Direction: What approximate value will come in place of the question mark ($x$) in the following question? (You are not expected to calculate the exact value). $1559.95 - 7.99 \times 24.96 - x^2 = 1154$

### Concept & Strategy This question evaluates your ability to apply **Decimal Approximation** combined with the **BODMAS** rule. In competitive exams, dealing with numbers like 1559.95 wastes time. The strategy is to round each decimal to its nearest whole integer before performing any operations, especially before squaring or finding square roots. ### Step-by-Step Solution **Calculation:** Step 1: Approximate all given values to their nearest integers. * $1559.95 \approx 1560$ * $7.99 \approx 8$ * $24.96 \approx 25$ Step 2: Rewrite the equation using these approximated values. $$ 1560 - 8 \times 25 - x^2 = 1154 $$ Step 3: Apply BODMAS (Multiplication before Subtraction). $$ 1560 - 200 - x^2 = 1154 $$ Step 4: Perform the subtraction. $$ 1360 - x^2 = 1154 $$ Step 5: Isolate $x^2$. $$ x^2 = 1360 - 1154 $$ $$ x^2 = 206 $$ Step 6: Find the approximate square root. We know that $14^2 = 196$ and $15^2 = 225$. 206 is closer to 196. Since the question asks for an approximate value and 14 is one of our options, $x \approx 14$. ### Exam Strategy & Shortcut **Mental Anchor Points:** Memorize squares up to 30. Once you reach $1360 - x^2 = 1154$, you can quickly estimate $1350 - 1150 = 200$. What square is near 200? The answer is 14 ($196$). You can skip the precise subtraction and instantly lock in option (a) without needing to write down the final algebraic steps. ### Common Pitfall The most common trap is attempting to multiply $7.99 \times 24.96$ exactly. This will lead to an unwieldy decimal ($199.4304$) that takes a minute to calculate and drastically increases the chance of a careless arithmetic error. Always round first! ### Final Answer **Therefore, the correct answer is 14.**