Condition and Grouping Questions for CAT 2026 — Set 1 with Solutions

Practicse Question

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Condition and Grouping for CAT Case 1

Direction for question 1-4: Answer the question on the basis of the inforamtion given below:

Hometowns of five friends, Abhijeet, Ajay, Ajit, Anil and Arijit are five different towns out of Agra, Ahmedabad, Ahmednagar, Allahabad and Amritsar (in some order). Each friend attends a college in the hometown of exactly one other friend.Additionally the following points are known:

1. Abhijeet attends college in either Ahmedabad or Allahabad.

2. Ajay attends college in Ahmedabad.

3. Ajit does not attend college in Agra.

4. Anil's hometown is Ahmedabad.

5. Arijit attends college in Agra.

Q1. What is Anil's college town?

1. Ahmedabad

2. Agra

3. Amritsar

4. Allahabad

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Frequently Asked Questions — Condition and Grouping for CAT 2026

What is Condition and Grouping in the context of CAT?

Condition and Grouping refers to Permutations and Combinations problems where you must select or arrange items with specific restrictions — such as 'A and B must always be together', 'C must never be selected', or 'at least 2 women must be in the group'.

How many Condition and Grouping questions appear in CAT?

CAT typically has 2–4 P&C questions in total per year, with at least 1–2 involving conditional arrangements or selection restrictions. This sub-topic is medium-to-high difficulty and can differentiate high scorers.

What is the strategy for 'always together' type problems?

'Always together': Treat the constrained group as a single unit. For example, if A and B must always be together, treat {A,B} as one element. Arrange (n-1) elements, then multiply by the internal arrangements of the unit (2! if order matters).

How do I handle 'never together' problems?

'Never together': Total arrangements MINUS the arrangements where the restricted items ARE together. This complement counting approach is faster than directly counting valid arrangements.

What is the gap method in condition problems?

The gap method is used when no two specific items should be adjacent. First, arrange the unrestricted items (n elements), which creates (n+1) gaps. Then place the restricted items in these gaps: P(n+1, k) ways.

How are conditional selection problems different from conditional arrangement problems?

In conditional combination (selection), order does not matter — you are just choosing a subset satisfying conditions. In conditional arrangement, order matters. Always identify whether the problem is about selection or arrangement before applying formulas.

What are the most common constraints tested in CAT grouping problems?

Common constraints in CAT: (1) At least k of type X must be selected, (2) Exactly k women (or men) in a committee, (3) Two specific people cannot be in the same group, (4) A must be selected if B is selected, (5) Fixed positions for specific members.

How should I approach solving condition and grouping problems in CAT?

Step 1: Identify if it is a selection or arrangement problem. Step 2: Check for 'always together', 'never together', 'at least', or 'at most' conditions. Step 3: Use the appropriate formula or complement approach. Step 4: Verify using smaller numbers if unsure.