solve all the following problems

Directions: Each group of questions in this section is based on a set of conditions. In answering some of the questions, it may be

useful to draw a rough diagram. Choose the response that most accurately and completely answers each question and blacken

the corresponding space on your answer sheet.

Questions 1–5

A company employee generates a series of five-digit product

codes in accordance with the following rules:

The codes use the digits 0, 1, 2, 3, and 4, and no others.

Each digit occurs exactly once in any code.

The second digit has a value exactly twice that of the

first digit.

The value of the third digit is less than the value of the

fifth digit.

1. If the last digit of an acceptable product code is 1, it

must be true that the

(A) first digit is 2

(B) second digit is 0

(C) third digit is 3

(D) fourth digit is 4

(E) fourth digit is 0

2. Which one of the following must be true about any

acceptable product code?

(A) The digit 1 appears in some position before the

digit 2.

(B) The digit 1 appears in some position before the

digit 3.

(C) The digit 2 appears in some position before the

digit 3.

(D) The digit 3 appears in some position before the

digit 0.

(E) The digit 4 appears in some position before the

digit 3.

3. If the third digit of an acceptable product code is not 0,

which one of the following must be true?

(A) The second digit of the product code is 2.

(B) The third digit of the product code is 3.

(C) The fourth digit of the product code is 0.

(D) The fifth digit of the product code is 3.

(E) The fifth digit of the product code is 1.

4. Any of the following pairs could be the third and

fourth digits, respectively, of an acceptable product

code, EXCEPT:

(A) 0, 1

(B) 0, 3

(C) 1, 0

(D) 3, 0

(E) 3, 4

5. Which one of the following must be true about any

acceptable product code?

(A) There is exactly one digit between the digit 0

and the digit 1.

(B) There is exactly one digit between the digit 1

and the digit 2.

(C) There are at most two digits between the digit 1

and the digit 3.

(D) There are at most two digits between the digit 2

and the digit 3.

(E) There are at most two digits between the digit 2

and the digit 4.

GO ON TO THE NEXT PAGE

Questions 6–10

Exactly three films—Greed, Harvest, and Limelight—are

shown during a film club’s festival held on Thursday, Friday,

and Saturday. Each film is shown at least once during the

festival but never more than once on a given day. On each day

at least one film is shown. Films are shown one at a time. The

following conditions apply:

On Thursday Harvest is shown, and no film is shown after

it on that day.

On Friday either Greed or Limelight, but not both, is

shown, and no film is shown after it on that day.

On Saturday either Greed or Harvest, but not both, is

shown, and no film is shown after it on that day.

6. Which one of the following could be a complete and

accurate description of the order in which the films are

shown at the festival?

(A) Thursday: Limelight, then Harvest; Friday:

Limelight; Saturday: Harvest

(B) Thursday: Harvest; Friday: Greed, then

Limelight; Saturday: Limelight, then Greed

(C) Thursday: Harvest; Friday: Limelight; Saturday:

Limelight, then Greed

(D) Thursday: Greed, then Harvest, then Limelight;

Friday: Limelight; Saturday: Greed

(E) Thursday: Greed, then Harvest; Friday:

Limelight, then Harvest; Saturday: Harvest

7. Which one of the following CANNOT be true?

(A) Harvest is the last film shown on each day of the

festival.

(B) Limelight is shown on each day of the festival.

(C) Greed is shown second on each day of the

festival.

(D) A different film is shown first on each day of the

festival.

(E) A different film is shown last on each day of the

festival.

8. If Limelight is never shown again during the festival

once Greed is shown, then which one of the following is

the maximum number of film showings that could occur

during the festival?

(A) three

(B) four

(C) five

(D) six

(E) seven

9. If Greed is shown exactly three times, Harvest is shown

exactly twice, and Limelight is shown exactly once, then

which one of the following must be true?

(A) All three films are shown on Thursday.

(B) Exactly two films are shown on Saturday.

(C) Limelight and Harvest are both shown on

Thursday.

(D) Greed is the only film shown on Saturday.

(E) Harvest and Greed are both shown on Friday.

