Directions: Find the wrong number in the series. 40960, 10240, 2560, 640, 200, 40, 10

### Concept & Logic The sequence features rapidly decreasing large numbers, suggesting a pattern of division by a constant factor. Let's test the ratio between terms. ### Step-by-Step Solution 1. Start from either end. The smaller numbers at the end are easier to work with. Let's look at $40$ and $10$: - $40 / 4 = 10$. 2. Now test this "divide by 4" hypothesis from the beginning: - $40960 / 4 = 10240$ - $10240 / 4 = 2560$ - $2560 / 4 = 640$ - $640 / 4 = 160$ (The given sequence has 200 here, so 200 is incorrect). 3. Verify the rest of the sequence with the corrected number: - $160 / 4 = 40$. This matches the next number in the given series. ### Exam Strategy & Shortcut When dealing with large numbers, don't start calculating from the left if it's difficult. Look at the right side of a decreasing sequence. The ratio between $40$ and $10$ immediately gives away the rule (divide by $4$), which you can then quickly verify. ### Common Pitfall Attempting long division on $40960$ manually when you could just look at the last two terms to deduce the probable pattern. ### Final Answer Therefore, the correct answer is **200**.