$X$ is a collection of certain odd numbers whereas $Y$ is a collection of certain even numbers. $T$ consists of the numbers all of which are either from $X$ or from $Y$. Is every number of $T$ from $Y$? Statement I : The sum of any two numbers belonging to $T$ is even. Statement II : If both $p$ and $q$ are picked from $T$, then $(p - 1)q$ is even.
Detailed Explanation:
Statement I: Sum of any two numbers in T is even → all numbers have same parity (all even OR all odd). Example: T = {2,4} (all from Y) or T = {1,3} (all from X). Insufficient alone.
Statement II: (p-1)q is even for any p,q from T → satisfied when all are even (q even) OR all are odd (p-1 even). Example: T = {2,4} or T = {1,3}. Insufficient alone.
Both together: Both statements allow T to be entirely even (every number from Y) OR entirely odd (no number from Y). Cannot determine definitively.
Therefore, the question cannot be answered even using both statements, making Option 4 the correct answer.
Question 1 of 2 Numerical Problems
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