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2026
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.

Explanation

Statement I indicates that the sum of any two numbers in T is even, suggesting that both numbers must come from the same subset (either X or Y). However, without knowing if T exclusively consists of even or odd numbers, we cannot determine if all numbers are from Y. Statement II supports that if both numbers are from T, (p − 1)q is even, but it also does not clarify the nature of numbers in T. Thus, both statements do not provide sufficient clarity to definitively conclude whether all numbers in T are from Y.

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