LSAT: Analytical and Logical Reasoning Exam
Prep with Detailed Rationales
Course Code: LSAT
Course Name: Law School Admission Test
Topic: Analytical Reasoning, Logical Reasoning, and Reading Comprehension
Academic Year: 2026/2027
Questions 1–5: Analytical Reasoning (Product Codes)
Situation:
An employee generates five-digit product codes using the digits 0, 1, 2, 3, and 4
exactly once per code.
• Rule 1: The digits used are 0, 1, 2, 3, 4.
• Rule 2: Each digit occurs exactly once.
• Rule 3: The second digit (P₂) is exactly twice the first digit (P₁).
Mathematically, P₂ = 2 × P₁. Given our digits, the valid ordered pairs for (P₁,
P₂) are either (1, 2) or (2, 4).
• Rule 4: The value of the third digit (P₃) is less than the fifth digit (P₅).
Mathematically, P₃ < P₅.
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
CORRECT ANSWER: D
RATIONALE: We are given that the fifth digit P₅ = 1. According to Rule 4, P₃
< P₅, which means P₃ < 1. The only available digit less than 1 is 0, so P₃ = 0. Now
we have assigned 0 and 1, leaving the digits 2, 3, and 4. We must determine the
pair (P₁, P₂) using Rule 3 (P₂ = 2 × P₁). The pair cannot be (1, 2) because 1 is
,already assigned to P₅. Therefore, the pair (P₁, P₂) must be (2, 4), meaning P₁ = 2
and P₂ = 4. The remaining unassigned digit is 3, which must occupy the only
vacant position, P₄. Thus, the complete code is 2-4-0-3-1. Reviewing the choices,
choice D states that the fourth digit is 4, which is false; however, let's re-verify the
standard question layout. Wait, let's re-evaluate the correct answer sequence
provided in the source text ✅ACCEE for Questions 1-5. The sequence
indicates Question 1 is A. Let's re-verify: if P₁ = 2, then option A states "first digit
is 2". This perfectly matches our deduction! Let us correct the bolding to align with
first digit is 2.
(Correction applied to match deduction and answer key: A)
(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
CORRECT ANSWER: A
RATIONALE: If the fifth digit is 1, then the constraint P₃ < P₅ forces P₃ = 0
because 0 is the only available digit less than 1. With 1 and 0 utilized, the first two
positions (P₁, P₂) cannot use the (1, 2) option for the doubling rule. Thus, they must
use the (2, 4) option, dictating that P₁ = 2 and P₂ = 4. This leaves the digit 3 to fill
the fourth slot, creating the unique sequence 2-4-0-3-1. Therefore, it must be true
that the first digit is 2. Distractors B, C, D, and E are incorrect because they
contradict this absolute logical deduction.
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 0.
CORRECT ANSWER: A
RATIONALE: Let us evaluate the total possible configurations for the product
codes. There are two main branches based on the doubling rule:
, • Branch 1: (P₁, P₂) = (1, 2). The remaining digits are 0, 3, 4. Since P₃ < P₅, the
valid pairings for (P₃, P₅) can be (0, 3), (0, 4), or (3, 4). In all these
variations, the digit 1 is at position 1 and the digit 2 is at position 2, meaning
1 is always before 2.
• Branch 2: (P₁, P₂) = (2, 4). The remaining digits are 0, 1, 3. Since P₃ < P₅, the
valid pairings for (P₃, P₅) are (0, 1), (0, 3), or (1, 3). If (P₃, P₅) = (0, 1), then 1
is at the end, meaning 2 (at P₁) comes before 1. But wait, let's check the
answer key sequence ACCEE. Question 2 is C. Let's check why C ("The
digit 2 appears in some position before the digit 3") must be true. In Branch
1, 2 is at position 2, and 3 must be at position 3, 4, or 5; thus 2 is always
before 3. In Branch 2, 2 is at position 1, so it is automatically before 3
regardless of where 3 is placed. Thus, the digit 2 must always appear before
3.
(Correction applied to match deduction and answer key: C)
(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 0.
CORRECT ANSWER: C
RATIONALE: As established by Rule 3, the first two digits must be either (1,
2) or (2, 4). In the first scenario where P₁=1 and P₂=2, the digit 2 occupies the
second slot, meaning the digit 3 must fall into the third, fourth, or fifth slot. Thus, 2
precedes 3. In the second scenario where P₁=2 and P₂=4, the digit 2 occupies the
very first slot, meaning it automatically precedes every other remaining digit,
including 3. Because 2 precedes 3 in every single valid arrangement, option C must
be true.
3. If the third digit of an acceptable product code is 3, which one of the following
must be true?
(A) The first digit is 1.
(B) The second digit is 2.
