Comprehension
Seven science students— John, Kate, Luz, Mark, Nelson, Olga, and Pat— are to be divided into three groups. One group will consist of three students, and the other groups will consist of two students each. The following conditions apply to the assignment of students to groups:
John cannot be assigned to the group to which Luz is assigned
Nelson must be assigned to the group to which Pat is assigned.
Olga must be assigned to the group consisting of three students.
Question: 1
Which of the following is an acceptable assignment of students to groups?
Which of the following is an acceptable assignment of students to groups?
Show Hint
When checking options in a logic game, start with the most concrete rules. Here, "Olga must be in the group of three" and "Nelson must be with Pat" are very specific and can help you eliminate choices quickly.
Updated On: Oct 4, 2025
- John, Kate, and Mark; Luz, Nelson, and Olga; Pat
- John, Mark, and Olga; Kate and Luz; Nelson and Pat
- Kate, Luz, and Olga; John and Nelson; Mark and Pat
- Mark, Nelson, and Pat; John and Kate; Luz and Olga
- Nelson, Olga, and Pat; John and Luz; Kate and Mark
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
This question requires us to check each of the proposed group assignments against the given rules. The correct answer will be the one that satisfies all conditions.
Step 2: Detailed Explanation:
Let's list the rules and group structure for easy reference:
Structure: One group of 3, two groups of 2. Total 7 students.
Rule 1: John and Luz are in different groups (J \(\neq\) L).
Rule 2: Nelson and Pat are in the same group ({N, P}).
Rule 3: Olga is in the group of three ({O, ?, ?}).
Now, let's test each option:
(A) \{J, K, M\, \{L, N, O\}, \{P\}} - Structure: This has groups of 3, 3, and 1. This violates the required structure of 3, 2, 2. VIOLATION.
(B) \{J, M, O\, \{K, L\}, \{N, P\}} - Structure: Groups of 3, 2, 2. OK. - Rule 3 (Olga): O is in the group of three. OK. - Rule 2 (Nelson/Pat): N and P are together in a group. OK. - Rule 1 (John/Luz): J is in the first group, L is in the second group. They are in different groups. OK. - All rules are satisfied. This is an acceptable assignment.
(C) \{K, L, O\, \{J, N\}, \{M, P\}} - Rule 2 (Nelson/Pat): N and P are in different groups. VIOLATION.
(D) \{M, N, P\, \{J, K\}, \{L, O\}} - Rule 3 (Olga): O is in a group of two. The rule says O must be in the group of three. VIOLATION.
(E) \{N, O, P\, \{J, L\}, \{K, M\}} - Rule 1 (John/Luz): J and L are in the same group. VIOLATION.
Step 3: Final Answer:
Option (B) is the only assignment that satisfies the group structure and all three given conditions.
This question requires us to check each of the proposed group assignments against the given rules. The correct answer will be the one that satisfies all conditions.
Step 2: Detailed Explanation:
Let's list the rules and group structure for easy reference:
Structure: One group of 3, two groups of 2. Total 7 students.
Rule 1: John and Luz are in different groups (J \(\neq\) L).
Rule 2: Nelson and Pat are in the same group ({N, P}).
Rule 3: Olga is in the group of three ({O, ?, ?}).
Now, let's test each option:
(A) \{J, K, M\, \{L, N, O\}, \{P\}} - Structure: This has groups of 3, 3, and 1. This violates the required structure of 3, 2, 2. VIOLATION.
(B) \{J, M, O\, \{K, L\}, \{N, P\}} - Structure: Groups of 3, 2, 2. OK. - Rule 3 (Olga): O is in the group of three. OK. - Rule 2 (Nelson/Pat): N and P are together in a group. OK. - Rule 1 (John/Luz): J is in the first group, L is in the second group. They are in different groups. OK. - All rules are satisfied. This is an acceptable assignment.
(C) \{K, L, O\, \{J, N\}, \{M, P\}} - Rule 2 (Nelson/Pat): N and P are in different groups. VIOLATION.
(D) \{M, N, P\, \{J, K\}, \{L, O\}} - Rule 3 (Olga): O is in a group of two. The rule says O must be in the group of three. VIOLATION.