10. If Limelight is shown exactly three times, Harvest is

shown exactly twice, and Greed is shown exactly once,

then which one of the following is a complete and

accurate list of the films that could be the first film

shown on Thursday?

(A) Harvest

(B) Limelight

(C) Greed, Harvest

(D) Greed, Limelight

(E) Greed, Harvest, Limelight

GO ON TO THE NEXT PAGE.

Questions 11–17

A cruise line is scheduling seven week-long voyages for the

ship Freedom. Each voyage will occur in exactly one of the

first seven weeks of the season: weeks 1 through 7. Each

voyage will be to exactly one of four destinations:

Guadeloupe, Jamaica, Martinique, or Trinidad. Each

destination will be scheduled for at least one of the weeks. The

following conditions apply to Freedom’s schedule:

Jamaica will not be its destination in week 4.

Trinidad will be its destination in week 7.

Freedom will make exactly two voyages to Martinique,

and at least one voyage to Guadeloupe will occur in some

week between those two voyages.

Guadeloupe will be its destination in the week preceding

any voyage it makes to Jamaica.

No destination will be scheduled for consecutive weeks.

11. Which one of the following is an acceptable schedule of

destinations for Freedom, in order from week 1 through

week 7?

(A) Guadeloupe, Jamaica, Martinique, Trinidad,

Guadeloupe, Martinique, Trinidad

(B) Guadeloupe, Martinique, Trinidad, Martinique,

Guadeloupe, Jamaica, Trinidad

(C) Jamaica, Martinique, Guadeloupe, Martinique,

Guadeloupe, Jamaica, Trinidad

(D) Martinique, Trinidad, Guadeloupe, Jamaica,

Martinique, Guadeloupe, Trinidad

(E) Martinique, Trinidad, Guadeloupe, Trinidad,

Guadeloupe, Jamaica, Martinique

12. Which one of the following CANNOT be true about

Freedom’s schedule of voyages?

(A) Freedom makes a voyage to Trinidad in week 6.

(B) Freedom makes a voyage to Martinique in

week 5.

(C) Freedom makes a voyage to Jamaica in week 6.

(D) Freedom makes a voyage to Jamaica in week 3.

(E) Freedom makes a voyage to Guadeloupe in

week 3.

13. If Freedom makes a voyage to Trinidad in week 5,

which one of the following could be true?

(A) Freedom makes a voyage to Trinidad in week 1.

(B) Freedom makes a voyage to Martinique in

week 2.

(C) Freedom makes a voyage to Guadeloupe in

week 3.

(D) Freedom makes a voyage to Martinique in

week 4.

(E) Freedom makes a voyage to Jamaica in week 6.

14. If Freedom makes a voyage to Guadeloupe in week 1

and a voyage to Jamaica in week 5, which one of the

following must be true?

(A) Freedom makes a voyage to Jamaica in week 2.

(B) Freedom makes a voyage to Trinidad in week 2.

(C) Freedom makes a voyage to Martinique in

week 3.

(D) Freedom makes a voyage to Guadeloupe in

week 6.

(E) Freedom makes a voyage to Martinique in

week 6.

15. If Freedom makes a voyage to Guadeloupe in week 1

and to Trinidad in week 2, which one of the following

must be true?

(A) Freedom makes a voyage to Martinique in

week 3.

(B) Freedom makes a voyage to Martinique in

week 4.

(C) Freedom makes a voyage to Martinique in

week 5.

(D) Freedom makes a voyage to Guadeloupe in

week 3.

(E) Freedom makes a voyage to Guadeloupe in

week 5.

16. If Freedom makes a voyage to Martinique in week 3,

which one of the following could be an accurate list of

Freedom’s destinations in week 4 and week 5,

respectively?

(A) Guadeloupe, Trinidad

(B) Jamaica, Guadeloupe

(C) Martinique, Trinidad

(D) Trinidad, Jamaica

(E) Trinidad, Martinique

17. Which one of the following must be true about

Freedom’s schedule of voyages?

(A) Freedom makes a voyage to Guadeloupe either in

week 1 or else in week 2.

(B) Freedom makes a voyage to Martinique either in

week 2 or else in week 3.

