Directions: Find the wrong number in the series. 445, 221, 109, 46, 25, 11, 4

### Concept & Logic The sequence decreases by roughly half at each step. This implies a logic of division by $2$, combined with an addition or subtraction step. ### Step-by-Step Solution 1. Because the numbers are halved roughly, let's test the formula $(x - c) / 2 = y$ or working backwards: $y \times 2 + c = x$. Working backwards with multiplication is usually easier. 2. Let's examine the smaller terms (right to left): - $4 \times 2 + 3 = 11$ - $11 \times 2 + 3 = 25$ 3. The pattern seems to be: multiply the current number by $2$ and add $3$ to get the preceding number. 4. Let's continue testing this moving left: - $25 \times 2 + 3 = 53$. (The sequence has 46 here, so 46 is incorrect). 5. Let's verify that $53$ fixes the rest of the sequence: - $53 \times 2 + 3 = 106 + 3 = 109$ (Matches) - $109 \times 2 + 3 = 218 + 3 = 221$ (Matches) - $221 \times 2 + 3 = 442 + 3 = 445$ (Matches) ### Exam Strategy & Shortcut When division leaves remainders, flip the series and use multiplication. Spotting that $(11 \times 2) + 3 = 25$ takes just a few seconds. Applying it immediately reveals that $46$ breaks the rule. ### Common Pitfall Trying to strictly apply division from the left side and struggling with the remainders (e.g., $(445 - 3) / 2 = 221$). Working backwards with multiplication removes fractional math. ### Final Answer Therefore, the correct answer is **46**.