Jamboree and GMAT Club Contest: Recently, editors of leading dailies

First stimulus: several letters of complaint about an advertisement are received.
Second stimulus: Ninety per cent of those who complained accused it of carrying racist undertones.
Third stimulus: Sucrocorp owns over twenty per cent of the market share for cheeses.
Conclusion: at least twenty per cent of consumers do not find the advertisement controversial.

Evidently, we see a big gap between what the stimuli provide and what conclusion has been made from those stimuli. The new term will be the key to identify the answer. Because it is very clear that Answer C mentions such term "percent of consumers", it is very likely that this is the answer. However, we can understand it by putting in numbers:

- There are two type of people: those who use the product and those who do not. Those who use take the percentage of over 20% (choose 20 as minimum). Those who do not use take the number of 100-20 = 80.
- Within those who use and who do not use, we have two types of people: complain about the advertisement and do not complain about the advertisement. Then we have:
a) Those who use: 20
- Total complaints: x
- Complain about the advertisement: a
- Complain but NOT about the advertisement: x-a
=> Those who do not complain about the advertisement (= those who do not complain + complain but not about the advertisement) = (20 - x) + (x - a) = 20 - a (we assume that one person makes only one complain)
b) Those who not use: 80
- Total complaints: y
- Complain about the advertisement: b
- Complain but NOT about the advertisement: y-b
=> Those who do not complain about the advertisement (= those who do not complain + complain but not about the advertisement) = (80 - y) + (y - b) = 80 - b

The second stimulus says that "Ninety per cent of those who complained accused it of carrying racist undertones". Thus we have: a + b = 0.9(x+y)

Conclusion says: "at least twenty per cent of consumers do not find the advertisement controversial".
This means that: 20 - a + 80 - b >= 0.2.20 = 4 (Note: we multiple by 20, not 100 because we mention the customers, it means that these are the people who USE the product). Combined with the stimulus, we want to find out: (a + b) =< 96???

Answer C states clearly: "The eighty per cent of consumers who do not buy Sucrocorp cheese consider the advertisement objectionable." This means we have 80%*80 = 64 = b. So the conclusion asks: does "a =< 96 - 64 = 32" ?
Clearly, because a =<x =< 20 (because we assume that one complaint is equivalent to one person), the maximum of "a" is 20. Thus, conclusion always holds.

Thus, Answer C is the best choice.

Note: even when from the conclusion: "at least twenty per cent of consumers do not find the advertisement controversial", you use 20% of 100, then a + b will be smaller than a number which is much smaller than 96. More specifically: 100 - (a + b) >= 20 => a + b =< 80. With b = 64, a =< 16 (ALWAYS).




Which of the following is an assumption of the argument?

A. Dislike of an advertisement has no impact on the likelihood that a consumer will purchase the product.
B. Sucrocorp’s consumers are aware of its advertisements.
C. The eighty per cent of consumers who do not buy Sucrocorp cheese consider the advertisement objectionable.
D. Most consumers in the dairy market prefer certain types of cheese to others.
E. Most of the complaints against the advertisement were by people who have themselves been the victims of racist attacks.