Study the following information carefully and answer the questions given below.
Seven persons- P, Q, R, S, T, U and V go on a picnic on different days in a week starting from Monday to Sunday but not necessarily in the same order. Only one person goes on picnic each day.
U goes to the picnic on Wednesday. Only one person goes between U and T. Only three persons go between T and S. Q goes immediately before R. V goes to the picnic after P but none of them go before S.
On which of the following day does S go to the picnic?
Correct Answer :
Monday
Solution :
The correct option is Monday.
Let us step-by-step determine the schedule of the seven persons (P, Q, R, S, T, U, V) going on a picnic from Monday to Sunday:
1. U goes to the picnic on Wednesday:
- Monday:
- Tuesday:
- Wednesday: U
- Thursday:
- Friday:
- Saturday:
- Sunday:
2. Only one person goes between U and T:
T can go either on Monday or on Friday. Let us consider both possibilities:
- Case 1: T goes on Monday.
- Case 2: T goes on Friday.
3. Only three persons go between T and S:
- In Case 1 (T on Monday), counting 3 days after Monday (Tuesday, Wednesday, Thursday), S must go on Friday.
- In Case 2 (T on Friday), counting 3 days before Friday (Thursday, Wednesday, Tuesday), S must go on Monday.
4. V goes to the picnic after P, but none of them go before S:
This means both P and V go on picnic after S, and P goes before V (i.e., S ... P ... V).
- In Case 1, S is on Friday. Thus, P and V would have to go on Saturday and Sunday (with P before V).
- In Case 2, S is on Monday. All other persons go after S, satisfying the condition that none of P or V go before S.
5. Q goes immediately before R:
Q and R must occupy two consecutive available days.
- In Case 1 (T=Mon, U=Wed, S=Fri, P=Sat, V=Sun): The remaining empty days are Tuesday and Thursday. They are not consecutive, so Q and R cannot sit together. Thus, Case 1 is invalid.
- In Case 2 (S=Mon, U=Wed, T=Fri): The available empty days are Tuesday, Thursday, Saturday, and Sunday. Since Q goes immediately before R, and P goes before V (after S):
Putting Q and R on Thursday and Friday is impossible as Friday is T. So Q and R must be placed on Thursday and Friday? No, Thursday is adjacent to Wednesday (U) and Friday (T), so Thursday is a single slot. Thus Q and R must be on Saturday and Sunday (Q on Saturday, R on Sunday).
Then P and V must take the remaining slots: Tuesday and Thursday (P on Tuesday, V on Thursday, so V goes after P).
Let us verify the final arrangement for Case 2:
- Monday: S
- Tuesday: P
- Wednesday: U
- Thursday: V
- Friday: T
- Saturday: Q
- Sunday: R
All conditions are satisfied:
- U is on Wednesday.
- One person (P) between U and T (Friday).
- Three persons (P, U, V) between T (Friday) and S (Monday).
- Q goes immediately before R (Saturday and Sunday).
- V goes after P (P on Tuesday, V on Thursday), and neither goes before S.
Therefore, S goes to the picnic on Monday.
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