Questions:
Answers:
1.b. Because the first two statements are true, Eric is the youngest of the three, so the third statement must be false.
2. c. Because the first two sentences are true, both Josh and Darren saw more movies than Stephen.However, it is uncertain as to whether Darren saw more movies than Josh.
3. c. The first two statements give information about Zoe’s tulips and pansies. Information about any other kinds of flowers cannot be determined.
4. a. Because the first two statements are true, raspberries are the most expensive of the three.
5. a. If no wall-to-wall carpeting is pink and all the offices have wall-to-wall carpeting, none of the offices has pink wall-to-wall carpeting.
6.b. From the first two statements, we know that of the three classes, Class A has the highest enrollment, so the third statement must be false.
7. a. According to the first two statements, Fido weighs the most and Boomer weighs the least.
8. c. Although all of the trees in the park are flowering trees, it cannot be determined by the information given whether all dogwoods are flowering trees.
9. a. Since the Gaslight Commons costs more than the Riverdale Manor and the Livingston Gate costs more than the Gaslight Commons, it is true that the Livingston Gate costs the most.
10. a. From the first two statements, you know that the Kingston Mall has the most stores, so the Kingston Mall would have more stores than the Four Corners Mall.
11.b. We know from the first two statements that Lily runs fastest. Therefore, the third statement must be false.
12. a. From the first statement, we know that bran cereal has more fiber than both oat cereal and corn cereal. From the second statement, we know that rice cereal has less fiber than both corn and wheat cereals. Therefore, rice cereal has the least amount of fiber.
13. c. We only know that Jasmine weighs more than Jason. There is no way to tell whether Jasmine also weighs more than Jenna.
14. c. We know from the first two statements that Tuesday had the highest temperature, but we cannot know whether Monday’s temperature was higher than Tuesday’s.
15.b. Spot is bigger than King, and Ralph is bigger than Spot. Therefore, King must be smaller than Ralph.
16. a. There are fewer oranges than either apples or lemons, so the statement is true.
17 .b. Because the first two statements are true, Rebecca’s house is also northeast of the Shop and Save Grocery, which means that the third statement is false.
18. a. Joe is younger than Kathy and older than Mark, so Mark must be younger than Kathy.
19. c. We know only that long-tailed Gangles have spots.We cannot know for certain if long-tailed Gangles also have short hair.
20. c. The first two statements indicate that Battery Y lasts the least amount of time, but it cannot be determined if Battery Z lasts longer than Battery X.
21.b. Given the information in the first two statements, Bryant is sitting in front of both Jerome and Martina, so the third statement must be false.
22.b. Because the first two statements are true, Penfield is west of Centerville and southwest of Middletown. Therefore, the third statement is false.
23. c. Both the car and the train are quicker than the bus, but there is no way to make a comparison between the train and the car.
24. a. We know that there are Signots with buttons, or Lamels, and that there are yellow Signots, which have no buttons. Therefore, Lamels do not have buttons and cannot be yellow.
25. a. The market is one block west of the hotel. The drugstore is two blocks west of the hotel, so the drugstore is west of the market.
26. c. There is not enough information to verify the third statement.
27.b. Rulers are the most expensive item.
28.b. The first two statements indicate there are more yellow jelly beans than red and green.
29. c. Cloudy days are the most windy, but there is not enough information to compare the wind on the foggy days with the wind on the sunny days.
30. a. Of the three, the drugstore has the best selection of postcards.
31.b. This is the order of the cars from left to right: minivan, pickup, sedan, sport utility vehicle.
32. a. To the extent that a toothpick is useful, it has
value.
33. a. Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.
34.d. All baseball caps have brims, since baseball caps are hats (Fact 3) and all hats have brims (Fact 1). This rules out statement III—but it doesn’t follow that all caps, a category that may include caps that are not baseball caps, have brims (statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black.
35.b. The first statement cannot be true because only female birds lay eggs. Statement II is true because hens are chickens and chickens are birds. Statement III is also true because if only some chickens are hens, then some must not be hens.
36.d. None of the three statements is supported by the known facts.
37. c. Statements I and II are not supported by the facts. Statement III is true because if all storybooks have pictures and only some have words, then some storybooks have both words and pictures.
38.d. There is not enough information to support any of the statements. Robert is known to have a minvan, but it is not known which of his vehicles
is red. Robert may have a pickup or sport utility vehicle, so the second statement cannot
be supported. There is no way to know if Robert’s favorite color is red (statement III).
39. a. Since Maui is an island and islands are surrounded by water,Maui must be surrounded by water. There is not enough information to support statements II and III.
40. c. 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.
41.d. 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.
42.b. Since some pens don’t write, some writing utensils don’t write (statement I). Since there are blue pens and since pens are writing utensils, some writing utensils are blue (statement II). There is not enough information to support statement III.
