Q: The bookstore has a better selection of postcards than the newsstand does. The selection of postcards at the drugstore is better than at the bookstore. The drugstore has a better selection of postcards than the bookstore or the newsstand. If the first two statements are true, the third statement is
Solution: Of the three, the drugstore has the best selection of postcards.
Q: A jar of jelly beans contains more red beans than green. There are more yellow beans than red. The jar contains fewer yellow jelly beans than green ones. If the first two statements are true, the third statement is
Solution: The first two statements indicate there are more yellow jelly beans than red and green.
Q: Fact 1: All dogs like to run. Fact 2: Some dogs like to swim. Fact 3: Some dogs look like their masters. If the first three statements are facts, which of the following statements must also be a fact? I: All dogs who like to swim look like their masters. II: Dogs who like to swim also like to run. III: Dogs who like to run do not look like their masters.
Solution: Statement II is the only true statement. Since all dogs like to run, then the ones who like to swim also like to run. There is no support for statement I or statement III.
Q: Fact 1: Jessica has four children Fact 2: Two of the children have blue eyes and two of the children have brown eyes. Fact 3: Half of the children are girls. If the first three statements are facts, which of the following statements must also be a fact? I: At least one girl has blue eyes. II: Two of the children are boys. III: The boys have brown eyes.
Solution: Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.
Q: Fact 1: All drink mixes are beverages. Fact 2: All beverages are drinkable. Fact 3: Some beverages are red. If the first three statements are facts, which of the following statements must also be a fact? I: Some drink mixes are red. II: All beverages are drink mixes. III: All red drink mixes are drinkable.
Solution: If all drink mixes are beverages and some beverages are red, then some drink mixes are red (statement I). Since all beverages are drinkable and all drink mixes are beverages, then all red drink mixes must be drinkable (statement III). Statement II can be ruled out.
Q: Fact 1: All chickens are birds. Fact 2: Some chickens are hens. Fact 3: Female birds lay eggs. If the first three statements are facts, which of the following statements must also be a fact? I: All birds lay eggs. II: Some Hens are birds. III: Some chickens are not hens.
Solution: The first statement cannot be true because only female birds lay eggs. Statement II is true because some hens are chickens and all chickens are birds. Statement III is also true because if only some chickens are hens, then some must not be hens.
Q: Fact 1: Eyeglass frames cost between $35 and $350. Fact 2: Some eyeglass frames are made of titanium. Fact 3: Some eyeglass frames are made of plastic. If the first three statements are facts, which of the following statements must also be a fact? I: Titanium eyeglass frames cost more than plastic frames. II: Expensive eyeglass frames last longer than cheap frames. III: Only a few eyeglass frames cost less than $35.
Solution: There is no information in the facts to support statements I or II. Statement III is clearly wrong because, according to Fact 1, no frames cost less than $35.
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