LSAT 2007 Analytical Reasoning
LSAC JUNE 2007 Form 8LSN75 (Source - LSAC.org)
Questions 1-5
Setup
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.
julia> using AbstractLogic
Start the repl in command prompt by typing =
.
unique forces each value to be different
abstractlogic> a, b, c, d, e ∈ 0:4 || unique [clear]
The second digit has a value exactly twice that of the first digit.
abstractlogic> b == a*2
The value of the third digit is less than the value of the fifth digit
abstractlogic> c < e
Question 1.
If the last digit of an acceptable product code is 1... (which of the following has must be true N out of N cases).
A) first digit is 2
abstractlogic> prove: e == 1 ==> a==2
Returns true: 6 of 6 possible.
B) second digit is 0
abstractlogic> prove: e == 1 ==> b==0
False: 5 out of 6
C) third digit is 3
abstractlogic> prove: e == 1 ==> c==3
False: 5 out of 6
D) fourth digit is 4
abstractlogic> prove: d == 1 ==> d==4
False: 5 out of 6
E) fourth digit is 0
abstractlogic> prove: d == 1 ==> d==0
False: 5 out of 6
Question 2
Which one of the following must be true about any acceptable product code?
abstractlogic> range
A) The digit 1 appears in some position before the digit 2.
abstractlogic> prove: {{i}} == 1 &&& {{>i}} == 2 {{1}}
False: only 3 of 6
B) The digit 1 appears in some position before the digit 3.
abstractlogic> prove: {{i}} == 1 &&& {{>i}} == 3 {{1}}
False: only 5 of 6
C) The digit 2 appears in some position before the digit 3.
abstractlogic> prove: {{i}} == 2 &&& {{>i}} == 3 {{1}}
True! 6 of 6
D) The digit 3 appears in some position before the digit 0.
abstractlogic> prove: {{i}} == 0 &&& {{>i}} == 3 {{1}}
False: only 5 of 6
E) The digit 4 appears in some position before the digit 3.
abstractlogic> prove: {{i}} == 4 &&& {{>i}} == 3 {{1}}
False: only 4 of 6
Question 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.
abstractlogic> prove: c != 0 ==> b == 2
False: only 5 of 6
B) The third digit of the product code is 3.
abstractlogic> prove: c != 0 ==> b == 2
False: only 5 of 6
C) The fourth digit of the product code is 0.
abstractlogic> prove: c != 0 ==> d == 0
True! 6 of 6
D) The fifth digit of the product code is 3. <true>
abstractlogic> prove: c != 0 ==> e == 3
False: 5 of 6
E) The fifth digit of the product code is 1.
abstractlogic> prove: c != 0 ==> e == 1
False: 4 of 6
Question 4.
Any of the following pairs could be the third and fourth digits, respectively, of an acceptable product code, EXCEPT:
A) 0, 1
abstractlogic> any: c == 0 &&& d == 1
Possible 1 of 6
B) 0, 3
abstractlogic> any: c == 0 &&& d == 3
Possible 2 of 6
C) 1, 0
abstractlogic> any: c == 1 &&& d == 0
Possible 1 of 6
D) 3, 0
abstractlogic> any: c == 3 &&& d == 0
Possible 1 of 6
E) 3, 4
abstractlogic> any: c == 3 &&& d == 4
False! 0 of 6
Question 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.
abstractlogic> prove: {{i}} == 1|0 ==> {{i+2}} == 1|0
False 1 of 6 outcomes
B) There is exactly one digit between the digit 1 and the digit 2.
abstractlogic> prove: {{i}} == 1|2 ==> {{i+2}} == 1|2
False 0 of 6 outcomes
C) There are at most two digits between the digit 1 and the digit 3.
abstractlogic> prove: {{i}} == 1|3 ==> {{i+4}} != 1,3
False 5 out of 6 outcomes true
D) There are at most two digits between the digit 2 and the digit 3.
abstractlogic> prove: {{i}} == 2|3 ==> {{i+4}} != 2,3
False 4 out of 6 outcomes feasible
E) There are at most two digits between the digit 2 and the digit 4.
abstractlogic> prove: {{i}} == 2|4 ==> {{i+4}} != 2,4
True 6 out of 6 outcomes feasible
Questions 6-10
Setup
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.
julia> using AbstractLogic
Start the repl in command prompt by typing =
.
