Directions: Each item in this section contains a question followed by two statements. Answer each item using the following instructions:
(a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
(b) Select this option if the question can be answered using either statement alone
(c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
(d) Select this option if the question cannot be answered even using any of the statements

Question: 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.

Question

Directions: Each item in this section contains a question followed by two statements. Answer each item using the following instructions:
(a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
(b) Select this option if the question can be answered using either statement alone
(c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
(d) Select this option if the question cannot be answered even using any of the statements

Question: 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.

Accepted Answer

(d). T is composed of elements either entirely from X (odd) or entirely from Y (even). Statement I: sum of any two from T is even. If all from X (odd+odd=even) ✓, or all from Y (even+even=even) ✓. Both cases possible—can't distinguish. Statement II: (p–1)q is even. If p odd, p–1 even, product even regardless of q. If p even, p–1 odd, then q must be even. So if T from X (all odd), (p–1)q = even × odd = even ✓. If T from Y (all even), (p–1)q = odd × even = even ✓. Both work, insufficient. Together: still both cases satisfy both statements. Hence cannot determine—answer (d).

Explanation

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