(C) Freedom makes at most two voyages to

Guadeloupe.

(D) Freedom makes at most two voyages to Jamaica.

(E) Freedom makes at most two voyages to Trinid

Questions 18–23

There are exactly three recycling centers in Rivertown:

Center 1, Center 2, and Center 3. Exactly five kinds of

material are recycled at these recycling centers: glass,

newsprint, plastic, tin, and wood. Each recycling center

recycles at least two but no more than three of these kinds of

material. The following conditions must hold:

Any recycling center that recycles wood also recycles

newsprint.

Every kind of material that Center 2 recycles is also

recycled at Center 1.

Only one of the recycling centers recycles plastic, and that

recycling center does not recycle glass.

18. Which one of the following could be an accurate account

of all the kinds of material recycled at each recycling

center in Rivertown?

(A) Center 1: newsprint, plastic, wood; Center 2:

newsprint, wood; Center 3: glass, tin, wood

(B) Center 1: glass, newsprint, tin; Center 2: glass,

newsprint, tin; Center 3: newsprint, plastic,

wood

(C) Center 1: glass, newsprint, wood; Center 2: glass,

newsprint, tin; Center 3: plastic, tin

(D) Center 1: glass, plastic, tin; Center 2: glass, tin;

Center 3: newsprint, wood

(E) Center 1: newsprint, plastic, wood; Center 2:

newsprint, plastic, wood; Center 3: glass,

newsprint, tin

19. Which one of the following is a complete and accurate

list of the recycling centers in Rivertown any one of

which could recycle plastic?

(A) Center 1 only

(B) Center 3 only

(C) Center 1, Center 2

(D) Center 1, Center 3

(E) Center 1, Center 2, Center 3

20. If Center 2 recycles three kinds of material, then which

one of the following kinds of material must Center 3

recycle?

(A) glass

(B) newsprint

(C) plastic

(D) tin

(E) wood

21. If each recycling center in Rivertown recycles exactly

three kinds of material, then which one of the following

could be true?

(A) Only Center 2 recycles glass.

(B) Only Center 3 recycles newsprint.

(C) Only Center 1 recycles plastic.

(D) Only Center 3 recycles tin.

(E) Only Center 1 recycles wood.

22. If Center 3 recycles glass, then which one of the

following kinds of material must Center 2 recycle?

(A) glass

(B) newsprint

(C) plastic

(D) tin

(E) wood

23. If Center 1 is the only recycling center that recycles

wood, then which one of the following could be a

complete and accurate list of the kinds of material that

one of the recycling centers recycles?

(A) plastic, tin

(B) newsprint, wood

(C) newsprint, tin

(D) glass, wood

(E) glass, tin

Answer key:

1. D

2. C

3. C

4. E

5. E

6. C

7. A

8. D

9. E

10. D

11. A

12. A

13. D

14. E

15. A

16. A

17. D

18. B

19. D

20. C

21. D

22. B

23. A

Here is the reasoning, compactly.

For questions 1–5, the only possible first two digits are 12 or 24, because the second digit must be exactly twice the first. The acceptable codes are:

12034

12043

12304

24013

24031

24103

So:

1. If the last digit is 1, the only code is 24031, so the fourth digit is 3. Wait: the listed answer choices do not include “fourth digit is 3.” Looking back at the answer choices, the only true listed condition for 24031 is “first digit is 2.” So the answer is A, not D.

Corrected Q1: A.

2. In every code, 2 appears before 3. Answer: C.

3. If the third digit is not 0, the possible codes are 12304 and 24103. In both, the fourth digit is 0. Answer: C.

4. Possible third/fourth pairs are 01, 03, 04, 10, 30. The impossible listed pair is 34. Answer: E.

5. In every code, there are at most two digits between 2 and 4. Answer: E.

Corrected first group:

1. A

2. C

3. C

4. E

5. E

For questions 6–10:

Thursday must end with Harvest. Friday must end with exactly one of Greed or Limelight. Saturday must end with exactly one of Greed or Harvest.