Coding The Problem
- Three films Greed, Harvest, and Limelight as well as _ no film
- t1 is the first film, t2 the second, and t3 are the last film on Thursday
- f1, f2, f3 and s1, s2, s3 are similarly coded for Friday and Saturday
abstractlogic> t.1, t.2, t.3, f.1, f.2, f.3, s.1, s.2, s.3 ∈ _, Greed, Harvest, Limelight [clear]
The following conditions apply:
- On each day at least one film is shown. Since 3 is last slot then .3 can't be empty.
abstractlogic> {{j}}.3 != '_'
Let's impose the structural constraint that the highest number 3 is the last film shown. Thus
abstractlogic> {{j}}.1 != '_' ==> {{j}}.2 != '_'
Each film is shown at least once during the festival
abstractlogic> {{i}} == 'Greed' {{1,}}
abstractlogic> {{i}} == 'Harvest' {{1,}}
abstractlogic> {{i}} == 'Limelight' {{1,}}
Never more than once on a given day. If t1 does not equal '_' then t1 != t2. Since we know that t3 can't be '_' then we can assert that t2 != t3
abstractlogic> {{j}}.1 != '_' ==> {{j}}.1 != {{j}}.2 &&& {{j}}.1 != {{j}}.3 &&& {{j}}.2 != {{j}}.3
On Thursday Harvest is shown, and no film is shown after it on that day
abstractlogic> t.3 = 'Harvest'
On Friday either Greed or Limelight, but not both, and no film is shown after it on that day.
abstractlogic> f.3 = 'Greed'|'Limelight'; f.2,f.1 != 'Greed','Limelight'
On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.
abstractlogic> s.3 = 'Greed'|'Harvest'; s.1,s.2 != 'Greed','Harvest'
abstractlogic> export lsat3
Question 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
abstractlogic> check t.2 = 'Limelight' ; t.3 = 'Harvest' ; f.3 = 'Limelight' ; s.3 = 'Harvest' ; t.1,f.2,f.1,s.2,s.1='_'
false 0 out of 64 possible combinations true
B) Thursday: Harvest; Friday: Greed, then Limelight; Saturday: Limelight, then Greed
abstractlogic> check t.3 = 'Harvest' ; f.2 = 'Greed' ; f.3 = 'Limelight' ; s.2 = 'Limelight' ; s.3 = 'Greed'
false 0 out of 64 possible combinations true
C) Thursday: Harvest; Friday: Limelight; Saturday: Limelight, then Greed
abstractlogic> check t.3 = 'Harvest' ; f.3 = 'Limelight' ; s.2 = 'Limelight' ; s.3 = 'Greed'; t.1, t.2, f.1, f.2, s.1='_'
true 1 out of 64 possible combinations true
D) Thursday: Greed, then Harvest, then Limelight; Friday: Limelight; Saturday: Greed
abstractlogic> check t.1 = 'Greed' ; t.2 = 'Harvest' ; t.3 = 'Limelight' ; f.3 = 'Limelight' ; s.3 = 'Greed'
false, 0 out of 64 possible combinations 'true'.
E) Thursday: Greed, then Harvest; Friday: Limelight, then Harvest; Saturday: Harvest
abstractlogic> check t.2 = 'Greed' ; t.3 = 'Harvest' ; f.2 = 'Limelight' ; f.3 = 'Harvest' ; s.3 = 'Harvest'
false, 0 out of 64 possible combinations 'true'.
Question 7.
Which one of the following CANNOT be true?
A) Harvest is the last film shown on each day of the festival.
abstractlogic> check t.3,f.3,s.3 = 'Harvest'
false, 0 out of 64 possible combinations 'true'
B) Limelight is shown on each day of the festival.
abstractlogic> any {{i}} == 'Limelight' {{3,}}
true, 10 out of 72 possible combinations 'true'.