(E) \{N, O, P\, \{J, L\}, \{K, M\}} - Rule 1 (John/Luz): J and L are in the same group. VIOLATION.
Step 3: Final Answer:
Option (B) is the only assignment that satisfies the group structure and all three given conditions.
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Question: 2
If one of the groups of two consists of Luz and Mark, which of the following must be true?
If one of the groups of two consists of Luz and Mark, which of the following must be true?
Show Hint
In grouping games, once you place a block of students (like Nelson and Pat), look for the remaining "floaters" and see where they must go. Often, placing the big blocks first leaves only one possible place for the remaining individuals.
Updated On: Oct 4, 2025
- John is assigned to the group to which Kate is assigned.
- John is assigned to the group to which Nelson is assigned.
- Kate is assigned to the group to which Pat is assigned.
- Kate is assigned to a group consisting of two students.
- Nelson is assigned to the group consisting of three students.
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
This is a "must be true" question with a new condition. We need to follow the chain of deductions that results from this new information.
Step 2: Detailed Explanation:
1. New Condition: One of the 2-person groups is \{Luz, Mark\}.
2. Apply Rule 3 (Olga): Olga (O) must be in the 3-person group.
- Group of 3: \{O, ?, ?\}
3. Apply Rule 2 (Nelson/Pat): Nelson (N) and Pat (P) must be together. They can't be in the 3-person group with Olga because that would leave only one spot. So, they must form the other 2-person group.
- Group of 2: \{N, P\}
4. Identify the remaining students: The students placed so far are L, M, O, N, P. The remaining students are John (J) and Kate (K).
5. Place the remaining students: The only available spots are the two remaining places in the 3-person group with Olga.
- Therefore, John and Kate must be in the group with Olga.
- Group of 3: \{O, J, K\}
6. Check for consistency:
- Final groups: \{O, J, K\}, \{L, M\}, \{N, P\}.
- Structure (3, 2, 2): OK.
- Rule 1 (J \(\neq\) L): J is in the first group, L is in the second. OK.
- Rule 2 ({N, P}): OK.
- Rule 3 (O in group of 3): OK.
- The arrangement is valid.
7. Evaluate the options: Based on our deduction that the groups must be \{O, J, K\}, \{L, M\}, \{N, P\}, let's see which statement must be true.
- (A) John is assigned to the group to which Kate is assigned. Yes, they are both in the group with Olga. This must be true.
- (B) John is assigned to the group to which Nelson is assigned. False.
- (C) Kate is assigned to the group to which Pat is assigned. False.
- (D) Kate is assigned to a group of two students. False, she is in the group of three.
- (E) Nelson is assigned to the group of three students. False, he is in a group of two.
Step 3: Final Answer:
The initial condition forces Nelson and Pat into one 2-person group, leaving John and Kate to fill the remaining spots in the 3-person group with Olga. Therefore, John and Kate must be in the same group.
This is a "must be true" question with a new condition. We need to follow the chain of deductions that results from this new information.
Step 2: Detailed Explanation:
1. New Condition: One of the 2-person groups is \{Luz, Mark\}.
2. Apply Rule 3 (Olga): Olga (O) must be in the 3-person group.
- Group of 3: \{O, ?, ?\}
3. Apply Rule 2 (Nelson/Pat): Nelson (N) and Pat (P) must be together. They can't be in the 3-person group with Olga because that would leave only one spot. So, they must form the other 2-person group.
- Group of 2: \{N, P\}
4. Identify the remaining students: The students placed so far are L, M, O, N, P. The remaining students are John (J) and Kate (K).
5. Place the remaining students: The only available spots are the two remaining places in the 3-person group with Olga.
- Therefore, John and Kate must be in the group with Olga.
- Group of 3: \{O, J, K\}
6. Check for consistency:
- Final groups: \{O, J, K\}, \{L, M\}, \{N, P\}.
- Structure (3, 2, 2): OK.
- Rule 1 (J \(\neq\) L): J is in the first group, L is in the second. OK.
- Rule 2 ({N, P}): OK.
