30+ CAT Remainder Questions PDF Download with Answers

Overview: Master CAT remainder questions with this complete guide, reviewed by Supergrads CAT Faculty (IIM Alumni, 10+ years of CAT coaching experience) and verified against official CAT answer keys from 2019 to 2025. It covers all key theorems with solved examples, a quick-reference formula table, 15 solved CAT remainder questions and answers in full MCQ format, a 6-mistake error guide, and a 4-week practice plan. Whether you are a beginner or an advanced aspirant, this is the only resource you need to score 2–3 guaranteed marks from remainder questions for CAT 2026 QA.

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Key Takeaways

• CAT remainder questions appear in every paper 2 to 3 questions per year, making them the highest ROI sub-topic in the entire CAT QA section.
• Three theorems,Fermat’s Little Theorem, Euler’s Theorem, and the Cyclicity Method,solve roughly 85% of all remainder questions CAT that have appeared since 2017.
• The single biggest mark-loss is applying the wrong theorem. The decision framework in this blog eliminates that mistake and helps you identify the right theorem in under 10 seconds.
• remainder questions CAT fall under Number System in the CAT 2026 syllabus. They carry +3 marks each, with a −1 penalty for incorrect MCQ answers as per the CAT exam pattern.
• A structured 4-week, 60-question practice plan is enough to go from zero to 80%+ accuracy,even if you have never studied number theory before.

Table of Contents

1. Why Are CAT Remainder Questions High-ROI?
2. Weightage of CAT Remainder Questions (2019–2026)
3. Key Formulas for CAT Remainder Questions
4. Understanding Each Theorem with Solved Examples
5. 15 Solved CAT Remainder Questions and Answers with MCQ Options
6. Which Theorem to Use When — Decision Guide
7. 6 Common Mistakes in CAT Remainder Questions
8. 4-Week Practice Plan for CAT Remainder Questions

Why Are CAT Remainder Questions High-ROI?

Open any CAT previous year paper from 2019 to 2025 and you will find at least two remainder questions for CAT. That is not a coincidence. It reflects how consistently the CAT exam tests modular arithmetic—because it separates aspirants who have memorised formulas from those who genuinely understand them.

CAT remainder questions come under the Number System chapter of Quantitative Ability. They are among the most rewarding topics in the entire CAT 2026 syllabus for three clear reasons.

• Predictable pattern. The same four or five theorems appear year after year in remainder questions CAT. Unlike paragraph-based DILR sets, there is no new question type to surprise you once you know the theorems.
• Time-efficient. A well-prepared aspirant solves a CAT 2026 remainder question in 30–90 seconds. That is faster than most Geometry or Permutation & Combination questions at equal marks.
• Compounding marks. Getting just two remainder questions for CAT right adds +6 marks. At the 99th percentile boundary, that frequently means a 2–3 percentile point shift. Check the full CAT 2026 exam pattern for section-wise time allocation and scoring details.

According to the CAT Quantitative Aptitude syllabus, Number System is consistently the most heavily weighted chapter in QA. Within it, remainder questions CAT and remainder theorem for CAT problems are the most predictable sub-topic to score on.

💡 Expert Insight: Rahul Agarwal, CAT 99.8 percentiler  (IIM Ahmedabad, Batch 2025), says: “Remainder questions gave me 3 guaranteed marks in 4 minutes flat. Every serious CAT 2026 aspirant must master this topic before anything else in Number System. The theorems are mechanical once you practise them 20–30 times. After that, you just pattern-match in the exam.”

Weightage of CAT Remainder Questions (2019–2026)

The table below is based on analysis of official CAT papers and answer keys by the Supergrads faculty team. Difficulty ratings reflect actual student performance data across 15,000+ Supergrads mock takers in the CAT 2024–25 cycles, not subjective estimates.

Understanding this year-wise trend is essential if you are building your CAT 2026 study plan. It shows that remainder questions for CAT have appeared in every single paper since 2019, with no signs of dropping out of scope.

CAT Year	No. of Remainder Questions	Difficulty Level	Primary Theorems Tested
CAT 2019	2	Medium	Cyclicity, Basic Remainder
CAT 2020	2	Medium–Hard	Fermat’s, Successive Division
CAT 2021	3	Medium	Euler’s, Wilson’s, Cyclicity
CAT 2022	2	Hard	Fermat’s, Factorial Remainders
CAT 2023	3	Medium–Hard	Euler’s, Cyclicity, Basic
CAT 2024	2	Medium	Fermat’s, Successive Division
CAT 2025	2–3	Medium–Hard	Fermat’s, Euler’s, Modular Arithmetic
CAT 2026 (Expected)	2–3	Medium–Hard	All major theorems in scope

Marking Scheme: +3 for every correct answer | −1 for incorrect MCQ | No negative marking for TITA (Type In The Answer).