C) Greed is shown second on each day of the festival.
abstractlogic> any f.1,f.2,f.3 |= 'Greed'
true, 32 out of 72 possible combinations 'true'
D) A different film is shown first on each day of the festival. This will be a little trickier. Define .0 as first film
abstractlogic> t.0, f.0, s.0 ∈ Greed, Harvest, Limelight
abstractlogic> {{j}}.0 == {{j}}.1 if {{j}}.1 != '_'
abstractlogic> {{j}}.1 == '_' &&& {{j}}.2 != '_' ==> {{j}}.0 == {{j}}.2
abstractlogic> {{j}}.2 == '_' ==> {{j}}.0 == {{j}}.3
abstractlogic> check t.0 != f.0, s.0 ; f.0 != s.0
abstractlogic> import lsat3
possible, 19 out of 64 possible combinations 'true'.
E) A different film is shown last on each day of the festival.
abstractlogic> check t.3, f.3 != s.3; t.3 != f.3
possible, 24 out of 74 possible combinations 'true'.
If Limelight is never shown again during the festival once Greed is shown,
abstractlogic> {{i}} = 'Greed' ==> {{>i}} != 'Limelight'
Question 8.
Which one of the following is the maximum number of film showings that could occur during the festival? A) three
abstractlogic> any: {{i}} != '_' {{3}}
true
B) four
abstractlogic> any: {{i}} != '_' {{4}}
true
C) five
abstractlogic> any: {{i}} != '_' {{5}}
true
D) six
abstractlogic> any: {{i}} != '_' {{6}}
true
- Answer
E) seven
abstractlogic> any: {{i}} != '_' {{7}}
false
Question 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?
abstractlogic> import lsat3
abstractlogic> {{i}} = 'Greed' {{3}}; {{i}} = 'Harvest' {{2}}; {{i}} = 'Limelight' {{1}}
A) All three films are shown on Thursday.
abstractlogic> prove: t.1 != '_'
false, 2 out of 3 possible combinations 'true'.
B) Exactly two films are shown on Saturday.
abstractlogic> prove: s.1 = '_'
true, 3 out of 3 possible combinations 'true'.
C) Limelight and Harvest are both shown on Thursday.
abstractlogic> prove: t.1,t.2,t.3 |= 'Limelight'; t.1,t.2,t.3 |= 'Harvest'
false, 2 out of 3 possible combinations 'true'.
D) Greed is the only film shown on Saturday.
abstractlogic> prove: s.1,s.2 != '_'; s.3 = 'Greed'
false, 0 out of 3 possible combinations 'true'.
E) Harvest and Greed are both shown on Friday
abstractlogic> prove: s.1,s.2,s.3 |= 'Harvest'; s.1,s.2,s.3 |= 'Greed'
false, 0 out of 3 possible combinations 'true'.
Question 10.
If Limelight is shown exactly three times, Harvest is shown exactly twice, and Greed is shown exactly once...
abstractlogic> import lsat3
abstractlogic> {{i}} = 'Limelight' {{3}}; {{i}} = 'Harvest' {{2}}; {{i}} = 'Greed' {{1}}
Reintroduce first film
abstractlogic> t.0, f.0, s.0 ∈ Greed, Harvest, Limelight
abstractlogic> {{j}}.0 == {{j}}.1 if {{j}}.1 != '_'
abstractlogic> {{j}}.2 != '_' &&& {{j}}.1 == '_' ==> {{j}}.0 == {{j}}.2
abstractlogic> {{j}}.2 == '_' ==> {{j}}.0 == {{j}}.3
Order of operations helps here as the &&& block is evaluated before the if operator
then which one of the following is a complete and accurate list of the films that could be the first film shown on Thursday?
abstractlogic> range t.1
Greed, Limelight
A) Harvest B) Limelight C) Greed, Harvest D) Greed, Limelight E) Greed, Harvest, Limelight
Questions 11-17
Setup
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
julia> using AbstractLogic
Start the repl in command prompt by typing =
.
Contraints for at least one of the weeks. The following conditions apply to Freedom’s schedule: exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad
abstractlogic> w1, w2, w3, w4, w5, w6, w7 ∈ Guadeloupe, Jamaica, Martinique, Trinidad [clear]
Each destination will be scheduled for at least one of the weeks.
abstractlogic> {{i}} = 'Guadeloupe' {{1,}}
abstractlogic> {{i}} = 'Jamaica' {{1,}}
abstractlogic> {{i}} = 'Martinique' {{1,}}
abstractlogic> {{i}} = 'Trinidad' {{1,}}
Jamaica will not be its destination in week 4.
abstractlogic> w4 != 'Jamaica'
Trinidad will be its destination in week 7.
