Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the difference between the digits of a two-digit number? I. The sum of the digits of that number is 8. II. One-fifth of that number is 15 less than half of 44.

Concept & Logic If a statement allows you to determine the exact original two-digit number, you can easily identify its individual digits and calculate any relationship between them, including their difference. Step-by-Step Solution * **Goal:** Find the absolute difference between the digits of an unknown two-digit number $N$. * **Evaluating Statement I:** The sum of the digits is 8. Possible numbers are 17, 26, 35, 44, 53, 62, 71, 80. The difference between the digits could be 6 (for 17), 4 (for 26), 2 (for 35), 0 (for 44), etc. We cannot determine a single unique difference. Thus, Statement I alone is not sufficient. * **Evaluating Statement II:** One-fifth of that number is 15 less than half of 44. Let the number be $N$. Translate the statement into a direct algebraic equation: $$\frac{N}{5} = \frac{44}{2} - 15$$ $$\frac{N}{5} = 22 - 15$$ $$\frac{N}{5} = 7 \implies N = 35$$ Since the exact number is definitively 35, its digits are 3 and 5. The difference between the digits is $5 - 3 = 2$. Thus, Statement II alone provides everything needed to answer the question. Exam Strategy & Shortcut (MANDATORY) Notice that Statement II is an equation with only one variable ($N$ with constant numbers like 15 and 44). Any single-variable linear equation will yield exactly one solution. Once you see that Statement II isolates the entire number, you know it is sufficient without even doing the arithmetic. Common Pitfall (MANDATORY) Students sometimes think "difference between the digits" requires knowing which digit comes first to determine a positive or negative sign. In aptitude tests, "difference" implicitly means the absolute positive difference between the two values unless directional order is explicitly stated. Final Answer **Therefore, the correct answer is that the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.**