In a certain code language, “234' means 'spark and fire', '456' means 'spark is cause' and “258 means 'fire is effect'. Which of the following numerals is used for 'cause'?

Options

A. 3
B. 4
C. 5
D. 6

Answer

To solve the problem step by step, we will analyze the given coded messages and identify which numeral corresponds to the word 'cause'.

### Step 1: Analyze the given codes
We have three coded messages:
1. "234" means "spark and fire"
2. "456" means "spark is cause"
3. "258" means "fire is effect"

### Step 2: Identify common words and numerals
- In the first code "234" (spark and fire) and the second code "456" (spark is cause), the common word is "spark".
- The common numeral in these two codes is "4". Thus, we can conclude that:
- **4 = spark**

### Step 3: Identify the numeral for 'fire'
- Now, looking at the first code "234" (spark and fire) and the third code "258" (fire is effect), the common word is "fire".
- The common numeral in these two codes is "2". Thus, we can conclude that:
- **2 = fire**

### Step 4: Identify the numeral for 'cause'
- Next, we analyze the second code "456" (spark is cause) and the third code "258" (fire is effect).
- The common word in these two codes is "5". Thus, we can conclude that:
- **5 = is**

- Now, we know:
- 4 = spark
- 2 = fire
- 5 = is

### Step 5: Determine the numeral for 'cause'
- In the second code "456", we have:
- 4 = spark
- 5 = is
- Therefore, the remaining numeral "6" must correspond to "cause".

Thus, we conclude that:
- **6 = cause**

### Final Answer
The numeral used for 'cause' is **6**.

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