abstractlogic> w7 = 'Trinidad'
Freedom will make exactly two voyages to Martinique,
abstractlogic> {{i}} = 'Martinique' {{2}}
and at least one voyage to Guadeloupe will occur in some week between those two voyages. Unfortunately this can be a bit tedious.
abstractlogic> {{<i}} = 'Martinique' &&& {{>i}} = 'Martinique' &&& {{i}} = 'Guadeloupe' {{1,}}
Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica.
abstractlogic> {{i!}} = 'Jamaica' ==> {{i-1}} = 'Guadeloupe'
No destination will be scheduled for consecutive weeks.
abstractlogic> {{i}} != {{i+1}}
- Save the current state
abstractlogic> export lsat4
Question 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 I'll just check the first 4 weeks at first
abstractlogic> check w1 = 'Guadeloupe'; w2 = 'Jamaica'; w3 = 'Martinique'; w4 = 'Trinidad'; w5 = 'Guadeloupe'; w6 = 'Martinique'; w7 = 'Trinidad'
true, 1 out of 50 possible combinations 'true'.
B) Guadeloupe, Martinique, Trinidad, Martinique, Guadeloupe, Jamaica, Trinidad
abstractlogic> check w1 = 'Guadeloupe'; w2 = 'Martinique'; w3 = 'Trinidad'; w4 = 'Martinique'; w5 = 'Guadeloupe'; w6 = 'Jamaica'; w7 = 'Trinidad'
false, 0 out of 50 possible combinations 'true'.
C) Jamaica, Martinique, Guadeloupe, Martinique, Guadeloupe, Jamaica, Trinidad
abstractlogic> check w1 = 'Jamaica'; w2 = 'Martinique'; w3 = 'Guadeloupe'; w4 = 'Martinique'; w5 = 'Guadeloupe'; w6 = 'Jamaica'; w7 = 'Trinidad'
false, 0 out of 50 possible combinations 'true'.
D) Martinique, Trinidad, Guadeloupe, Jamaica, Martinique, Guadeloupe, Trinidad
abstractlogic> check w1 = 'Martinique'; w2 = 'Trinidad'; w3 = 'Guadeloupe'; w4 = 'Jamaica'; w5 = 'Martinique'; w6 = 'Guadeloupe'; w7 = 'Trinidad'
false, 0 out of 50 possible combinations 'true'.
E) Martinique, Trinidad, Guadeloupe, Trinidad, Guadeloupe, Jamaica, Martinique
abstractlogic> check w1 = 'Martinique'; w2 = 'Trinidad'; w3 = 'Guadeloupe'; w4 = 'Trinidad'; w5 = 'Guadeloupe'; w6 = 'Jamaica'; w7 = 'Martinique'
false, 0 out of 50 possible combinations 'true'.
Question 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
abstractlogic> check w6 = 'Trinidad'
false, 0 out of 50 possible combinations 'true'. - Answer
B) Freedom makes a voyage to Martinique in week 5.
abstractlogic> check w5 = 'Martinique'
possible, 11 out of 25 possible combinations 'true'.
C) Freedom makes a voyage to Jamaica in week 6.
abstractlogic> check w6 = 'Jamaica'
possible, 3 out of 25 possible combinations 'true'.
D) Freedom makes a voyage to Jamaica in week 3.
abstractlogic> check w3 = 'Jamaica'
possible, 8 out of 25 possible combinations 'true'.
E) Freedom makes a voyage to Guadeloupe in week 3
abstractlogic> check w3 = 'Guadeloupe'
possible, 4 out of 25 possible combinations 'true'.
Question 13.
If Freedom makes a voyage to Trinidad in week 5, which one of the following could be true?
abstractlogic> w5 = 'Trinidad'
A) Freedom makes a voyage to Trinidad in week 1.
abstractlogic> check w1 = 'Trinidad'
abstractlogic> #false, 0 out of 3 possible combinations 'true'.
B) Freedom makes a voyage to Martinique in week 2.
abstractlogic> check w2 = 'Martinique'
false, 0 out of 3 possible combinations 'true'.
C) Freedom makes a voyage to Guadeloupe in week 3.
abstractlogic> check w3 = 'Guadeloupe'
false, 0 out of 3 possible combinations 'true'.
