Directions: Find the wrong number in the series. 19, 26, 33, 46, 59, 74, 91

### Concept & Logic The series grows at a steady, moderate pace. We should evaluate the first-level differences between the numbers to spot an underlying progression. ### Step-by-Step Solution 1. Find the differences between consecutive terms: - $26 - 19 = 7$ - $33 - 26 = 7$ - $46 - 33 = 13$ - $59 - 46 = 13$ - $74 - 59 = 15$ - $91 - 74 = 17$ 2. The differences $13, 15, 17$ at the end form a clear pattern of consecutive odd numbers starting from $13$. 3. If we project this "consecutive odd numbers" pattern backward, the differences should be $7, 9, 11, 13, 15, 17$. 4. Let's apply this sequence of differences starting from the first term: - $19 + 7 = 26$ (Correct) - $26 + 9 = 35$. (The sequence gives 33, making it the wrong number). 5. Verify the rest of the sequence with $35$: - $35 + 11 = 46$ (Matches) - $46 + 13 = 59$ (Matches) ### Exam Strategy & Shortcut When a difference series looks "messy" at the start ($7, 7$) but clean at the end ($13, 15, 17$), trust the clean end. Work backwards to figure out what the messy start *should* have been to maintain the pattern. ### Common Pitfall Seeing $7, 7, 13, 13$ and trying to force a pattern where differences repeat in pairs, completely ignoring that $15$ and $17$ break that assumed rule. Always look at the whole sequence of differences. ### Final Answer Therefore, the correct answer is **33**.