`7 " "4" "5" "9" "?" "52.5" "160.5`

Options

A. 32
B. 16
C. 14
D. 20

Answer

To solve the number series question `7, " ", 4, " ", 5, " ", 9, "?", 52.5, 160.5`, we need to identify the pattern in the series. Let's break it down step by step.

### Step 1: Identify the pattern
We observe the numbers in the series: `7, 4, 5, 9, ?, 52.5, 160.5`. We need to find the missing number represented by the question mark.

### Step 2: Analyze the first few numbers
Let's look at the first two numbers:
- From `7` to `4`, it seems we are decreasing.
- From `4` to `5`, we are increasing.

### Step 3: Determine the operations
1. **From 7 to 4**: We can see that if we multiply `7` by `0.5`, we get `3.5`, which is not `4`. However, if we subtract `3` from `7`, we get `4`.
2. **From 4 to 5**: If we add `1` to `4`, we get `5`.

### Step 4: Look for a consistent pattern
Let's apply the same logic to the next numbers:
- **From 5 to 9**: If we add `4` to `5`, we get `9`.

### Step 5: Find the missing number
Now, we need to find the number that comes after `9`:
- If we follow the pattern of adding, we can try adding `10.5` to `9` to find the question mark:
- `9 + 10.5 = 19.5`.

### Step 6: Verify the next numbers
Now, let's check if this fits with the next numbers in the series:
- **From 19.5 to 52.5**: If we multiply `19.5` by `2.5`, we get `48.75`, which is not `52.5`.
- However, if we check `19.5 + 33 = 52.5`, it works.
- **From 52.5 to 160.5**: If we multiply `52.5` by `3.05`, we get `160.5`.

### Conclusion
The missing number that fits the pattern is `20`.

Thus, the complete series is: `7, 4, 5, 9, 20, 52.5, 160.5`.

### Final Answer
The number that should come in place of the question mark is **20**.

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