Directions: Each question below consists of a number. Your task is to follow the following steps in order to find the result from the given alternatives. Step I: Multiply the number by 3 and add the square of the number. Step II: Divide the result obtained after Step I by 5 and add 6. Step III: Divide the result obtained after Step II by 3 and then square the resulting number. 6

### Concept & Logic This is a sequential algorithm problem. You must take an initial input value and pass it through a series of mathematical transformations, using the output of each step as the strict input for the next. ### Step-by-Step Solution * **Given Input:** $x = 6$ * **Step I: Multiply the number by 3 and add the square of the number.** $$\text{Result}_1 = 3(6) + 6^2$$ $$\text{Result}_1 = 18 + 36 = 54$$ * **Step II: Divide the result obtained after Step I by 5 and add 6.** $$\text{Result}_2 = \frac{54}{5} + 6$$ $$\text{Result}_2 = 10.8 + 6 = 16.8$$ * **Step III: Divide the result obtained after Step II by 3 and then square the resulting number.** $$\text{Result}_3 = \left( \frac{16.8}{3} \right)^2$$ $$\text{Result}_3 = (5.6)^2$$ Calculate $5.6 \times 5.6$: $$5.6^2 = 31.36$$ ### Exam Strategy & Shortcut Instead of fully calculating $5.6^2$, use unit digit and magnitude estimation. $5^2 = 25$ and $6^2 = 36$, so the answer must be around 31. The unit digit of $5.6 \times 5.6$ will end in a $6$ (since $6 \times 6 = 36$). Looking at the options, 31.36 is the only one in the correct range and ending with the correct decimal digit. ### Common Pitfall Applying mathematical operations in the wrong order within a step. For example, in Step II, students might add 6 first and then divide by 5, rather than dividing the previous result strictly by 5 first before adding the constant 6. Read the sequence phrasing literally. ### Final Answer **Therefore, the correct answer is 31.36.**