Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ? I. S likes W7. II. R likes W2. III. U likes W1. IV. V likes W3.
I, III and IV
This problem is a logic puzzle where we need to determine which watch each person likes based on a set of given conditions. We can use a process of elimination and direct assignment to solve it.
Watch Assignments: Initial Facts
We are given the following information:
- Seven persons: P, Q, R, S, T, U, V
- Seven watches: $W_1, W_2, W_3, W_4, W_5, W_6, W_7$
- Each person likes a different watch.
Applying Direct Information
Let's start by assigning watches based on the most direct clues:
- T likes $W_5$.
- Q likes $W_4$.
Constraints and Deductions
P and R Constraints
We know that P and R do not like odd-numbered watches. The odd-numbered watches are $W_1, W_3, W_5, W_7$. The even-numbered watches are $W_2, W_4, W_6$. Therefore, P and R must like watches from the set {$W_2, W_4, W_6$}. Since Q already likes $W_4$, P and R must like watches from the set {$W_2, W_6$}.
P's Watch Preference
P likes prime-numbered watches. The prime-numbered watches are $W_2, W_3, W_5, W_7$. Combining this with the previous deduction (P likes from {$W_2, W_6$}), the only common watch is $W_2$. Therefore, P likes $W_2$.
R's Watch Preference
From the constraint that P and R like from {$W_2, W_6$}, and knowing P likes $W_2$, R cannot like $W_2$. Therefore, R likes $W_6$.
U's Watch Preference
U does not like $W_2, W_3, W_6, W_7$. This means U must like watches from the set {$W_1, W_4, W_5$}. We already know Q likes $W_4$ and T likes $W_5$. So, U cannot like $W_4$ or $W_5$. Therefore, U likes $W_1$.
S's Watch Preference
S likes $W_2$ or $W_7$. We know P likes $W_2$. Therefore, S cannot like $W_2$. Therefore, S likes $W_7$.
V's Watch Preference
Let's summarize the assignments so far:
| Person | Watch |
| P | $W_2$ |
| Q | $W_4$ |
| R | $W_6$ |
| T | $W_5$ |
| U | $W_1$ |
| S | $W_7$ |
The only remaining person is V, and the only remaining watch is $W_3$. Therefore, V likes $W_3$.
Evaluating the Statements
Now let's check the given statements based on our deductions:
- Statement I: S likes $W_7$. - This is correct, as deduced above.
- Statement II: R likes $W_2$. - This is incorrect. We deduced that R likes $W_6$.
- Statement III: U likes $W_1$. - This is correct, as deduced above.
- Statement IV: V likes $W_3$. - This is correct, as deduced above.
Conclusion
Statements I, III, and IV are correct. This corresponds to Option 2.
Important Questions from Logical Puzzle
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If ‘A’ denotes ‘+’, ‘B’ denotes ‘×’, ‘C’ denotes ‘–’ and ‘D’ denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
21 A 34 C 6 B (72 D 9) A 13 B 1 + (56 D 4) = ?
By interchanging the given two signs, which of the following equations will NOT be correct?
+ and ×
l. 180 - 32 + 3 × 148 ÷ 37 = 88
II. 204 ÷ 17 × 23 + 5 - 97 = 50
