Directions: Study the following information carefully and answer the questions given below: Seven students J, K, L, M, N, O and P takes admission in a SCHOOL in seven different days viz., Monday to Sunday of a week but not necessarily in the same order. Two students take admission between K and N. K takes admission before N. O takes admission in one of the day after M. J takes admission on Wednesday. Only one student takes admission between J and M. L takes admission before M and after K. P does not take admission on Sunday.
N takes admission in which of the following days?
Thursday
This problem is a logic puzzle involving the scheduling of seven students (J, K, L, M, N, O, P) admitting into a school over seven days of a week (Monday to Sunday). We need to determine the admission day for student N based on the given clues.
Step-by-Step Deduction of Admission Schedule
Let's break down the information and deduce the schedule:
- Clue 1: J takes admission on Wednesday.
- Wednesday: J
- Clue 2: Only one student takes admission between J and M.
- Since J is on Wednesday, M can either be on Monday (M -> X -> J) or Friday (J -> X -> M).
- Case 1: M is on Monday. The sequence is M (Mon), Tue (X), J (Wed). This fits the clue.
- Case 2: M is on Friday. The sequence is J (Wed), Thu (X), M (Fri). This also fits the clue.
- Clue 3: L takes admission before M and after K. This establishes the order K → L → M.
- Consider Case 1 (M is on Monday): If M is on Monday, K and L must be admitted before Monday, which is impossible in a Monday-Sunday week. Therefore, Case 1 is invalid.
- Consider Case 2 (M is on Friday): M is on Friday. The schedule is: Mon, Tue, J (Wed), Thu, M (Fri), Sat, Sun. Since K → L → M, L must be admitted before Friday, and K must be admitted before L. The available slots before Friday are Monday, Tuesday, and Thursday. L cannot be Thursday because that would imply K must be before Thursday, potentially clashing with J or the structure. Let's try placing L on Tuesday. If L is on Tuesday, K must be on Monday to satisfy K → L.
- Tentative Schedule based on Clues 1, 2, 3:
- Monday: K
- Tuesday: L
- Wednesday: J
- Thursday: (Empty)
- Friday: M
- Saturday: (Empty)
- Sunday: (Empty)
- Clue 4: Two students take admission between K and N. K takes admission before N. (K _ _ N)
- From the tentative schedule, K is admitted on Monday. For two students to be between K and N, N must be admitted on Thursday (K (Mon), Tue, Wed, N (Thu)).
- The students admitted on Tuesday and Wednesday are L and J, respectively. This fits the condition of two students between K and N.
- Updated Schedule:
- Monday: K
- Tuesday: L
- Wednesday: J
- Thursday: N
- Friday: M
- Saturday: (Empty)
- Sunday: (Empty)
- Clue 5: O takes admission in one of the days after M.
- M is admitted on Friday. The days after Friday are Saturday and Sunday. So, O must be admitted on either Saturday or Sunday.
- Clue 6: P does not take admission on Sunday.
- The remaining students are O and P. The remaining days are Saturday and Sunday.
- Since P cannot be admitted on Sunday, P must be admitted on Saturday.
- Consequently, O must be admitted on Sunday.
Final Admission Schedule
Based on the step-by-step deduction, the complete admission schedule is:
| Day | Student |
|---|---|
| Monday | K |
| Tuesday | L |
| Wednesday | J |
| Thursday | N |
| Friday | M |
| Saturday | P |
| Sunday | O |
Conclusion for N's Admission Day
According to the derived schedule, student N takes admission on Thursday.
Therefore, the correct option is 3.
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