- Rule 3 (O in group of 3): OK.
- The arrangement is valid.
7. Evaluate the options: Based on our deduction that the groups must be \{O, J, K\}, \{L, M\}, \{N, P\}, let's see which statement must be true.
- (A) John is assigned to the group to which Kate is assigned. Yes, they are both in the group with Olga. This must be true.
- (B) John is assigned to the group to which Nelson is assigned. False.
- (C) Kate is assigned to the group to which Pat is assigned. False.
- (D) Kate is assigned to a group of two students. False, she is in the group of three.
- (E) Nelson is assigned to the group of three students. False, he is in a group of two.
Step 3: Final Answer:
The initial condition forces Nelson and Pat into one 2-person group, leaving John and Kate to fill the remaining spots in the 3-person group with Olga. Therefore, John and Kate must be in the same group.
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Question: 3
If Nelson is assigned to the group to which Olga is assigned, which of the following can be true?
If Nelson is assigned to the group to which Olga is assigned, which of the following can be true?
Show Hint
For "can be true" questions, your goal is to construct just one valid scenario that makes the statement in the option true. As soon as you find one such scenario, you have your answer.
Updated On: Oct 4, 2025
- Kate is assigned to the group to which John is assigned.
- Kate is assigned to the group to which Mark is assigned.
- Luz is assigned to the group to which Olga is assigned.
- John is assigned to the group consisting of three students.
- Pat is assigned to a group consisting of two students.
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
This is a "can be true" (possibility) question with a new condition. We need to find an option that could be true in at least one valid scenario that fits the new condition.
Step 2: Detailed Explanation:
1. New Condition: Nelson (N) is in the same group as Olga (O). 2. Apply Rule 3 (Olga): O must be in the 3-person group. Since N is with O, N is also in the 3-person group. 3. Apply Rule 2 (Nelson/Pat): N must be with Pat (P). Since N is in the 3-person group, P must also be in the 3-person group. 4. Deduce the 3-person group: We now know the 3-person group is composed of Olga, Nelson, and Pat. - Group of 3: \{O, N, P\}. 5. Identify remaining students and groups: The remaining students are John (J), Kate (K), Luz (L), and Mark (M). They must form the two 2-person groups. 6. Apply Rule 1 (J \(\neq\) L): John and Luz cannot be in the same group. Since the remaining students must be split into two pairs, and J and L cannot be a pair, they must be in different groups. 7. Construct the 2-person groups: - Let's place J in one group and L in the other. - Group 2a: \{J, ?\} - Group 2b: \{L, ?\} - The remaining students are K and M. They must fill the remaining spots. There are two possibilities for the pairs: - Possibility 1: \{J, K\} and \{L, M\} - Possibility 2: \{J, M\} and \{L, K\} 8. Evaluate the options based on these possibilities: - (A) Kate is assigned to the group to which John is assigned. This is true in Possibility 1 (\{J, K\}). Since we have found a valid scenario where this is true, this "can be true". - (B) Kate is assigned to the group to which Mark is assigned. This happens in none of our valid scenarios. In Possibility 1, K is with J and M is with L. In Possibility 2, K is with L and M is with J. They are never together. - (C) Luz is assigned to the group to which Olga is assigned. False. Olga is in the group of 3, and Luz is in a group of 2. - (D) John is assigned to the group of three students. False. John must be in a group of two. - (E) Pat is assigned to a group of two students. False. We deduced that Pat must be in the group of three. Step 3: Final Answer:
The initial condition forces the 3-person group to be \{Olga, Nelson, Pat\}. The remaining four students must be split into two pairs, with the constraint that John and Luz are in separate pairs. A possible valid arrangement is the groups \{J, K\} and \{L, M\}. In this scenario, Kate is in the same group as John.
This is a "can be true" (possibility) question with a new condition. We need to find an option that could be true in at least one valid scenario that fits the new condition.
