What is X in the sequence 132, 129, 124, 117, 106, 93, X ?

To solve this, we will use the 'Method of Differences' which is a standard tool for such questions [7, 16].\n\n1. **Find the Gaps**: Let's look at how much each number decreases from the previous one:\n * 132 to 129 -> decrease by **3**\n * 129 to 124 -> decrease by **5**\n * 124 to 117 -> decrease by **7**\n * 117 to 106 -> decrease by **11**\n * 106 to 93 -> decrease by **13**\n\n2. **Analyze the Pattern**: The gaps are 3, 5, 7, 11, 13.\n * Is it odd numbers? The sequence of odd numbers would be 3, 5, 7, **9**, 11. But here, **9 is missing**.\n * Since 9 is not a prime number (3x3=9), but all others in our list are, the pattern is clearly **consecutive prime numbers**.\n\n3. **Predict the Next Step**: We need the next prime number after 13.\n * 14, 15, 16 are not prime.\n * The next prime is **17**.\n\n4. **Calculate Final Answer**: Apply this gap to the last number in the series.\n * 93 - 17 = 76.\n\nThis matches option (C).