>a\)
But we do not know anything about b!
Insufficient

A



Hi chetan2u,

Hope you are doing well and many many advance wishes for Diwali.

I have checked all the responses which people have posted for this question and everyone has assumed that (a+b+c+d)/d is greater than one, which is true, and then prove c>b.

I would like to inquire if (a+b+c+d)/d is greater than 1, lets suppose 2 then how can we prove that c>b. Because then the equation will be c>a+2b.

Waiting for your response ahead and Many thanks in advance.

Rahul, a very happy Diwali to you too in advance and I am sure the festival season here is bringing smiles to everyone at your place.

If you are taking it as 2, then equation will be c=a+2b
Since a and b are positive values, then c is something, a, added to twice of b, making c greater than b.
That is, a added to 2b has to be more than just b => a+2b>b or c>b
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