X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of whic…

Question

Directions: The question is followed by two statements. Answer using the codes given in the options.

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.

1. A. The question can be answered using one of the statements alone, but cannot be answered using the other statement alone.
2. B. The question can be answered using either statement alone.
3. C. The question can be answered using both the statements together, but cannot be answered using either statement alone.
4. D. The question cannot be answered even using both the statements together. (Correct answer)

Correct Answer

Option D — The question cannot be answered even using both the statements together.

Detailed Solution & Explanation

The correct answer is Option D (cannot be answered even together).

Key Points

• T is drawn entirely from the odd set X or the even set Y.
• Statement I (sum of any two in T is even) forces all elements of T to share the same parity — but that could be all-odd (from X) or all-even (from Y).
• Statement II ((p−1)q even for any p, q) likewise only guarantees a single parity for T, not which one.

Additional Information

• Both statements are consistent with T being entirely odd (answer No) or entirely even (answer Yes), so even together they cannot decide — Option D.