A team of six members is to be selected from ten members M1, M2, M3, M4, M5, M6, M7, M8, M9 and M10. M5 cannot be selected with M10. M6 cannot be selected with M1. M3 to be selected with M9. M4 to be selected with M7. M8 cannot be selected with M5. Which of the following members can be selected in a team?
M1, M2, M3, M8, M9, M10
Team Selection Problem Analysis
The problem asks us to find a valid team of six members selected from a pool of ten members (M1 to M10), subject to several specific conditions or constraints.
Understanding the Constraints for Team Selection
We have a total of 10 members: M1, M2, M3, M4, M5, M6, M7, M8, M9, M10. We need to select a team of 6 members. The constraints are:
- Constraint 1: M5 cannot be selected with M10. (M5 and M10 are mutually exclusive)
- Constraint 2: M6 cannot be selected with M1. (M6 and M1 are mutually exclusive)
- Constraint 3: M3 to be selected with M9. (If M3 is in the team, M9 must be in, and vice versa. They form a pair that must be together or both excluded)
- Constraint 4: M4 to be selected with M7. (If M4 is in the team, M7 must be in, and vice versa. They form a pair that must be together or both excluded)
- Constraint 5: M8 cannot be selected with M5. (M8 and M5 are mutually exclusive)
Now, let's examine each given option and check if it satisfies all these constraints for selecting a team of 6.
Checking Each Option Against Constraints
Option 1: M2, M3, M5, M7, M8, M9
Team Members: {M2, M3, M5, M7, M8, M9}
- Constraint 1 (M5 & M10): M5 is in, M10 is not. Satisfied.
- Constraint 2 (M6 & M1): M6 is not, M1 is not. Satisfied.
- Constraint 3 (M3 & M9): M3 is in, M9 is in. Satisfied.
- Constraint 4 (M4 & M7): M4 is not, M7 is in. Not satisfied. If M7 is selected, M4 must also be selected.
- Constraint 5 (M8 & M5): M8 is in, M5 is in. Not satisfied. M8 and M5 cannot be together.
Option 1 violates Constraints 4 and 5. Therefore, it is not a valid team.
Option 2: M2, M3, M4, M7, M8, M10
Team Members: {M2, M3, M4, M7, M8, M10}
- Constraint 1 (M5 & M10): M5 is not, M10 is in. Satisfied.
- Constraint 2 (M6 & M1): M6 is not, M1 is not. Satisfied.
- Constraint 3 (M3 & M9): M3 is in, M9 is not. Not satisfied. If M3 is selected, M9 must also be selected.
- Constraint 4 (M4 & M7): M4 is in, M7 is in. Satisfied.
- Constraint 5 (M8 & M5): M8 is in, M5 is not. Satisfied.
Option 2 violates Constraint 3. Therefore, it is not a valid team.
Option 3: M1, M2, M3, M8, M9, M10
Team Members: {M1, M2, M3, M8, M9, M10}
- Constraint 1 (M5 & M10): M5 is not, M10 is in. Satisfied.
- Constraint 2 (M6 & M1): M6 is not, M1 is in. Satisfied.
- Constraint 3 (M3 & M9): M3 is in, M9 is in. Satisfied.
- Constraint 4 (M4 & M7): M4 is not, M7 is not. Satisfied (neither is selected, which is allowed by the 'to be selected with' rule).
- Constraint 5 (M8 & M5): M8 is in, M5 is not. Satisfied.
Option 3 satisfies all the specified constraints. Therefore, this is a valid team.
Option 4: M1, M2, M3, M4, M7, M8
Team Members: {M1, M2, M3, M4, M7, M8}
- Constraint 1 (M5 & M10): M5 is not, M10 is not. Satisfied.
- Constraint 2 (M6 & M1): M6 is not, M1 is in. Satisfied.
- Constraint 3 (M3 & M9): M3 is in, M9 is not. Not satisfied. If M3 is selected, M9 must also be selected.
- Constraint 4 (M4 & M7): M4 is in, M7 is in. Satisfied.
- Constraint 5 (M8 & M5): M8 is in, M5 is not. Satisfied.
Option 4 violates Constraint 3. Therefore, it is not a valid team.