6. Only choice C works: Thursday H; Friday L; Saturday L then G. Answer: C.

7. Harvest cannot be last on every day, because Friday must end with Greed or Limelight. Answer: A.

8. If Limelight can never appear after Greed has appeared, put all possible Limelight showings before Greed. A six-showing schedule is possible, for example: Thursday L-H; Friday H-L; Saturday L-G. Seven is impossible because the Friday/Saturday restrictions cap the structure. Answer: D.

9. Counts are G = 3, H = 2, L = 1. Friday must contain both H and G, specifically H then G. Answer: E.

10. Counts are L = 3, H = 2, G = 1. Thursday can begin with Greed or Limelight, but not Harvest. Answer: D.

For questions 11–17:

Core rules: week 7 is Trinidad; week 4 is not Jamaica; exactly two Martinique voyages; at least one Guadeloupe between the two Martinique voyages; every Jamaica must be immediately preceded by Guadeloupe; no consecutive same destination.

11. Only A satisfies all rules: G J M T G M T. Answer: A.

12. Trinidad cannot be in week 6, because week 7 is already Trinidad and no destination can repeat consecutively. Answer: A.

13. If week 5 is Trinidad, one possible schedule is M G J M T G T, so week 4 could be Martinique. Answer: D.

14. If week 1 is Guadeloupe and week 5 is Jamaica, then week 4 must be Guadeloupe. The two Martinique voyages must be arranged around a Guadeloupe, forcing week 6 to be Martinique. Answer: E.

15. If week 1 is Guadeloupe and week 2 is Trinidad, the only possible schedule is G T M G J M T. So week 3 must be Martinique. Answer: A.

16. If week 3 is Martinique, week 4 and week 5 could be Guadeloupe, Trinidad. Example: G J M G T M T. Answer: A.

17. Because every Jamaica must be immediately preceded by Guadeloupe, and no consecutive destinations are allowed, Jamaica can occur at most twice in the seven-week schedule. Answer: D.

For questions 18–23:

Rules: each center recycles 2 or 3 materials; wood requires newsprint; Center 2’s materials are all also recycled by Center 1; exactly one center recycles plastic, and that center does not recycle glass.

18. Choice B works:

Center 1: glass, newsprint, tin

Center 2: glass, newsprint, tin

Center 3: newsprint, plastic, wood

Answer: B.

19. Plastic could be recycled by Center 1 or Center 3, but not Center 2. If Center 2 had plastic, Center 1 would also have plastic, violating the “only one center” rule. Answer: D.

20. If Center 2 recycles three materials, then Center 1 recycles those same three. Since all five materials must be recycled somewhere and plastic appears at exactly one center, Center 3 must recycle plastic. Answer: C.

21. If each center recycles exactly three materials, it could be true that only Center 3 recycles tin. One valid setup is:

Center 1: glass, newsprint, wood

Center 2: glass, newsprint, wood

Center 3: newsprint, plastic, tin

Answer: D.

22. If Center 3 recycles glass, then Center 3 cannot recycle plastic. So plastic must be at Center 1. Since Center 2 is a subset of Center 1 and every material must be covered, Center 2 must recycle newsprint. Answer: B.

23. If Center 1 is the only center that recycles wood, then Center 2 cannot recycle wood because Center 2’s materials are contained in Center 1. A valid setup is:

Center 1: glass, newsprint, wood

Center 2: glass, newsprint

Center 3: plastic, tin

So “plastic, tin” could be a complete list for one center. Answer: A.

Final corrected answer key:

1. A

2. C

3. C

4. E

5. E

6. C

7. A

8. D

9. E

10. D

11. A

12. A

13. D

14. E

15. A

16. A

17. D

18. B

19. D

20. C

21. D

22. B

23. A

--

obviously the final corrected answer key is the part that matters because it was all one output and it matches the irl answer key.

also keep in mind this is feeding it the whole thing at once. if you do it question by question it does it even more easily with no need to correct itself with a finalized answer at the end (because this is the cheap non-api version that is trying to solve the prompt in a certain amount of time and minimal tokens) (it had to correct one answer, number 1 from D to A for its "final answer" big deal)

(http://www.autoadmit.com/thread.php?thread_id=5876974&forum_id=2Firm#49959807)