43. c. If Mary always tells the truth, then both Ann and Mary have cats (statements I and II), and Ann is lying (statement III).
44.b. 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.
45.d. After all the switches were made,Max is directly behind the dog, James is alongside the dog on the left, Ruby is alongside the dog on the right, and Rachel is behind Max.
46.b. Nurse Kemp has worked more shifts in a row than Nurse Calvin; therefore, Kemp has worked more than eight shifts. The number of Kemp’s shifts plus the number of Rogers’s shifts (five) cannot equal fifteen or more, the number of Miller’s shifts. Therefore, Kemp has worked nine shifts in a row (5 + 9 = 14).
47. c. If Randy is two months older than Greg, then Ned is three months older than Greg and one month older than Randy. Kent is younger than both Randy and Ned. Ned is the oldest.
48. c. After all the switches were made, Shawn is in front of the house. Ross is in the alley behind the house,Michael is on the north side, and Jed is on the south.
49.d. After all the switches were made, Mr. Kirk worked on Tuesday. Mr. Carter worked on Monday, Ms. Johnson on Wednesday, and Ms. Falk on Thursday.
50. a. Mr. Temple has the most seniority, but he does not want the job. Next in line is Mr. Rhodes, who has more seniority than Ms. West or Ms. Brody.
51.b. Tall, thin, and middle-aged are the elements of the description repeated most often and are therefore the most likely to be accurate.
52.b. Beth won the biggest prize, described as a higher medal than Jamie’s, which we’ve been told was a silver medal. Roberta and Michele both won bronze medals, which are lower ranking medals than silver. Beth is also described as having competed more times than Roberta— who has competed seven times. Jamie is described as having competed fewer times than Roberta, and Michele has competed three times. Therefore, Beth has competed more times than the others and has won the biggest prize to date.
53. c. After all the switching was done, Jenkins was directly behind the receiver. Calvin and Burton had fallen. Zeller remained in the rear.
54.d. Alexis is farther away than Frances, who is five miles away, and closer than Samantha, who is seven miles away.
55. a. Baxter should be assigned to study with Carter. Baxter cannot be assigned with Adam, because they have already been together for seven class periods. If Baxter is assigned to work with Dennis, that would leave Adam with Carter, but Carter does not want to work with Adam.
56. a. If George is sitting at Henry’s left, George’s seat is 252. The next seat to the left, then, is 251.
Answers:
1.b. Because the first two statements are true, Eric is the youngest of the three, so the third statement must be false.
2. c. Because the first two sentences are true, both Josh and Darren saw more movies than Stephen.However, it is uncertain as to whether Darren saw more movies than Josh.
3. c. The first two statements give information about Zoe’s tulips and pansies. Information about any other kinds of flowers cannot be determined.
4. a. Because the first two statements are true, raspberries are the most expensive of the three.
5. a. If no wall-to-wall carpeting is pink and all the offices have wall-to-wall carpeting, none of the offices has pink wall-to-wall carpeting.
6.b. From the first two statements, we know that of the three classes, Class A has the highest enrollment, so the third statement must be false.
7. a. According to the first two statements, Fido weighs the most and Boomer weighs the least.
8. c. Although all of the trees in the park are flowering trees, it cannot be determined by the information given whether all dogwoods are flowering trees.
9. a. Since the Gaslight Commons costs more than the Riverdale Manor and the Livingston Gate costs more than the Gaslight Commons, it is true that the Livingston Gate costs the most.
10. a. From the first two statements, you know that the Kingston Mall has the most stores, so the Kingston Mall would have more stores than the Four Corners Mall.
11.b. We know from the first two statements that Lily runs fastest. Therefore, the third statement must be false.
12. a. From the first statement, we know that bran cereal has more fiber than both oat cereal and corn cereal. From the second statement, we know that rice cereal has less fiber than both corn and wheat cereals. Therefore, rice cereal has the least amount of fiber.
13. c. We only know that Jasmine weighs more than Jason. There is no way to tell whether Jasmine also weighs more than Jenna.
14. c. We know from the first two statements that Tuesday had the highest temperature, but we cannot know whether Monday’s temperature was higher than Tuesday’s.
15.b. Spot is bigger than King, and Ralph is bigger than Spot. Therefore, King must be smaller than Ralph.
16. a. There are fewer oranges than either apples or lemons, so the statement is true.
17 .b. Because the first two statements are true, Rebecca’s house is also northeast of the Shop and Save Grocery, which means that the third statement is false.
18. a. Joe is younger than Kathy and older than Mark, so Mark must be younger than Kathy.
19. c. We know only that long-tailed Gangles have spots.We cannot know for certain if long-tailed Gangles also have short hair.
20. c. The first two statements indicate that Battery Y lasts the least amount of time, but it cannot be determined if Battery Z lasts longer than Battery X.