Solving just 2 CAT remainder questions correctly = +6 marks. That can shift your percentile by 1–2 points at competitive score ranges. Refer to the CAT cut-off for IIM to understand exactly how much those marks matter at the top colleges.

Key Formulas for CAT Remainder Questions - Quick Reference Table

Bookmark this table before you move to the solved examples. It covers every theorem tested in CAT 2026 remainder questions and answers over the past decade.

The “When to Use” column is the most important part. Knowing which theorem to reach for is the real skill tested in remainder questions for CAT-not the calculation itself. For the full topic list, check the CAT Quantitative Aptitude syllabus.

Theorem / Method	Formula / Rule	When to Use	Quick Example
Basic Division Algorithm	Dividend = Divisor × Quotient + Remainder	Always - foundation for all CAT remainder questions	17 = 5×3+2, Remainder = 2
Polynomial Remainder Theorem	If f(x) is divided by (x − a), remainder = f(a)	Polynomial expressions divided by a linear term	f(x) = x² + 2x divided by (x − 3), f(3) = 15
Fermat’s Little Theorem	If p is prime and gcd(a,p) = 1, then a(p−1) ≡ 1 (mod p)	Divisor is a prime number and base is not a multiple of divisor	26 ≡ 1 (mod 7), so 2100 ≡ 2 (mod 7)
Euler’s Theorem	If gcd(a, n) = 1, then aφ(n) ≡ 1 (mod n)	Divisor is composite and coprime to the base	φ(10) = 4, so 34 ≡ 1 (mod 10)
Wilson’s Theorem	If p is prime, then (p − 1)! ≡ −1 (mod p)	Factorial divided by a prime number	16! ≡ 16 (mod 17)
Cyclicity Method	Unit digits of powers of any base repeat in a fixed cycle	Finding unit digit of an, or remainder when dividing by 10	Powers of 2 cycle: 2, 4, 8, 6 (period 4). 2101 has unit digit 2

💡 Cyclicity Values to Memorise: Cyclicity of 2, 3, 7, 8 = 4 | Cyclicity of 4, 9 = 2 | Cyclicity of 5, 6 = 1. This shortcut is also covered in our CAT short tricks guide.

Understanding Each Theorem for CAT Remainder Questions

This is the most important section of the blog. Each theorem below is directly tested in CAT remainder questions every year.

The goal here is not just to show you the formula- it is to help you understand why each theorem works, so you can apply it correctly under CAT exam pressure even when the question is phrased differently. For faster mental calculation techniques, also check our CAT short tricks guide.

1. Basic Division Algorithm and Modular Arithmetic

Every remainder questions CAT ultimately reduces to this single rule. Before learning any advanced theorem, you must be completely fluent with modular notation.

Dividend = Divisor × Quotient + Remainder

In modular notation, 17 ≡ 2 (mod 5) means “17 leaves remainder 2 when divided by 5.” This notation appears directly in remainder questions for CAT at all difficulty levels.

Solved Example: A number N divided by 6 leaves remainder 4. Find the remainder when 3N is divided by 6.

Solution:
N = 6k + 4 for some integer k
3N = 18k + 12
18k is divisible by 6, and 12 = 2 × 6 + 0
So 3N = 6(3k + 2) + 0
Remainder = 0.

2. Fermat’s Little Theorem (Most Tested in CAT Remainder Questions)

This is the theorem that appears most frequently in CAT remainder questions involving large powers. It accounts for roughly 40% of all remainder-related marks in CAT previous year papers.

The key condition to check first: your divisor must be a prime number.

Rule: When your divisor is a prime number p and the base a is not a multiple of p, then a^(p−1) ≡ 1 (mod p). Cycle length = (p − 1).

How to apply Fermat’s Theorem in 3 steps:

1. Confirm the divisor is prime.
2. Divide the exponent by (p − 1) and find the remainder r.
3. Compute a^r (mod p). That is your answer.

Solved Example: Find the remainder when 2¹⁰⁰ is divided by 7.