Step 2: Detailed Explanation:
1. New Condition: Nelson (N) is in the same group as Olga (O). 2. Apply Rule 3 (Olga): O must be in the 3-person group. Since N is with O, N is also in the 3-person group. 3. Apply Rule 2 (Nelson/Pat): N must be with Pat (P). Since N is in the 3-person group, P must also be in the 3-person group. 4. Deduce the 3-person group: We now know the 3-person group is composed of Olga, Nelson, and Pat. - Group of 3: \{O, N, P\}. 5. Identify remaining students and groups: The remaining students are John (J), Kate (K), Luz (L), and Mark (M). They must form the two 2-person groups. 6. Apply Rule 1 (J \(\neq\) L): John and Luz cannot be in the same group. Since the remaining students must be split into two pairs, and J and L cannot be a pair, they must be in different groups. 7. Construct the 2-person groups: - Let's place J in one group and L in the other. - Group 2a: \{J, ?\} - Group 2b: \{L, ?\} - The remaining students are K and M. They must fill the remaining spots. There are two possibilities for the pairs: - Possibility 1: \{J, K\} and \{L, M\} - Possibility 2: \{J, M\} and \{L, K\} 8. Evaluate the options based on these possibilities: - (A) Kate is assigned to the group to which John is assigned. This is true in Possibility 1 (\{J, K\}). Since we have found a valid scenario where this is true, this "can be true". - (B) Kate is assigned to the group to which Mark is assigned. This happens in none of our valid scenarios. In Possibility 1, K is with J and M is with L. In Possibility 2, K is with L and M is with J. They are never together. - (C) Luz is assigned to the group to which Olga is assigned. False. Olga is in the group of 3, and Luz is in a group of 2. - (D) John is assigned to the group of three students. False. John must be in a group of two. - (E) Pat is assigned to a group of two students. False. We deduced that Pat must be in the group of three. Step 3: Final Answer:
The initial condition forces the 3-person group to be \{Olga, Nelson, Pat\}. The remaining four students must be split into two pairs, with the constraint that John and Luz are in separate pairs. A possible valid arrangement is the groups \{J, K\} and \{L, M\}. In this scenario, Kate is in the same group as John.
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Question: 4
If Mark is assigned to a group to which neither John nor Pat is assigned, which of the following must be true?
If Mark is assigned to a group to which neither John nor Pat is assigned, which of the following must be true?
Show Hint
For complex "must be true" questions, the key is often to systematically enumerate all possible valid scenarios. The statement that is true in every single one of those scenarios is the correct answer. If a statement is true in one scenario but false in another, it only "can be true."
Updated On: Oct 4, 2025
- John is assigned to the group to which Kate is assigned.
- John is assigned to the group to which Nelson is assigned.
- Kate is assigned to the group to which Luz is assigned.
- Kate is assigned to the group to which Nelson is assigned.
- Kate is assigned to the group to which Olga is assigned.
Show Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
This is a "must be true" question where we deduce group assignments based on given restrictions. Step 2: Detailed Explanation:
1. Initial deductions:
- Nelson (N) must be with Pat (P), forming a 2-person group.
- Olga (O) must be in the 3-person group.
- Mark (M) cannot be with John (J) or P/N. 2. Determine possible groupings:
- Remaining students: John (J), Kate (K), Luz (L), Mark (M).
- The 3-person group must include O and two others.
- The remaining two form the other 2-person group. - Considering all rules, there are two valid scenarios: 1. G1={O,J,K}, G2={N,P}, G3={L,M} 2. G1={O,L,M}, G2={N,P}, G3={J,K} 3. Check the options:
- (A) John with Kate: true in both scenarios. ✅ - (B) John with Nelson: false - (C) Kate with Luz: false - (D) Kate with Nelson: false - (E) Kate with Olga: true in one scenario only Step 3: Final Answer:
The only statement that is always true is that John is in the same group as Kate.
Answer: (A). (Note: The provided key (E) is incorrect.)
This is a "must be true" question where we deduce group assignments based on given restrictions. Step 2: Detailed Explanation:
1. Initial deductions:
- Nelson (N) must be with Pat (P), forming a 2-person group.
- Olga (O) must be in the 3-person group.
- Mark (M) cannot be with John (J) or P/N. 2. Determine possible groupings:
- Remaining students: John (J), Kate (K), Luz (L), Mark (M).
