Question 1 of 64
ThinkCAT Practice SetQANumber Systems • Integral SolutionsHard
For which of the following values of does the equation have integral solutions?
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Number Systems • Diophantine & Integral Solutions Practice Drills (64 Qs)• Convenor Master Key Verified
CAT Diophantine & Number Theory Integral Solutions Questions (60+ Questions)
Linear Diophantine Equations ax + by = c, Non-Negative Solutions, and Bounded Integer Constraints
64 Total Questions
MCQ: 43 (+3 / -1)
TITA: 21 (0 Negative Penalty)
CAT Direct Answer Fact Sheet & Citation Summary
Structured Knowledge Graph • Verified Academic Analysis
Updated for CAT 2026: 1 November 2026
Curated Practice Bank
64 Qs
43 MCQ + 21 TITA
99%ile Score Benchmark
28–31 Marks (out of 66 in QA, ~10 net correct questions)
Scoring Scheme
+3 / -1 / 0
Zero penalty on TITA
Testing Interface
TCS iON CBT
On-Screen Calc Enabled
IIM Exam Strategy & Score Maximization Directives
1Prioritize high-yield arithmetic & algebra questions first to secure the 85th percentile sectional cutoff in the first 20 minutes.
2TITA questions carry zero negative penalty (0 marks for wrong answers); attempt all TITA questions before the sectional timer runs out.
3Use the on-screen digital calculator only for complex 3-digit divisions; mental math approximations save 35–45 seconds per question.
Editorial & Academic Authority: Verified by ThinkCAT Academic & Editorial Council.
Citation Format: ThinkCAT Academic Archive (thinkcat.in)
Exam Hall Pitfalls & Elimination Tactics: Diophantine & Integral Solutions Practice Drills
- 1Forgetting that non-negative integer solutions include ZERO (0, 1, 2...), while positive requires \ge 1.
Interactive Problem Sets (8 Modules)
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Set 01: Integral Solutions
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Set 02: Integral Solutions
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12 QuestionsPro Pass
Set 03: Integral Solutions
Difficulty: Easy
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Set 04: Integral Solutions
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Set 05: Integral Solutions
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Set 06: Integral Solutions
Difficulty: Easy
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8 QuestionsPro Pass
Set 07: Integral Solutions
Difficulty: Easy
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2 QuestionsPro Pass
Set 08: Integral Solutions
Difficulty: Hard
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Official Exam Questions & Explanations (25 of 64)
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ThinkCAT Pro Topic DrillQA • Number Systems
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ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
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ThinkCAT Pro Topic DrillQA • Number Systems
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ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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Exam-Month Discount (Code: CAT200 applied)
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ThinkCAT Pro Topic DrillQA • Number Systems
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3,400+ Extra Drills
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30 Sectional Sprints
40-minute timed drills with RTI percentile curves
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Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
40-minute timed drills with RTI percentile curves
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₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
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Verified Derivations
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₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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Verified Derivations
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₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
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₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
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₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
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Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
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Verified Derivations
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Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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Exam-Month Discount (Code: CAT200 applied)
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ThinkCAT Pro Topic DrillQA • Number Systems
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This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
40-minute timed drills with RTI percentile curves
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ThinkCAT Pro Topic DrillQA • Number Systems
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3,400+ Extra Drills
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Verified Derivations
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₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
IIM convenor verified steps and shortcut methods
Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
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30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
IIM convenor verified steps and shortcut methods
Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
Topic-by-topic CAT practice with zero repetition
30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
IIM convenor verified steps and shortcut methods
Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
Topic-by-topic CAT practice with zero repetition
30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
IIM convenor verified steps and shortcut methods
Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
Topic-by-topic CAT practice with zero repetition
30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
IIM convenor verified steps and shortcut methods
Exam-Month Discount (Code: CAT200 applied)
₹799 ₹2,499
ThinkCAT Pro Topic DrillQA • Number Systems
Unlock 3,400+ Curated Practice Questions & Timed Sprints
This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.
3,400+ Extra Drills
Topic-by-topic CAT practice with zero repetition
30 Sectional Sprints
40-minute timed drills with RTI percentile curves
Verified Derivations
IIM convenor verified steps and shortcut methods
Exam-Month Discount (Code: CAT200 applied)
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Frequently Asked Questions about CAT Diophantine & Number Theory Integral Solutions Questions (60+ Questions)
What concepts are covered in the Diophantine & Integral Solutions Practice Drills practice module?
This module covers Integral Solutions with 64 verified problems ranging from core foundation to high-difficulty CAT exam hall level.
What is the recommended solving time for Diophantine & Integral Solutions Practice Drills questions?
The ideal target pace is 2.0 to 2.5 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.
Where can I find official past year CAT papers for Diophantine & Integral Solutions Practice Drills?
Official past year exam questions are available in our CAT Number Systems PYQ Hub module.
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