21.b. Given the information in the first two statements, Bryant is sitting in front of both Jerome and Martina, so the third statement must be false.
22.b. Because the first two statements are true, Penfield is west of Centerville and southwest of Middletown. Therefore, the third statement is false.
23. c. Both the car and the train are quicker than the bus, but there is no way to make a comparison between the train and the car.
24. a. We know that there are Signots with buttons, or Lamels, and that there are yellow Signots, which have no buttons. Therefore, Lamels do not have buttons and cannot be yellow.
25. a. The market is one block west of the hotel. The drugstore is two blocks west of the hotel, so the drugstore is west of the market.
26. c. There is not enough information to verify the third statement.
27.b. Rulers are the most expensive item.
28.b. The first two statements indicate there are more yellow jelly beans than red and green.
29. c. Cloudy days are the most windy, but there is not enough information to compare the wind on the foggy days with the wind on the sunny days.
30. a. Of the three, the drugstore has the best selection of postcards.
31.b. This is the order of the cars from left to right: minivan, pickup, sedan, sport utility vehicle.
32. a. To the extent that a toothpick is useful, it has
value.
33. a. Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.
34.d. All baseball caps have brims, since baseball caps are hats (Fact 3) and all hats have brims (Fact 1). This rules out statement III—but it doesn’t follow that all caps, a category that may include caps that are not baseball caps, have brims (statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black.
35.b. The first statement cannot be true because only female birds lay eggs. Statement II is true because hens are chickens and chickens are birds. Statement III is also true because if only some chickens are hens, then some must not be hens.
36.d. None of the three statements is supported by the known facts.
37. c. Statements I and II are not supported by the facts. Statement III is true because if all storybooks have pictures and only some have words, then some storybooks have both words and pictures.
38.d. There is not enough information to support any of the statements. Robert is known to have a minvan, but it is not known which of his vehicles
is red. Robert may have a pickup or sport utility vehicle, so the second statement cannot
be supported. There is no way to know if Robert’s favorite color is red (statement III).
39. a. Since Maui is an island and islands are surrounded by water,Maui must be surrounded by water. There is not enough information to support statements II and III.
40. c. 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.
41.d. 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.
42.b. Since some pens don’t write, some writing utensils don’t write (statement I). Since there are blue pens and since pens are writing utensils, some writing utensils are blue (statement II). There is not enough information to support statement III.
43. c. If Mary always tells the truth, then both Ann and Mary have cats (statements I and II), and Ann is lying (statement III).
44.b. 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.
45.d. After all the switches were made,Max is directly behind the dog, James is alongside the dog on the left, Ruby is alongside the dog on the right, and Rachel is behind Max.
46.b. Nurse Kemp has worked more shifts in a row than Nurse Calvin; therefore, Kemp has worked more than eight shifts. The number of Kemp’s shifts plus the number of Rogers’s shifts (five) cannot equal fifteen or more, the number of Miller’s shifts. Therefore, Kemp has worked nine shifts in a row (5 + 9 = 14).
47. c. If Randy is two months older than Greg, then Ned is three months older than Greg and one month older than Randy. Kent is younger than both Randy and Ned. Ned is the oldest.
48. c. After all the switches were made, Shawn is in front of the house. Ross is in the alley behind the house,Michael is on the north side, and Jed is on the south.
49.d. After all the switches were made, Mr. Kirk worked on Tuesday. Mr. Carter worked on Monday, Ms. Johnson on Wednesday, and Ms. Falk on Thursday.
50. a. Mr. Temple has the most seniority, but he does not want the job. Next in line is Mr. Rhodes, who has more seniority than Ms. West or Ms. Brody.
51.b. Tall, thin, and middle-aged are the elements of the description repeated most often and are therefore the most likely to be accurate.
52.b. Beth won the biggest prize, described as a higher medal than Jamie’s, which we’ve been told was a silver medal. Roberta and Michele both won bronze medals, which are lower ranking medals than silver. Beth is also described as having competed more times than Roberta— who has competed seven times. Jamie is described as having competed fewer times than Roberta, and Michele has competed three times. Therefore, Beth has competed more times than the others and has won the biggest prize to date.
53. c. After all the switching was done, Jenkins was directly behind the receiver. Calvin and Burton had fallen. Zeller remained in the rear.
54.d. Alexis is farther away than Frances, who is five miles away, and closer than Samantha, who is seven miles away.
55. a. Baxter should be assigned to study with Carter. Baxter cannot be assigned with Adam, because they have already been together for seven class periods. If Baxter is assigned to work with Dennis, that would leave Adam with Carter, but Carter does not want to work with Adam.
56. a. If George is sitting at Henry’s left, George’s seat is 252. The next seat to the left, then, is 251.
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