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