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.

X is a collection of certain odd numbers whereas Y is a collection of…

Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
Select this option if the question can be answered using either statement alone
Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
Select this option if the question cannot be answered even using any of the statements

Answer

Select this option if the question cannot be answered even using any of the statements

We need to know whether all numbers in T are even.
Statement I: sum of any two numbers in T is even. So T cannot contain one odd and one even together; all members have same parity. Could be all even or all odd. Not sufficient.
Statement II: for any p,q in T, (p−1)q is even. If any odd q is chosen, then p−1 must be even for every p, so all p are odd. If all q are even, then all members are even. Again T is forced to be all odd or all even. Not sufficient.
Together still do not tell whether T is all even or all odd.

Select this option if the question cannot be answered even using any of the statements

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