You said:

This is from the LSAT logic games. Eight people are standing in the ticket-holders’

line at the theater, from first to eighth place. F, G,

H, and I are women, and J, K, L, and M are men.

The third person in line is either G or K.

H is standing somewhere behind G and

somewhere ahead of M.

I is standing in an odd-numbered position.

The sixth person in line is a woman. Question: If F is standing directly between J and L,

which one of the following pairs of people

could be standing next to each other?

(A) G and K

(B) H and I

(C) H and M

(D) I and L

(E) I and M

ChatGPT

To solve this logic puzzle, we'll use the given constraints to arrange the eight people in line and determine which pairs can stand next to each other.

Constraints:

Positions: There are 8 positions, numbered 1 through 8.

People: Women (F, G, H, I), Men (J, K, L, M).

Third Position: Occupied by either G or K.

Order of H, G, M: G stands ahead of H, and H stands ahead of M.

I's Position: I is in an odd-numbered position.

Sixth Position: Occupied by a woman.

F's Position: F stands directly between J and L (either J-F-L or L-F-J).

Solution Steps:

Assign Position 3:

Let's place G in position 3 (since the third person is either G or K).

Place I:

I must be in an odd-numbered position (1, 5, or 7).

Position 1 is available, so we place I there.

Assign the Sixth Position:

The sixth position must be occupied by a woman.

F could be in the sixth position as part of the J-F-L sequence.

Positioning J, F, L:

Let's arrange J-F-L in positions 5, 6, and 7 respectively.

This satisfies the condition that F is directly between J and L.

Place H and M:

H must stand somewhere behind G and ahead of M.

Place H in position 4 and M in position 8.

Place K:

The only remaining position is 2, so K occupies it.

Final Arrangement:

Position Person

1 I

2 K

3 G

4 H

5 J

6 F

7 L

8 M

Checking Possible Adjacent Pairs:

(A) G and K: Yes (Positions 2 and 3).

(B) H and I: No (Positions 4 and 1).

(C) H and M: No (Positions 4 and 8).

(D) I and L: No (Positions 1 and 7).

(E) I and M: No (Positions 1 and 8).

Conclusion:

Only G and K could be standing next to each other based on the given constraints.

Answer: A

You said:

6. Which one of the following statements must

be true?

(A) All four women are standing adjacently.

(B) All four men are standing adjacently.

(C) All four women are not standing

adjacently.

(D) All four men are not standing adjacently.

(E) None of these statements must be true.

ChatGPT

To determine which statement must be true based on the given constraints, we'll analyze each option by systematically considering all possible arrangements of the eight people in line.

Given Constraints:

Positions: There are 8 positions in line, numbered 1 through 8.

People:

Women: F, G, H, I

Men: J, K, L, M

Specific Constraints:

Constraint 1: The third person in line is either G or K.

Constraint 2: H is standing somewhere behind G and somewhere ahead of M.

Constraint 3: I is standing in an odd-numbered position (positions 1, 3, 5, or 7).

Constraint 4: The sixth position is occupied by a woman.

Option Analysis:

Option A: All four women are standing adjacently.

Possibility: It's possible to arrange all four women adjacently without violating any constraints.

Example Arrangement:

Position Person

1 I (W)

2 G (W)

3 H (W)

4 F (W)

5 K (M)

6 L (M)

7 J (M)

8 M (M)

Conclusion: Since it's possible but not necessary, Option A is not a must-be-true statement.

Option B: All four men are standing adjacently.

Constraint Conflict: Due to the given constraints, arranging all four men adjacently is impossible.

Reasoning:

The sixth position must be occupied by a woman.

The third position must be either G (woman) or K (man).

I must be in an odd-numbered position.

H must be behind G and ahead of M, affecting the positions of both men and women.

Conclusion: It's impossible to have all four men adjacent. However, since the statement is that they are adjacent, and we cannot arrange it, Option B is not true.

Option C: All four women are not standing adjacently.

Possibility: As shown in Option A, it's possible for all four women to stand adjacently.

Conclusion: Since it's possible for them to be adjacent, Option C is not a must-be-true statement.

Option D: All four men are not standing adjacently.

Constraint Analysis:

Given the constraints, the four men cannot stand adjacently.

Explanation:

Constraint on Position 6: Since the sixth position must be a woman, the men cannot occupy positions 5-8 together.

Constraint on Position 3: If K (man) is in position 3, G (woman) must be placed elsewhere, affecting the sequence of H and M.

Constraints on H, G, and M: Their required order makes it impossible to arrange all four men adjacent without violating these constraints.

Conclusion: The arrangement where all four men are adjacent is impossible. Therefore, Option D must be true.

Option E: None of these statements must be true.

Since we've established that Option D must be true, Option E is incorrect.

Answer:

D) All four men are not standing adjacently.

(http://www.autoadmit.com/thread.php?thread_id=5623934&forum_id=2#48276604)

Eight people — K, L, M, N, O, P, Q, and R — were

all born under one of three astrological signs:

Sagittarius, Taurus, or Virgo. At least two people

were born under each sign.

K, L, and R were all born under different

signs.

There is no more than one Virgo (and possi-

bly none) among L, M, and Q.

If M was born under Sagittarius, then N was

born under Taurus and O was born under

Virgo.

If M was born under Taurus, then O was

also born under Taurus and P was born

under Sagittarius. Question: If exactly three people, including Q and R,

were born under Virgo, which one of the

following is a complete and accurate list of

the people who could have been born

under Sagittarius?

