In a shopping mall, five water bottles labelled as A, B, C, D and E were placed in a rack. The bottle A has less price than the bottle B. The bottle C has less price than the bottle D. The bottle B has less price than the bottle C and bottle A has more price than the bottle E.
D
Solving the Water Bottle Price Puzzle
This question asks us to determine which water bottle has the maximum price based on a series of comparative statements about the prices of five bottles labelled A, B, C, D, and E.
Analyzing the Given Price Conditions
We are given the following conditions:
- The price of bottle A is less than the price of bottle B. Mathematically, this can be written as: \( \text{Price(A)} \lt \text{Price(B)} \)
- The price of bottle C is less than the price of bottle D. Mathematically: \( \text{Price(C)} \lt \text{Price(D)} \)
- The price of bottle B is less than the price of bottle C. Mathematically: \( \text{Price(B)} \lt \text{Price(C)} \)
- The price of bottle A is more price than the bottle E. Mathematically: \( \text{Price(A)} \gt \text{Price(E)} \) or \( \text{Price(E)} \lt \text{Price(A)} \)
Combining the Price Relationships
Let's combine these relationships step-by-step to create a single ordering of the bottle prices from least expensive to most expensive.
- From the first condition, we have \( \text{A} \lt \text{B} \).
- The third condition tells us \( \text{B} \lt \text{C} \). Combining this with \( \text{A} \lt \text{B} \), we get the chain: \( \text{A} \lt \text{B} \lt \text{C} \).
- The second condition tells us \( \text{C} \lt \text{D} \). We can add this to our existing chain: \( \text{A} \lt \text{B} \lt \text{C} \lt \text{D} \).
- The fourth condition tells us \( \text{E} \lt \text{A} \). This means bottle E is cheaper than bottle A. We can place E at the beginning of our chain: \( \text{E} \lt \text{A} \lt \text{B} \lt \text{C} \lt \text{D} \).
Determining the Bottle with Maximum Price
Our combined chain of inequalities is \( \text{E} \lt \text{A} \lt \text{B} \lt \text{C} \lt \text{D} \). This shows the bottles ordered from the lowest price to the highest price.
In this sequence, the bottle on the far left (E) has the lowest price, and the bottle on the far right (D) has the highest price.
Therefore, if a customer wants to buy a bottle of maximum price, they should buy bottle D.
Conclusion
By carefully analyzing and combining the given price relationships, we determined the order of prices for the five water bottles: E < A < B < C < D. The bottle with the maximum price is D.
Revision Table: Water Bottle Price Analysis
Let's summarize the key price comparisons and the final order:
| Given Condition | Inequality |
|---|---|
| Price A < Price B | \( \text{A} \lt \text{B} \) |
| Price C < Price D | \( \text{C} \lt \text{D} \) |
| Price B < Price C | \( \text{B} \lt \text{C} \) |
| Price A > Price E (or E < A) | \( \text{E} \lt \text{A} \) |
Combining these leads to the final order:
| Overall Price Order (Lowest to Highest) |
|---|
| \( \text{E} \lt \text{A} \lt \text{B} \lt \text{C} \lt \text{D} \) |
From this order, it is clear that bottle D has the maximum price among the five bottles.
Additional Information on Price Comparison Logic
Problems like this involve deductive reasoning based on comparative statements. To solve them, it's helpful to visualize the relationships or write them down as inequalities.
- When given statements like "X is less than Y" and "Y is less than Z", you can deduce that "X is less than Z". This is the transitive property of inequality.
- In our case, A < B and B < C allowed us to deduce A < C. Then, combining A < C with C < D allowed us to deduce A < D.
- By systematically combining all given relationships, you can build a complete or partial ordering of all the items being compared.
- Once the items are ordered (or their relative positions are known), it's easy to identify the minimum or maximum value in the set.
- Always ensure you use all the given information to get the most accurate ordering possible.
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