Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question. What is the two-digit number? I. The difference between the two-digit number and the number formed by interchanging the digits is 27. II. The difference between the two digits is 3. III. The digit at unit's place is less than that at ten's place by 3.

Concept & Logic To uniquely identify a two-digit number, we need two independent linear equations to solve for the two variables (the individual digits). $$Original Number = 10x + y$$ Step-by-Step Solution * **Analyze Statement I:** The difference between the number and its reverse is 27. * Calculation for I: $|(10x+y) - (10y+x)| = 27 \implies 9|x-y| = 27 \implies |x-y| = 3$. (Insufficient alone) * **Analyze Statement II:** The absolute difference between the digits is 3. So, $|x-y| = 3$. This is mathematically identical to Statement I. (Insufficient alone) * **Analyze Statement III:** The unit's digit is less than the ten's digit by 3. This gives us the exact order: $x - y = 3$. (Insufficient alone) * **Test Combinations:** All three statements essentially provide the same core piece of information: the difference between the digits is 3. We are completely missing a crucial second independent equation (such as the sum or product of the digits). * Because we only know $x - y = 3$, the number could easily be 41, 52, 63, 74, 85, or 96. Exam Strategy & Shortcut Realize immediately that "difference of digits" and "difference between a number and its reversed form" are the exact same mathematical property in disguise. If no statement provides an independent metric like a sum, product, or ratio, finding the exact unique number is impossible. Common Pitfall Test-takers often assume that a single linear equation is sufficient if the variables are restricted to single digits (0-9). While the digit restriction limits the possibilities, it rarely narrows it down to a single unique answer unless the sum or product is explicitly provided. Final Answer **Therefore, the correct answer is Even with all I, II and III, answer cannot be given.**