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A group of friends went to an ice-cream parlour and ordered

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A group of friends went to an ice-cream parlour and ordered  [#permalink]

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New post 30 Apr 2018, 08:58
4
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A
B
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D
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Difficulty:

  95% (hard)

Question Stats:

48% (02:14) correct 52% (02:18) wrong based on 46 sessions

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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 and people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour and 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.

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Re: A group of friends went to an ice-cream parlour and ordered  [#permalink]

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New post 30 Apr 2018, 10:52
itisSheldon wrote:
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 and people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour and 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.


So there are 4 kinds of people here: Those who ate only chocolate (a), those who ate only strawberry (b), those who ate both (c) and those who ate neither (d). We are given that: a+b > 0, c > 0, and d > 0. So the total number of people have to be greater than 3, at least. We have to answer whether (a+c) > (b+c) or whether a > b.

(1) Total people who went to ice-cream parlour, (a+b+c+d) has to be greater than d. So ratio of Total : neither = (a+b+c+d) : d must be > 1. And this statement says that the ratio of (a+c) : (b+c) is greater than this ratio, which means a+c : b+c is also > 1 OR a+c > b+c. This gives us YES as an answer to the question asked. Sufficient.

(2) Given a+b > b+c OR a > c. But this doesnt help us in answering whether a > b or not. Not sufficient.

Hence A answer
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A group of friends went to an ice-cream parlour and ordered  [#permalink]

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New post 30 Apr 2018, 15:26
itisSheldon wrote:
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 and people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour and 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.

1. Choco + Both/ Strawb + Both >Total / None. Since Total is always > than None, so the right part >1, hence numerator in left part > denominator. Sufficient

2. Choco + Strawb > Strawb + Both => Choco + Strawb> Strawb+ Both =>Choco>Both - doesn't help us much. Insufficient.

Answer (A)
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Re: A group of friends went to an ice-cream parlour and ordered  [#permalink]

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New post 17 May 2018, 07:57
1) The ratio of the number of people who ate chocolate ice-cream and people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour and the number of people who did not eat any type of ice-cream.

Chocolate/strawberry=Total/Neither
This can have two cases
Examples
I) 1/4>1/5
Total/neither ratio <1

2) 5>4
Total/neither>1

We know total >neither here in this case so only 2nd case holds here

Chocolate/strawberry> Total/Neither so it is also > 1
So sufficient

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.


Suppose total of one ice cream=5
I) strawberry =4 chocolate=1
Strawberry>chocolate

II) strawberry=2 chocolate=3
Strawberry<chocolate

Both cases so Insufficient
A is answer

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Re: A group of friends went to an ice-cream parlour and ordered  [#permalink]

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New post 20 May 2018, 01:38
Strawberry No Strawberry
Chocolate C A
No Chocolate B D

St1: The ratio of the number of people who ate chocolate ice-cream and people who ate strawberry ice-cream was greater than the ratio of the total number of people who went to ice-cream parlour and the number of people who did not eat any type of ice-cream.

(A+C) / (B+C) > (A+B+C+D) / D

Subtrating 1 from both sides,

((A+C) / (B+C)) -1 > ((A+B+C+D) / D) - 1
(A-B) / (B+C) > (A+B+C) / D

since RHS is positive, so LHS should be positve,
therefore, A-B> 0 => A>B

st2: 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.

A +B > B +C
so, A > C

insufficient
Re: A group of friends went to an ice-cream parlour and ordered &nbs [#permalink] 20 May 2018, 01:38
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