Solution:
p = 7 (prime), so 2⁶ ≡ 1 (mod 7)
Divide the exponent: 100 = 6 × 16 + 4
So 2¹⁰⁰ ≡ 2⁴ = 16 ≡ 2 (mod 7)
Remainder = 2.

This exact question appeared as a CAT 2026 remainder question in mock tests and has a near-identical version in CAT 2020 and 2022 papers. Practise it until the three steps feel automatic.

3. Euler’s Theorem (For Composite Divisors)

Euler’s Theorem generalises Fermat’s for cases where the divisor is not prime. It is the second most commonly tested theorem in CAT 2026 remainder questions and answers.

For any n and base a where gcd(a, n) = 1: a^φ(n) ≡ 1 (mod n).

Euler’s Totient: φ(n) = n × ∏(1 − 1/p) for each prime p dividing n.

Key φ values to memorise for CAT remainder questions: φ(10) = 4, φ(12) = 4, φ(8) = 4, φ(9) = 6, φ(100) = 40.

Solved Example: Find the remainder when 3¹⁰⁰ is divided by 100.

Solution:
φ(100) = 40. Since gcd(3, 100) = 1, we get 3⁴⁰ ≡ 1 (mod 100)
100 = 40 × 2 + 20, so 3¹⁰⁰ ≡ 3²⁰ (mod 100)
3²⁰ = (81)⁵. 81² = 6561 ≡ 61. 61 × 81 ≡ 41. 41 × 81 ≡ 21
Remainder = 21.

4. Wilson’s Theorem (Factorials + Prime Divisors)

Use this theorem only when a factorial is divided by a prime number. It gives you an instant answer in under 15 seconds, making it the fastest theorem to apply in any CAT 2026 remainder question.

Rule: If p is prime, then (p − 1)! ≡ −1 (mod p), which is the same as (p − 1)! ≡ (p − 1) (mod p).

Solved Example: Find the remainder when 16! is divided by 17.

Solution:
17 is prime.
By Wilson’s Theorem: 16! ≡ −1 (mod 17) ≡ 16 (mod 17)
Remainder = 16.

Total solving time: approximately 10 seconds once the setup is recognised. This type of CAT 2026 remainder question is a gift, it appears roughly once every 2–3 years in CAT papers and can be solved faster than almost any other QA question.

5. Cyclicity Method (Unit Digits)

The unit digit of any integer’s powers repeats in a fixed cycle. This method is essential for remainder questions CAT involving unit digits or division by 10, and it is the easiest theorem to master.

Cyclicity values to memorise for CAT remainder questions:

• Cyclicity of 2, 3, 7, 8 = 4
• Cyclicity of 4, 9 = 2
• Cyclicity of 5, 6 = 1

Solved Example: What is the unit digit of 7²³⁵?

Solution:
Cyclicity of 7 = 4 (pattern: 7, 9, 3, 1)
235 = 4 × 58 + 3
Unit digit of 7²³⁵ = unit digit of 7³ = 343
Unit digit = 3.

Unit digit questions based on cyclicity are among the easiest remainder questions CAT to score on. They require no complex computation just the memorised cycle and one division step. Never skip these in the exam. Check the complete CAT QA syllabus to see where cyclicity fits in the Number System chapter.

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CAT Remainder Questions and Answers - 15 Solved PYQs with MCQ Options

Below are 15 carefully selected CAT remainder questions and answers in full MCQ format, organised from Easy to Hard. Each includes four options, a step-by-step solution, and the theorem used.

The difficulty progression mirrors what you will encounter in an actual CAT 2026 paper. Work through all 15 in order, then practise further using the full set of CAT PYQs 2017–2026 filtered by Number System.

Easy CAT 2026 Remainder Questions - Level 1

Q1: What is the remainder when 51 is divided by 7?

(A) 1     (B) 2     (C) 3     (D) 4

Correct Answer: (B) 2
Solution: 51 = 7 × 7 + 2. Remainder = 2.
Theorem Used: Basic Division Algorithm

Q2: What is the unit digit of 4⁵³?

(A) 2     (B) 4     (C) 6     (D) 8

Correct Answer: (B) 4
Solution: Cyclicity of 4 = 2 (pattern: 4, 6, 4, 6...). Since 53 is odd, unit digit = 4.
Theorem Used: Cyclicity Method

Q3: A number when divided by 5 gives remainder 3. What is the remainder when the square of that number is divided by 5?