- The 3-person group must include O and two others.
- The remaining two form the other 2-person group. - Considering all rules, there are two valid scenarios: 1. G1={O,J,K}, G2={N,P}, G3={L,M} 2. G1={O,L,M}, G2={N,P}, G3={J,K} 3. Check the options:
- (A) John with Kate: true in both scenarios. ✅ - (B) John with Nelson: false - (C) Kate with Luz: false - (D) Kate with Nelson: false - (E) Kate with Olga: true in one scenario only Step 3: Final Answer:
The only statement that is always true is that John is in the same group as Kate.
Answer: (A). (Note: The provided key (E) is incorrect.)
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Question: 5
If John and Olga are assigned to different groups from each other, which of the following CANNOT be true?
If John and Olga are assigned to different groups from each other, which of the following CANNOT be true?
Show Hint
For "CANNOT be true" questions, look for direct contradictions. If a premise forces a person into a certain type of group (e.g., a group of 2), then any statement that places them in a different type of group (e.g., a group of 3) must be the answer.
Updated On: Oct 4, 2025
- John is assigned to the group to which Mark is assigned.
- Luz is assigned to the group to which Kate is assigned.
- Nelson is assigned to the group to which Olga is assigned.
- John is assigned to the group consisting of three members.
- John and Kate are assigned to different groups from each other.
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
This is a "CANNOT be true" (impossibility) question. We are asked to identify a statement that cannot hold under the given conditions. The new condition specifies that John (J) and Olga (O) are in different groups. Step 2: Detailed Explanation:
1. Apply Rule 3 (Olga): Olga must be in the group of three members. This is fixed for all possible arrangements. 2. Apply the new condition: Since John is in a different group from Olga, he cannot be in the 3-person group. This forces John into one of the two 2-person groups. 3. Analyze the options: - (D) states that "John is assigned to the group consisting of three members." - Based on our deduction, this is impossible because John cannot be in Olga's 3-person group. Therefore, (D) is a direct contradiction and cannot be true. 4. Check other options: - For example, (C) states "Nelson is assigned to the group to which Olga is assigned." - We can construct a valid scenario where this is true: if Nelson is with Olga in the 3-person group and Pat joins them, the remaining students can form the two 2-person groups while obeying all other rules. - Therefore, (C) is possible and not the correct answer for "CANNOT be true." 5. Conclusion: Among all the options, only (D) directly contradicts the rules and new condition. Step 3: Final Answer:
Given that Olga is in the 3-person group and John is in a different group, John cannot be in the 3-person group. Therefore, the statement "John is assigned to the group consisting of three members" is impossible. Answer: (D). (Note: The provided answer key listing (C) appears to be incorrect.)
This is a "CANNOT be true" (impossibility) question. We are asked to identify a statement that cannot hold under the given conditions. The new condition specifies that John (J) and Olga (O) are in different groups. Step 2: Detailed Explanation:
1. Apply Rule 3 (Olga): Olga must be in the group of three members. This is fixed for all possible arrangements. 2. Apply the new condition: Since John is in a different group from Olga, he cannot be in the 3-person group. This forces John into one of the two 2-person groups. 3. Analyze the options: - (D) states that "John is assigned to the group consisting of three members." - Based on our deduction, this is impossible because John cannot be in Olga's 3-person group. Therefore, (D) is a direct contradiction and cannot be true. 4. Check other options: - For example, (C) states "Nelson is assigned to the group to which Olga is assigned." - We can construct a valid scenario where this is true: if Nelson is with Olga in the 3-person group and Pat joins them, the remaining students can form the two 2-person groups while obeying all other rules. - Therefore, (C) is possible and not the correct answer for "CANNOT be true." 5. Conclusion: Among all the options, only (D) directly contradicts the rules and new condition. Step 3: Final Answer:
Given that Olga is in the 3-person group and John is in a different group, John cannot be in the 3-person group. Therefore, the statement "John is assigned to the group consisting of three members" is impossible. Answer: (D). (Note: The provided answer key listing (C) appears to be incorrect.)
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