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.
How many persons go after V?
Correct Answer :
Three
Solution :
The correct answer/option is Three.
Step-by-step Explanation:
Let us arrange the seven days of the week starting from Monday to Sunday: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
1. Use the fixed condition:
- "U goes to the picnic on Wednesday."
So, Wednesday = U.
2. Determine the position of T:
- "Only one person goes between U and T."
This gives two possibilities for T:
Case 1: T goes on Monday.
Case 2: T goes on Friday.
3. Determine the position of S:
- "Only three persons go between T and S."
In Case 1 (T on Monday): Counting three persons after Monday (Tuesday, Wednesday, Thursday), S must go on Friday.
In Case 2 (T on Friday): Counting three persons before Friday (Thursday, Wednesday, Tuesday), S must go on Monday.
4. Use the condition for V and P:
- "V goes to the picnic after P but none of them go before S."
This means both P and V must go on days after S. Therefore, S must be scheduled earlier in the week to leave at least two available days after S for P and V.
In Case 1, S is on Friday. The only days after Friday are Saturday and Sunday (2 days). Since P and V must both be after S, P and V would have to occupy Saturday and Sunday. However, we also have to place Q and R such that "Q goes immediately before R". But only Monday, Tuesday, Thursday are left before S, and Q and R can take two adjacent days there (Monday-Tuesday or Tuesday-Wednesday, but Wednesday is occupied by U, so Monday-Tuesday). Let's check:
- If Q = Monday, R = Tuesday, U = Wednesday, T = Thursday (Wait, in Case 1, T is Monday, so this is impossible).
Let's evaluate carefully:
Testing Case 2 (S on Monday, T on Friday):
Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
S is on Monday.
U is on Wednesday.
T is on Friday.
Remaining empty days: Tuesday, Thursday, Saturday, Sunday.
- Condition: "Q goes immediately before R."
The only available consecutive empty days are Saturday and Sunday (or none others, since Tuesday and Thursday are separated by Wednesday). Thus, Q = Saturday and R = Sunday.
Now, the remaining days to fill are Tuesday and Thursday for P and V.
- Condition: "V goes to the picnic after P..."
So, P = Tuesday and V = Thursday.
Final Schedule Verification:
- Monday: S
- Tuesday: P
- Wednesday: U
- Thursday: V
- Friday: T
- Saturday: Q
- Sunday: R
All conditions satisfied:
1. U is on Wednesday.
2. One person (P) between U and T (Friday).
3. Three persons (P, U, V) between T (Friday) and S (Monday).
4. Q (Saturday) goes immediately before R (Sunday).
5. V (Thursday) goes after P (Tuesday), and neither goes before S (Monday).
Question Answer:
"How many persons go after V?"
V goes on Thursday. The persons who go after V are T (Friday), Q (Saturday), and R (Sunday).
Therefore, exactly Three persons go after V.
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