(A) 1     (B) 2     (C) 3     (D) 4

Correct Answer: (D) 4
Solution: N ≡ 3 (mod 5), so N² ≡ 9 ≡ 4 (mod 5). Remainder = 4.
Theorem Used: Modular Arithmetic

Q4: Find the remainder when 1! + 2! + 3! + ... + 10! is divided by 6.

(A) 0     (B) 1     (C) 2     (D) 3

Correct Answer: (D) 3
Solution: From 3! = 6 onwards, every factorial is divisible by 6. Only 1! + 2! = 1 + 2 = 3 contributes a remainder. Remainder = 3.
Theorem Used: Factorial Property

Q5 (CAT 2019): The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder. What is n?

(A) 127     (B) 253     (C) 307     (D) 371

Correct Answer: (C) 307
Solution: If both numbers leave the same remainder when divided by n, then n must divide their difference: 34041 − 32506 = 1535. Factorising: 1535 = 5 × 307. The only three-digit factor is 307. This is a classic CAT remainder question from the 2019 paper-full solution is also available in our CAT previous year papers section.
Theorem Used: Basic Division Property

Medium CAT 2026 Remainder Questions - Level 2

Q6: Find the remainder when 2¹⁰⁰ is divided by 7.

(A) 1     (B) 2     (C) 4     (D) 6

Correct Answer: (B) 2
Solution: 7 is prime. By Fermat’s Little Theorem, 2⁶ ≡ 1 (mod 7). Divide the exponent: 100 = 6 × 16 + 4. So 2¹⁰⁰ ≡ 2⁴ = 16 ≡ 2 (mod 7).
Theorem Used: Fermat’s Little Theorem

Q7: Find the remainder when 2²⁵⁶ is divided by 17.

(A) 0     (B) 1     (C) 2     (D) 16

Correct Answer: (B) 1
Solution: 17 is prime. By Fermat’s Little Theorem, 2¹⁶ ≡ 1 (mod 17). Note that 256 = 16 × 16, so 2²⁵⁶ = (2¹⁶)¹⁶ ≡ 1¹⁶ = 1 (mod 17).
Theorem Used: Fermat’s Little Theorem

Q8 (CAT 2021): After dividing a number successively by 3, 4 and 7, the remainders are 2, 1 and 4 respectively. What is the remainder when 84 divides the same number?

(A) 31     (B) 43     (C) 53     (D) 63

Correct Answer: (C) 53
Solution (work backwards from the last division):
Last step: number at that stage = 7k + 4
Before that: 4(7k + 4) + 1 = 28k + 17
Before that: 3(28k + 17) + 2 = 84k + 53
Remainder when divided by 84 = 53. This is one of the most frequently referenced CAT remainder questions from recent papers. See more questions like this in our CAT mock test series.
Theorem Used: Successive Division - Reverse Method

Q9: What is the remainder when 16! is divided by 17?

(A) 1     (B) 8     (C) 15     (D) 16

Correct Answer: (D) 16
Solution: 17 is prime. By Wilson’s Theorem: (17 − 1)! = 16! ≡ −1 ≡ 16 (mod 17).
Theorem Used: Wilson’s Theorem

Q10 (CAT 2022): A number divided by 899 leaves remainder 63. Find the remainder when the same number is divided by 29.

(A) 3     (B) 5     (C) 7     (D) 9

Correct Answer: (B) 5
Solution: 899 = 29 × 31. So N = 899k + 63. Since 63 = 29 × 2 + 5, we get N ≡ 5 (mod 29). Remainder = 5.
Theorem Used: Basic Modular Arithmetic

Hard CAT Remainder Questions - Level 3

Q11 (CAT 2023): Let p = 1! + (2 × 2!) + (3 × 3!) + ... + (10 × 10!). What is the remainder when p + 2 is divided by 11!?

(A) 0     (B) 1     (C) 2     (D) 10

Correct Answer: (B) 1
Solution: Use the telescoping identity: n × n! = (n+1)! − n!. Summing from n=1 to 10, the series telescopes to p = 11! − 1. So p + 2 = 11! + 1. Remainder when divided by 11! = 1.
Theorem Used: Factorial Telescoping Identity

Q12: What is the remainder when 11¹⁰⁵ + 13¹⁰⁵ is divided by 144?

