35, 48, 99, 120, 195, 234

Options

A. 99
B. 120
C. 195
D. 234

Explanation

To solve the problem of identifying the pattern in the series 35, 48, 99, 120, 195, 234, we can break it down step by step.

### Step 1: Identify the Pattern
Let's analyze the numbers in the series:
- **35**: This can be expressed as \(5 \times 7\).
- **48**: This can be expressed as \(6 \times 8\).
- **99**: This can be expressed as \(9 \times 11\).
- **120**: This can be expressed as \(10 \times 12\).
- **195**: This can be expressed as \(13 \times 15\).
- **234**: This can be expressed as \(14 \times 16\).

### Step 2: Grouping Odd and Even Products
From the analysis, we can see that:
- The first two numbers (35 and 48) are products of odd and even numbers.
- The next two numbers (99 and 120) follow the same pattern.
- The last two numbers (195 and 234) also follow this pattern.

### Step 3: Continuing the Pattern
Now, let's see the products:
- The odd numbers used are 5, 9, 13 (in the products).
- The even numbers used are 6, 10, 14 (in the products).

Following this pattern, the next odd number should be 15 and the next even number should be 16. However, since we already have 14 and 16, we should check the next odd number after 13, which is 15.

### Step 4: Calculate the Next Number
The next number in the series should be:
- \(15 \times 17 = 255\)

### Step 5: Identify the Incorrect Number
Now, let's compare the last number in the series (234) with what we calculated (255). Since 234 is not equal to 255, we can conclude that 234 is the incorrect number in the series.

### Conclusion
The correct number that should replace 234 is 255.

### Final Answer
The next number in the series should be **255**.

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