The Little Blue Reasoning Book - Brandon Royal [73]
Problem 39: Valley High School
Choice E. With reference to the following diagram, if all physics students study math and no math students study French, then it must be true that no physics students study French. In referring to the diagram below, the little black circle (i.e., physics) must stay inside the larger black circle representing math students.
Again, the best way to eliminate wrong answer choices is to see which ones “could be true.” Choice A is incorrect because the smaller dotted circle could be anywhere as long as it partially overlaps with the larger dotted circle representing English students. Choice B is incorrect because the little black circle representing physics students may or may not be within the larger dotted circle representing English students. Choice C is very tricky indeed because the small solid circle could be expanded to fit perfectly in the larger math circle. In this case, all physics students could be math students and all math students could be physics students, however unlikely. Choice D is also tricky. Should the large dotted circle representing English students be quite large, then it would be true that most math students study English but that most English students are not also studying math.
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Problem 40: Little Italy
1. Not inferable. We cannot infer that Antonio’s restaurant is the best in the city. We could, however, infer that his restaurant is among the best Italian restaurants in the city.
2. Not inferable. We can infer that Antonio is good at preparing Italian food, but we cannot infer logically that he “likes” preparing Italian food. He may in fact find preparing food very tedious and boring.
3. Not inferable. There is nothing to say that three out of every four Food and Beverage consultants do not also recommend a number of other Italian restaurants in the city. Which restaurant they recommend most is unclear.
4. Not inferable. This is a tad technical. “Antonio’s customers prefer his style of Italian cooking by a ratio of 2 to 1.” This original statement does not contain a logical comparative. In other words, it could be comparing Antonio’s Italian cooking to mice, dog food, or to the common cold.
The following is a statement from which a proper inference could be drawn: “Antonio’s customers prefer his style of Italian cooking to that of other comparable Italian restaurants by a ratio of 2 to 1.”
5. Not inferable. We simply do not know.
6. Not inferable. Tricky — even if Antonio is a connoisseur of Italian food, capable of preparing high-quality dishes, we do not know that he actually prepares high-quality food or whether he uses the highest-quality ingredients. For all we know, customers love Antonio’s restaurant because of its location and ambience, not because the food is necessarily great. Note that the qualitative terms such as “well-known,” “famous,” or “successful” may not translate to their often-assumed monetary equivalents of “rich” or “profitable.”
7. Not inferable. For all we know, Little Italy is a very popular restaurant even though it is inefficiently run and barely breaks even.
8. Not inferable. We cannot tell what would happen in another city or, for that matter, even in another location within Devon city.
9. Not inferable. We do not know. Customers may crowd the restaurant paying top dollar or they may fill the restaurant paying moderate prices.
10. Not inferable. Again, this is subtle. We may infer that Antonio spent a number of years preparing to become an Italian connoisseur, but he may have attained his reputation as an Italian connoisseur in a relatively short period of time.
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APPENDIX III – ANALOGIES
Problem 41: Analogy Exercise
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1. RED is to PINK as BLACK is to GRAY. The relationship is one of intensity or degree. Pink is a muted form of red; gray is a muted form of black. White is the opposite of black, while dark is a characteristic of black.
C. Type of Analogy: Degree
2. HEAT