CAT Number System: Concepts, Topics & PYQs

Number-system volume changes by slot, but divisibility, factors, remainders, digits and integer constraints repeatedly appear and are often TITA-friendly. For CAT preparation, the useful question is not “Have I finished the chapter?” but can I recognise the version of the concept CAT hides inside a word problem and choose an efficient method under time pressure?

What to know

The core checklist for this topic is: Integers, divisibility, primes, factors, HCF/LCM, remainders; and modular arithmetic, units digit, factorials, highest power, surds/indices, base representation basics. Learn these as connected ideas rather than isolated formulas. CAT often combines two of them in one question.

Recurring CAT-style forms

Expect questions built around Count factors, remainder pattern, divisibility digit, trailing zeros, highest power, and integer solutions. The wording changes, but the mathematical structure repeats. Your first 20–30 seconds should be spent identifying that structure before writing equations.

Decision rules worth remembering

• Prime factorisation drives factor count/HCF/LCM
• Euler-style cycles only when useful
• trailing zeros from min powers of 2/5
• remainder arithmetic can simplify large powers

One original example

For 2⁴×3², the number of positive divisors is (4+1)(2+1)=15. Prime exponents turn a large-number problem into a counting problem.

The point of a worked example is not the answer; it is the choice of representation. After solving, ask whether a ratio table, base-100 assumption, sign chart, factorisation or diagram made the work shorter.

Common traps

• Applying divisibility rules blindly
• forgetting zero/negative integer cases
• counting 1 or n incorrectly as proper factors
• assuming cycles start at same place

These traps are valuable because they explain why a student can “know the formula” and still lose marks. Add the exact mistake to your error log when it occurs; do not simply write “silly mistake.”

How to practise

Start with 10–15 untimed questions until the first step becomes automatic. Then use mixed timed sets where this topic is not announced in advance. Finish with sectionals and mock review. Mastery checkpoint: Can factorise efficiently and recognise periodic remainder/unit-digit patterns.

Once that checkpoint is stable, move on rather than over-polishing one chapter. CAT QA is a portfolio of scoring areas; the objective is enough reliable topics to make question selection easy on exam day.