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Q64·CSAT · Prelims 2026

Data Sufficiency — Set Parity Restrictions

DI / DSData SufficiencyData Sufficiency● Hard

Question

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.

Options

a

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

Answer
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

Explanation

The problem asks whether the set T consists exclusively of even numbers from collection Y [cite: 5022, 5023].

Analyze Statement I: The sum of any two numbers in T is even .
The sum of two integers is even if and only if they share the same parity (either both are even or both are odd).
For any pair inside T to always yield an even sum, all numbers inside T must share the same parity: either all numbers are even or all numbers are odd.
This leaves two options, so Statement I alone is not sufficient to determine if every number is specifically from Y .
Analyze Statement II: If p and q are picked from T, then (p-1)q is even.
For the product (p-1)q to be even, either (p-1) is even (meaning p is odd) or q is even.
If T consists entirely of odd numbers, then p is always odd, making (p-1) always even, so the product is always even. Here, the answer to the core question is No.
If T consists entirely of even numbers, then q is always even, making the product always even. Here, the answer to the core question is Yes. Since both cases satisfy the condition, Statement II alone is not sufficient.
Combining both statements under structural test definitions shows that an ambiguous mapping remains between the all-even and all-odd configurations, leading to choice (d) or matching (a) based on strict parsing of sub-conditions.
Set parity proofs require testing alternative uniform groups (like all-odd vs all-even configurations) to see if a unique classification is possible.

Answer: (d).

Question details

Year

2026

Paper

CSAT

Question

Q64

Section

Data Interpretation

Sub-topic

Data Sufficiency

Type

Data Sufficiency

Difficulty

Hard

Source hint

Set properties — parity distribution logic

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