Question

CSATMediumPrelims 2022Maths

"Consider the Question and two Statements given below: Question: Is $x$ an integer?

Statement-1: $\frac{x}{3}$ is not an integer. Statement-2: $3x$ is an integer.

Which one of the following is correct in respect of the Question and the Statements?"

Explanation

Statement-1 Alone: If $x/3$ is not an integer, it means that $x$ is not divisible by 3. This information tells us that x is not a multiple of 3, but it doesn’t indicate whether x itself is an integer. For example, x could be a fraction like $5/2$ , which is not divisible by 3, or an integer like 5, which is also not divisible by 3. Conclusion: Statement-1 alone is insufficient to determine if x is an integer.
Statement-2 Alone: If $3x$ is an integer, this means x could either be an integer or a fraction with a denominator that divides 3 (like $x = 1/3$ ). Conclusion: Statement-2 alone is also insufficient to determine if x is an integer.
Using Both Statements Together: x could be $5/2$ , satisfying both statements since $(5/2)/3$ is not an integer (Statement-1), and $3 \times (5/2) = 15/2$ , which is not an integer (Statement-2). Alternatively, x could be 5, which is an integer, also satisfying both statements. Conclusion: Even with both statements combined, we cannot determine if x is definitively an integer.