Five friends A, B, C, D and E live in a society. All of them like the cars Brand P, Brand Q, Brand R, Brand S and Brand T, of a particular colour, blue, grey, white, silver and black but not in the order as given. a. A likes black car but not Brand T. b. D does not like silver car. He prefers Brand S. c. E does not like Brand R and Brand T. d. C likes blue Brand R. e. One of them likes Silver Brand Q f. B likes white car. Who likes Brand Q?
Logic Puzzle: Assigning Car Brands and Colors
This puzzle involves matching five friends (A, B, C, D, E) with specific car brands (P, Q, R, S, T) and colors (blue, grey, white, silver, black) based on a set of clues. The goal is to determine which friend likes Brand Q.
Analyzing the Clues
- Clue a: A likes black car, but not Brand T.
- Clue b: D prefers Brand S and does not like silver.
- Clue c: E dislikes Brand R and Brand T.
- Clue d: C likes the blue Brand R.
- Clue e: One friend likes Silver Brand Q.
- Clue f: B likes the white car.
Deductive Reasoning Steps
We can systematically deduce the preferences using a table or by listing the facts.
Initial Facts:
- From (d): C likes Brand R and the color is blue.
- From (f): B likes the color white.
- From (a): A likes the color black.
- From (b): D likes Brand S.
Table of Knowns:
| Friend | Brand | Color | Known Constraints |
| A | (P, Q, or T) | black | Not Brand T (a) |
| B | (P, Q, or T) | white | |
| C | R | blue | (d) |
| D | S | (grey) | Not silver (b) |
| E | (P or Q) | (silver or grey) | Not Brand R, Not Brand T (c) |
Step 1: Identify the owner of Silver Brand Q.
Consider clue (e): 'One of them likes Silver Brand Q'.
- C likes Brand R, so C cannot like Brand Q.
- D likes Brand S, so D cannot like Brand Q.
- A likes black. If A liked Brand Q, A would need to like Silver Brand Q, but A likes black. Thus, A cannot own Silver Brand Q.
- B likes white. If B liked Brand Q, B would need to like Silver Brand Q, but B likes white. Thus, B cannot own Silver Brand Q.
- The only remaining friend is E. Therefore, E must like Silver Brand Q.
Step 2: Update assignments based on E liking Silver Brand Q.
- E likes Brand Q and the color silver.
- This fits clue (c) as E does not like Brand R or Brand T.
Step 3: Complete the assignments.
- A likes black but not T. Brands R, S, Q are taken by C, D, E. So A must like Brand P. (A -> P, black).
- The only remaining brand for B is T. (B -> T, white).
- D likes Brand S. The only remaining color is grey. (D -> S, grey). This is consistent with D not liking silver.
Final Answer Derivation
Based on the deductions:
- A likes Brand P (black).
- B likes Brand T (white).
- C likes Brand R (blue).
- D likes Brand S (grey).
- E likes Brand Q (silver).
The friend who likes Brand Q is E.
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