(A) K, L, M, O

(B) K, L, M, P

(C) K, L, M, N, P

(D) K, L, M, O, P

(E) K, L, M, N, O, P

ChatGPT

To determine which people could have been born under Sagittarius, given the constraints, let's analyze the information step by step.

Given Information:

Astrological Signs:

Three signs: Sagittarius (S), Taurus (T), Virgo (V)

At least two people were born under each sign.

People:

Eight individuals: K, L, M, N, O, P, Q, R

Constraints:

Constraint 1: K, L, and R were all born under different signs.

Constraint 2: There is no more than one Virgo among L, M, and Q.

Constraint 3: If M was born under Sagittarius, then N was born under Taurus and O was born under Virgo.

Constraint 4: If M was born under Taurus, then O was also born under Taurus and P was born under Sagittarius.

Question Condition:

Exactly three people, including Q and R, were born under Virgo.

Step-by-Step Solution:

Determine the Number of People in Each Sign:

Since there are exactly three Virgos (V), including Q and R, the third Virgo must be one of the remaining people.

The remaining five people (K, L, M, N, O, P) must be divided between Sagittarius (S) and Taurus (T).

Since each sign must have at least two people, and we have five people left, one sign will have three and the other will have two.

Identify the Possible Third Virgo:

The third Virgo cannot be L or M (Constraint 2).

It also cannot be K (Constraint 1, as K and R would be in the same sign).

Therefore, the third Virgo must be either N or O.

Case Analysis:

Case 1: O is the third Virgo.

Assign Virgos: Q, R, O

Constraint 3 applies if M is in Sagittarius:

M in S

N in T

O in V (satisfied)

Assign K and L:

K and L must be in different signs (Constraint 1) and cannot be in V.

Assign K to S and L to T (or vice versa).

Assign Remaining People:

P can be in S.

People in Sagittarius: K, M, P

Case 2: N is the third Virgo.

Assign Virgos: Q, R, N

Constraint 4 applies if M is in Taurus:

M in T

O in T

P in S

Assign K and L:

Assign K to T and L to S (or vice versa).

People in Sagittarius: L, P

Determine Who Could Be in Sagittarius:

From both cases, the people who could have been born under Sagittarius are K, L, M, and P.

O cannot be in Sagittarius because when M is in S, O must be in V; when M is in T, O must be in T (Constraints 3 and 4).

N cannot be in Sagittarius because in all valid scenarios, N is either in T or V.

Answer:

B) K, L, M, P

You said:

If exactly four people were born under

Sagittarius, which one of the following

people CANNOT have been born under

Taurus?

(A) L

(B) M

(C) O

(D) P

(E) Q

ChatGPT

To solve this problem, we'll need to analyze the given constraints carefully and determine which person cannot be born under Taurus when exactly four people are born under Sagittarius.

Given Information:

People: K, L, M, N, O, P, Q, R

Astrological Signs: Sagittarius (S), Taurus (T), Virgo (V)

At least two people were born under each sign.

Constraints:

K, L, and R were all born under different signs.

There is no more than one Virgo among L, M, and Q.

If M was born under Sagittarius, then N was born under Taurus and O was born under Virgo.

If M was born under Taurus, then O was also born under Taurus and P was born under Sagittarius.

Question Condition:

Exactly four people were born under Sagittarius.

Objective:

Determine which person among L, M, O, P, or Q cannot have been born under Taurus.

Step-by-Step Solution:

Determine the Number of People in Each Sign:

Since there are exactly four Sagittarians (S) and eight people total, the remaining four people must be divided between Taurus (T) and Virgo (V).

Each sign must have at least two people, so Taurus and Virgo must each have exactly two people.

Assign K, L, and R to Different Signs:

Since K, L, and R are all born under different signs and there are three signs, they cover all the signs.

We'll consider the scenario where K is Sagittarius (S), L is Taurus (T), and R is Virgo (V).

Apply Constraint 2 (No More Than One Virgo Among L, M, Q):

Since L is assigned to Taurus, among M and Q, at most one can be a Virgo.

We have two Virgos in total (R and one other person).

Case Analysis for M:

Case 1: M is Virgo (V)

Virgos: R, M

Taurus: L, Q

Sagittarius: K, N, O, P

Case 2: M is Sagittarius (S)

Applying Constraint 3:

M is Sagittarius.

N is Taurus.

O is Virgo.

Virgos: R, O

Taurus: L, N

Sagittarius: K, M, P, Q

Case 3: M is Taurus (T)

Applying Constraint 4:

M is Taurus.

O is Taurus.

P is Sagittarius.

Taurus: L, M, O (This exceeds the allowed two people in Taurus)

Therefore, M cannot be Taurus in this scenario.

Determine Who Can Be Taurus:

M cannot be Taurus under these conditions.

O can be Taurus in some scenarios (e.g., when Q is Sagittarius).

P can be Taurus in some scenarios (e.g., swapping assignments with O).

Q can be Taurus or Sagittarius, depending on the case.

L is already assigned to Taurus.

Conclusion:

M is the person who cannot have been born under Taurus when exactly four people were born under Sagittarius.

Answer:

B) M

(http://www.autoadmit.com/thread.php?thread_id=5623934&forum_id=2#48276684)

overall pretty decent performance, especially considering GPT-4 would have done awful with these.

(http://www.autoadmit.com/thread.php?thread_id=5623934&forum_id=2#48276832)