(A) 0     (B) 36     (C) 72     (D) 108

Correct Answer: (C) 72
Solution: Write 11 = 12 − 1 and 13 = 12 + 1. Using the Binomial Theorem on (12−1)¹⁰⁵ + (12+1)¹⁰⁵, all even-powered terms cancel. The surviving terms include 2 × C(105,1) × 12 = 2520. 2520 ÷ 144 gives remainder 72.
Theorem Used: Binomial Theorem + Modular Arithmetic

Q13 (CAT PYQ): Find the remainder when 2¹⁰⁴⁰ is divided by 131.

(A) 0     (B) 1     (C) 2     (D) 130

Correct Answer: (B) 1
Solution: 131 is prime. By Fermat’s Little Theorem, 2¹³⁰ ≡ 1 (mod 131). Since 1040 = 130 × 8, we get 2¹⁰⁴⁰ = (2¹³⁰)⁸ ≡ 1⁸ = 1 (mod 131).
Theorem Used: Fermat’s Little Theorem

Q14 (CAT PYQ): A positive whole number M less than 100 is represented in base 2, base 3, and base 5. In all three cases the last digit is 1, while in exactly two out of three cases the leading digit is also 1. What is M?

(A) 13     (B) 31     (C) 63     (D) 73

Correct Answer: (A) 13
Solution: Last digit 1 in all three bases means M is odd, not divisible by 3, and not divisible by 5. Check M = 13: base 2 = 1101 (leading digit 1), base 3 = 111 (leading digit 1), base 5 = 23 (leading digit 2). Exactly two out of three have a leading digit of 1. Condition satisfied.
Theorem Used: Base Conversion + Elimination

Q15 (CAT 2026 Type): Set A contains all positive integers that, when divided by 2, 3, 4, 5, and 6, leave remainders 1, 2, 3, 4, and 5 respectively. How many integers between 0 and 100 belong to set A?

(A) 0     (B) 1     (C) 2     (D) 3

Correct Answer: (B) 1
Solution: In every case (divisor − remainder) = 1. So (A + 1) must be divisible by LCM(2, 3, 4, 5, 6) = 60. Therefore A = 60k − 1. For k=1: A = 59. For k=2: A = 119 > 100. Only one value qualifies. Count = 1 (A = 59).
Theorem Used: LCM + Modular Arithmetic

Once you have solved all 15 of these CAT remainder questions and answers, your next step is to attempt full-length mocks. Check your accuracy on Number System as a whole in our Supergrads CAT mock test series.

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Which Theorem to Use When - Decision Guide for CAT Remainder Questions

The biggest time-waster in remainder questions for CAT is not the calculation. It is spending 20–30 seconds deciding which theorem to apply.

Train yourself with this rule: check the divisor first, always. The table below maps every question type you will see in CAT Remainder Theorem Questions to the correct theorem and approximate solving time. Use it in every CAT mock test session until the mapping is instinctive.

Question Type	Key Identifier	Use This Theorem	Time Needed
an divided by p (p is prime)	Prime divisor, large power	Fermat’s Little Theorem	30–60 sec
an divided by N (N is composite)	Composite divisor, large power	Euler’s Theorem	60–90 sec
(p − 1)! divided by p (p is prime)	Factorial with prime divisor	Wilson’s Theorem	15–30 sec
Unit digit of an or remainder when divisor = 10	Unit digit question	Cyclicity Method	20–40 sec
Number divided successively by 3, then 4, then 7	Successive / repeated division	Successive Division - Reverse Method	60–90 sec
f(x) divided by (x − a)	Polynomial expression	Polynomial Remainder Theorem	30–60 sec
N², 2N, 3N remainders derived from N’s remainder	Derived remainders	Modular Arithmetic Rules	20–40 sec

💡 10-Second Exam Habit for CAT 2026 Remainder Questions: When you see a CAT Remainder Theorem Questions, ask in this order: (1) Is the divisor prime? → Fermat’s. (2) Is it composite with gcd = 1? → Euler’s. (3) Is there a factorial with a prime divisor? → Wilson’s. (4) Is it asking for a unit digit or divisor 10? → Cyclicity. This 10-second habit alone saves 30–40 seconds per remainder question for CAT. For more shortcuts, visit our CAT short tricks guide.

6 Common Mistakes in CAT Remainder Questions and How to Avoid Them

Even strong aspirants lose marks on CAT 2026 remainder questions due to avoidable errors. The six mistakes below are drawn directly from analysis of student performance across Supergrads’ CAT mock test series (15,000+ students, CAT 2024–25 batches).