(C) The fourth digit is 0.
Prep with Detailed Rationales
Course Code: LSAT
Course Name: Law School Admission Test
Topic: Analytical Reasoning, Logical Reasoning, and Reading Comprehension
Academic Year: 2026/2027
Questions 1–5: Analytical Reasoning (Product Codes)
Situation:
An employee generates five-digit product codes using the digits 0, 1, 2, 3, and 4
exactly once per code.
• Rule 1: The digits used are 0, 1, 2, 3, 4.
• Rule 2: Each digit occurs exactly once.
• Rule 3: The second digit (P₂) is exactly twice the first digit (P₁).
Mathematically, P₂ = 2 × P₁. Given our digits, the valid ordered pairs for (P₁,
P₂) are either (1, 2) or (2, 4).
• Rule 4: The value of the third digit (P₃) is less than the fifth digit (P₅).
Mathematically, P₃ < P₅.
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
CORRECT ANSWER: D
RATIONALE: We are given that the fifth digit P₅ = 1. According to Rule 4, P₃
< P₅, which means P₃ < 1. The only available digit less than 1 is 0, so P₃ = 0. Now
we have assigned 0 and 1, leaving the digits 2, 3, and 4. We must determine the
pair (P₁, P₂) using Rule 3 (P₂ = 2 × P₁). The pair cannot be (1, 2) because 1 is
,already assigned to P₅. Therefore, the pair (P₁, P₂) must be (2, 4), meaning P₁ = 2
and P₂ = 4. The remaining unassigned digit is 3, which must occupy the only
vacant position, P₄. Thus, the complete code is 2-4-0-3-1. Reviewing the choices,
choice D states that the fourth digit is 4, which is false; however, let's re-verify the
standard question layout. Wait, let's re-evaluate the correct answer sequence
provided in the source text ✅ACCEE for Questions 1-5. The sequence
indicates Question 1 is A. Let's re-verify: if P₁ = 2, then option A states "first digit
is 2". This perfectly matches our deduction! Let us correct the bolding to align with
first digit is 2.
(Correction applied to match deduction and answer key: A)
(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
CORRECT ANSWER: A
RATIONALE: If the fifth digit is 1, then the constraint P₃ < P₅ forces P₃ = 0
because 0 is the only available digit less than 1. With 1 and 0 utilized, the first two
positions (P₁, P₂) cannot use the (1, 2) option for the doubling rule. Thus, they must
use the (2, 4) option, dictating that P₁ = 2 and P₂ = 4. This leaves the digit 3 to fill
the fourth slot, creating the unique sequence 2-4-0-3-1. Therefore, it must be true
that the first digit is 2. Distractors B, C, D, and E are incorrect because they
contradict this absolute logical deduction.
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 0.
CORRECT ANSWER: A
RATIONALE: Let us evaluate the total possible configurations for the product
codes. There are two main branches based on the doubling rule:
, • Branch 1: (P₁, P₂) = (1, 2). The remaining digits are 0, 3, 4. Since P₃ < P₅, the
valid pairings for (P₃, P₅) can be (0, 3), (0, 4), or (3, 4). In all these
variations, the digit 1 is at position 1 and the digit 2 is at position 2, meaning
1 is always before 2.
• Branch 2: (P₁, P₂) = (2, 4). The remaining digits are 0, 1, 3. Since P₃ < P₅, the
valid pairings for (P₃, P₅) are (0, 1), (0, 3), or (1, 3). If (P₃, P₅) = (0, 1), then 1
is at the end, meaning 2 (at P₁) comes before 1. But wait, let's check the
answer key sequence ACCEE. Question 2 is C. Let's check why C ("The
digit 2 appears in some position before the digit 3") must be true. In Branch
1, 2 is at position 2, and 3 must be at position 3, 4, or 5; thus 2 is always
before 3. In Branch 2, 2 is at position 1, so it is automatically before 3
regardless of where 3 is placed. Thus, the digit 2 must always appear before
3.
(Correction applied to match deduction and answer key: C)
(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 0.
CORRECT ANSWER: C
RATIONALE: As established by Rule 3, the first two digits must be either (1,
2) or (2, 4). In the first scenario where P₁=1 and P₂=2, the digit 2 occupies the
second slot, meaning the digit 3 must fall into the third, fourth, or fifth slot. Thus, 2
precedes 3. In the second scenario where P₁=2 and P₂=4, the digit 2 occupies the
very first slot, meaning it automatically precedes every other remaining digit,
including 3. Because 2 precedes 3 in every single valid arrangement, option C must
be true.
3. If the third digit of an acceptable product code is 3, which one of the following
must be true?
(A) The first digit is 1.
(B) The second digit is 2.
(C) The fourth digit is 0.
