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 two-digit number? I. The difference between the two digits is 9. II. The sum of the digits is equal to the difference between the two digits.

Concept & Logic The core logic revolves around the properties of digits in a two-digit number. Digits can only range from $0$ to $9$, and the leading digit (tens place) cannot be $0$. Step-by-Step Solution * **Evaluating Statement I:** The difference between the two digits is $9$. Since the maximum possible digit is $9$ and the minimum is $0$, the only pair of digits with a difference of $9$ is $(9, 0)$. For a two-digit number, the tens digit cannot be $0$. Therefore, the tens digit must be $9$ and the unit digit must be $0$. The number is definitively $90$. Thus, Statement I alone is sufficient. * **Evaluating Statement II:** The sum of the digits is equal to the difference between the two digits. Let the digits be $x$ and $y$. $$x + y = x - y$$ $$2y = 0 \implies y = 0$$ This tells us the unit digit is $0$. However, the tens digit ($x$) could be any number from $1$ to $9$ (e.g., $10, 20, 30 \dots 90$). Since we cannot determine a unique number, Statement II alone is not sufficient. Exam Strategy & Shortcut (MANDATORY) For data sufficiency, always test statements completely independently before combining them. When dealing with digit differences, remember that extreme differences (like $9$) severely restrict the possible digit pairs. Recognizing that $9$ and $0$ are the *only* single digits separated by $9$ solves Statement I instantly without calculation. Common Pitfall (MANDATORY) Students often mistakenly combine both statements immediately without analyzing them individually first. Another pitfall is forgetting that a two-digit number cannot start with $0$ (i.e., $09$ is a one-digit number, not a two-digit number). Final Answer **Therefore, the correct answer is that 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.**