Based on the analysis of each option against all the team selection constraints, only Option 3 lists members that can be selected together in a team of six.
Revision Table: Constraint Checklist
| Option | Members | C1 (M5/M10) | C2 (M6/M1) | C3 (M3&M9) | C4 (M4&M7) | C5 (M8/M5) | Valid? |
|---|---|---|---|---|---|---|---|
| 1 | M2, M3, M5, M7, M8, M9 | OK (M5 in, M10 out) | OK (M6 out, M1 out) | OK (M3 in, M9 in) | FAIL (M7 in, M4 out) | FAIL (M8 in, M5 in) | No |
| 2 | M2, M3, M4, M7, M8, M10 | OK (M5 out, M10 in) | OK (M6 out, M1 out) | FAIL (M3 in, M9 out) | OK (M4 in, M7 in) | OK (M8 in, M5 out) | No |
| 3 | M1, M2, M3, M8, M9, M10 | OK (M5 out, M10 in) | OK (M6 out, M1 in) | OK (M3 in, M9 in) | OK (M4 out, M7 out) | OK (M8 in, M5 out) | Yes |
| 4 | M1, M2, M3, M4, M7, M8 | OK (M5 out, M10 out) | OK (M6 out, M1 in) | FAIL (M3 in, M9 out) | OK (M4 in, M7 in) | OK (M8 in, M5 out) | No |
Additional Information: Types of Selection Constraints
Problems involving team selection often include different types of constraints. Understanding these types helps in solving such logical reasoning questions:
- Mutually Exclusive: Two members cannot be in the same team together. If one is selected, the other must be excluded. Example: M5 cannot be selected with M10.
- Mandatory Pairing: Two members must be selected together. If one is in the team, the other must also be in. If one is not in the team, the other might or might not be, depending on other rules and team size, but for this problem's phrasing "to be selected with", it implies they are a dependent pair. Example: M3 to be selected with M9. If M3 is in, M9 must be in. If M9 is in, M3 must be in. If M3 is out, M9 must be out (otherwise M9 would be in without M3).
- Conditional Inclusion/Exclusion: The selection of one member depends on the selection or exclusion of another. Example: If A is selected, B must be selected. (This is similar to mandatory pairing but can be one-way).
- Minimum/Maximum Number: Constraints on the number of members from a certain group (e.g., at least 2 women, no more than 3 engineers). This problem didn't have this type.
Checking each option against every constraint systematically is a reliable way to solve this kind of logical puzzle.
Important Questions from Scheduling
A, B, C, D and E are five rivers. A is shorter than B but longer than E. C is the longest and D is a little shorter than B and a little longer than A. Which is the shortest river?
Seven games G1, G2, G3, G4, G5, G6 and G7 were played on seven different days of the same week from Monday to Sunday (not necessarily in the same order). Three games were played between G2 and G5. Two games were played between G6 and G4. G3 was played on Tuesday. G2 was played after G4. G7 was played on Friday. G6 was played after G2.
Which of the following statement is correct?
I. No game was played between G2 and G6.
II. G1 was played immediately before G5.
6 teachers P, Q, R, S, T, and U are to deliver the lecture. Each teacher will deliver lectures on one of the days from Monday to Saturday. Each teacher will deliver lectures on different days. There are 3 male and 3 female teachers. Each man is married to a woman. More than two persons deliver between T and U. R delivers on Friday but his wife does not deliver on Monday. P delivered on the next day of S. 2 people present between P and U. P's wife presents P's next day. T and U have the same gender. Which of the following statement is not correct?
Anuj, Ankit, Anu and Alka are teachers who teach Biology, History and Mathematics. Biology is the only subject taught by two teachers, one of whom is male. Two of the four are married to each other and they teach History and Biology respectively. Ankit teaches Biology and is unmarried.
Anu and Alka are females.Which subject does Anuj teach?
Six persons A, B, C, D, E and F work on six different days of a same week from Sunday to Friday (not necessarily in the same order). Three persons work between A and F. Two persons work between B and D. E works on Monday. C works after D, but before F.
Which of the following statement is correct?
I. B works on Friday.
II. C works on Wednesday.