Each mistake has a clear, specific fix you can apply from your very next practice session. For deeper paper analysis, check our CAT previous year papers resource.

#	Common Mistake	What to Do Instead
1	Applying Fermat’s Theorem when gcd(a, p) is not equal to 1	Always check gcd first. If a is a multiple of p, the remainder is 0 directly -  no theorem needed at all.
2	Getting the cyclicity period wrong - for example, thinking cyclicity of 2 is 2 instead of 4	Write out the first five powers of the base to confirm the pattern before applying. It takes 15 seconds and prevents a guaranteed wrong answer on any CAT Remainder Theorem Questions involving unit digits.
3	Skipping the “reduce exponent first” step in Fermat’s or Euler’s	Before any calculation, always write: exponent mod (p−1) for Fermat’s, or exponent mod φ(n) for Euler’s. That reduced exponent is what you substitute back.
4	Reconstructing Successive Division forward instead of backward	Always start from the last remainder. Write “Last → second last → first” at the top of your working as a reminder every time you attempt this type of CAT Remainder Theorem Questions.
5	Applying Wilson’s Theorem when the divisor is composite	Wilson’s Theorem is only valid when the divisor is prime. Always verify primality before applying it. If the divisor is composite, switch to Euler’s Theorem.
6	Spending more than 2 minutes on a hard CAT remainder question in the exam	If you cannot identify the correct theorem within 30 seconds, flag the question and move on. A wrong MCQ costs −1 as per the CAT exam pattern; an unanswered TITA costs 0.

4-Week Practice Plan for CAT Remainder Questions

Use this structured plan to go from zero to confident on CAT remainder questions. It assumes 30–45 minutes of focused daily practice and is designed for aspirants starting with no prior number theory background.

Pair this with the full CAT 2026 study plan for complete syllabus coverage. Once you finish Week 4, check the CAT IIM cut-offs to understand your percentile target and how many marks you need from QA.

Week	Focus	Daily Target	Resources	Weekly Goal
Week 1	Foundation: Basic Division & Cyclicity	Basic Division Algorithm + Cyclicity Method | 5 easy CAT Remainder Theorem Questions per day | No timers - focus on process	Toprankers CAT Study Material, CAT books guide, NCERT Chapter 1 (Number System)	30+ easy questions with 90% accuracy
Week 2	Core Theorems: Fermat’s & Euler’s	One theorem per day | 5 medium remainder questions for CAT applying that theorem | Revise formula table daily	Toprankers QA Syllabus Guide, recommended CAT books, Arun Sharma Number System chapter	25 medium questions with 80% accuracy | Keep an error log noting the exact step where each mistake happened
Week 3	Advanced: Wilson’s Theorem, Successive Division & PYQs	2 hard remainder questions CAT timed at 90 seconds each + 3 medium questions per day	CAT PYQs 2017–2026, CAT short tricks for calculation speed	Solve all 15 PYQs in this blog with full written step-by-step solutions | Categorise every error into Conceptual Gap, Silly Slip, or Wrong Theorem
Week 4	Speed Drills and Mock Integration	5 mixed-difficulty CAT Remainder Theorem Questions in 6 minutes (72 sec per question) | Integrate into full-length QA mocks	Supergrads CAT Mock Test Series, sectional QA tests	80%+ accuracy on remainder questions for CAT under full mock conditions | 100% theorem identification within 15 seconds

 Golden Error-Log Rule: After every practice session, tag each mistake as one of three types: Conceptual Gap (re-study the theorem) | Silly Slip (slow down and recheck) | Wrong Theorem Chosen (use the decision guide above). Aspirants who use this three-category log consistently reach 90%+ accuracy in under four weeks. This is what separates 95-percentilers from 99-percentilers on CAT Remainder Theorem Questions.

 Topper Insight: Priya Menon, CAT 99.9 percentiler (IIM Calcutta, Batch 2025) says: “I never solved more than 60 remainder questions for CAT in total. But I solved each one methodically, noted the theorem used, and understood why each step followed. That is the real preparation strategy - 60 deliberate questions beats 300 careless ones.” Check the CAT cut-off for IIM to set your percentile target and reverse-engineer how many QA marks you need.

Conclusion:

CAT remainder questions can be a high-scoring area if you focus on concepts, patterns, and consistent practice. With the right strategy and regular PYQ practice, you can solve them quickly and accurately.

 Master the basics, practice smartly, and turn remainders into easy marks in CAT Quant!