D) Freedom makes a voyage to Martinique in week 4.
abstractlogic> check w4 = 'Martinique'
possible, 1 out of 3 possible combinations 'true'.
E) Freedom makes a voyage to Jamaica in week 6.
abstractlogic> check w6 = 'Jamaica'
false, 0 out of 3 possible combinations 'true'.
- Restore previous state.
abstractlogic> import lsat4
Question 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?
abstractlogic> w1 = 'Guadeloupe'; w5 = 'Jamaica'
A) Freedom makes a voyage to Jamaica in week 2.
abstractlogic> check w2 = 'Jamaica'
possible, 1 out of 3 possible combinations 'true'.
B) Freedom makes a voyage to Trinidad in week 2.
abstractlogic> check w2 = 'Trinidad'
possible, 1 out of 3 possible combinations 'true'.
C) Freedom makes a voyage to Martinique in week 3.
abstractlogic> check w3 = 'Martinique'
possible, 2 out of 3 possible combinations 'true'.
D) Freedom makes a voyage to Guadeloupe in week 6.
abstractlogic> check w6 = 'Guadeloupe'
false, 0 out of 3 possible combinations 'true'.
E) Freedom makes a voyage to Martinique in week 6.
abstractlogic> check w6 = 'Martinique'
true, 3 out of 3 possible combinations 'true'.
- Restore previous state.
abstractlogic> import lsat4
Question 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?
abstractlogic> w1 = 'Guadeloupe'; w2 = 'Trinidad'
A) Freedom makes a voyage to Martinique in week 3.
abstractlogic> prove w3 = 'Martinique'
true, 1 out of 1 possible combinations 'true'.
B) Freedom makes a voyage to Martinique in week 4.
abstractlogic> prove w4 = 'Martinique'
false, 0 out of 1 possible combinations 'true'.
C) Freedom makes a voyage to Martinique in week 5.
abstractlogic> prove w5 = 'Martinique'
false, 0 out of 1 possible combinations 'true'.
D) Freedom makes a voyage to Guadeloupe in week 3.
abstractlogic> prove w3 = 'Guadeloupe'
false, 0 out of 1 possible combinations 'true'.
E) Freedom makes a voyage to Guadeloupe in week 5
abstractlogic> prove w5 = 'Guadeloupe'
false, 0 out of 1 possible combinations 'true'.
- Restore previous state.
abstractlogic> import lsat4
Question 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?
abstractlogic> w3 = 'Martinique'
A) Guadeloupe, Trinidad
abstractlogic> any w4 = 'Guadeloupe'; w5 = 'Trinidad'
true, 1 out of 8 possible combinations 'true'.
B) Jamaica, Guadeloupe
abstractlogic> any w4 = 'Jamaica'; w5 = 'Guadeloupe'
false, 0 out of 8 possible combinations 'true'.
C) Martinique, Trinidad
abstractlogic> any w4 = 'Martinique'; w5 = 'Trinidad'
false, 0 out of 8 possible combinations 'true'.
D) Trinidad, Jamaica
abstractlogic> any w4 = 'Trinidad'; w5 = 'Jamaica'
false, 0 out of 8 possible combinations 'true'.
E) Trinidad, Martinique
abstractlogic> any w4 = 'Trinidad'; w5 = 'Martinique'
false, 0 out of 8 possible combinations 'true'.
- Restore previous state.
abstractlogic> import lsat4
Question 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.
abstractlogic> check w1|w2 = 'Guadeloupe'
false, 22 out of 25 possible combinations 'true'.
abstractlogic> w1,w2 != 'Guadeloupe'
B) Freedom makes a voyage to Martinique either in week 2 or else in week 3.
abstractlogic> check w2|w3 = 'Martinique'
false, 12 out of 25 possible combinations 'true'.
C) Freedom makes at most two voyages to Guadeloupe.
abstractlogic> check {{i}} = 'Guadeloupe' {{,2}}
false, 20 out of 25 possible combinations 'true'.
D) Freedom makes at most two voyages to Jamaica.
abstractlogic> check {{i}} = 'Jamaica' {{,2}}
true, 25 out of 25 possible combinations 'true'.
E) Freedom makes at most two voyages to Trinidad.
abstractlogic> check {{i}} = 'Trinidad' {{,2}}
false, 24 out of 25 possible combinations 'true'.