CAT with Confidence: Diving into Complex Numbers, Calendar Puzzles, and PYQs on Critical Reasoning- Day 54

CAT with Confidence: Diving into Complex Numbers, Calendar Puzzles, and PYQs on Critical Reasoning- Day 54

Ongoing Event

CAT Application Date:01 Aug' 25 - 20 Sep' 25

Team Careers360Updated on 19 Jun 2025, 02:23 PM IST

Aspirants preparing for CAT 2024 should now concentrate on important topics like complex numbers and calendar-based aptitude questions, which often lead to confusion, particularly when differentiating between complex numbers and quadratic equations. Consistent practice and strong conceptual clarity are essential at this stage. Solving previous year questions and making use of helpful resources such as the calendar reasoning PDF can significantly enhance preparation and build confidence for the final exam.

LiveCAT 2025 Registration LIVE: IIM Kozhikode extends registration till September 20; MBA admission criteriaSep 13, 2025 | 9:43 PM IST

Candidates applying for CAT 2025 should keep their documents, including Class 10 and 12 mark sheets, a valid photo ID, graduation certificate, work experience proof (if applicable), and any other relevant papers, ready as these will be required during the registration process.

Read More

This Story also Contains

  1. Part-1: Quantitative Aptitude for CAT exam
  2. Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
  3. Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
  4. Short Tricks to Solve Complex Number Questions in CAT
  5. Short Tricks to Solve Calendar Puzzles Questions in CAT
CAT with Confidence: Diving into Complex Numbers, Calendar Puzzles, and PYQs on Critical Reasoning- Day 54
Complex Numbers Questions for CAT Exam

Part-1: Quantitative Aptitude for CAT exam

Aspirants can also download questions on complex numbers with answers pdf for more practice questions and references for their studies.

Important Concept/Formula Used in CAT complex numbers questions

Concepts and Formulas Used in CAT complex numbers Exam questions are given below:

  1. Contains real as well as imaginary parts.

Eg: 2+ 3i

Real part = 2

Imaginary part = 3

  1. iota (i) = -1

Great Lakes - PGDM & PGPM Admissions 2026

Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024

IBSAT 2025-ICFAI Business School MBA/PGPM 2026

IBSAT 2025-Your gateway to MBA/PGPM @ IBS Hyderabad and 8 other IBS campuses | Scholarships worth 10 CR

  1. The complex conjugate of (a+ ib) is (a- ib).

CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download Now

CAT Previous Years Questions On Complex Numbers

Q1. CAT 2023 complex numbers Questions and Answers are given below:

If z is a complex number, then the minimum value of |z- 1| + |z + 1| is ______.

[Based on MBA Entrance Exams]

CAT complex numbers problems with solutions are given below:

Solution:

If z = a+ ib

Then, |z- 1| = a-12+b2

and |z + 1| = a+12+b2

|z- 1| + |z + 1| = a-12+b2 + a+12+b2

This value is minimum if either a= 1 and b =0 or a =0 and b = 1

So, the minimum value of |z- 1| + |z + 1| = 2.

Q2. Complex numbers Questions with solutions are given below:

If the cube roots of unity are 1, ω, ω2, then find the roots of the equation (x − 1)3 + 64 = 0. where ω = 3-1 [Practice Question]

Complex numbers system problems with answer for CAT exam are given below:

Solution:

(x − 1)3 = −64 ⇒ x − 1 = (−64)1/3

x − 1 = −4, −4ω, −4ω2

x = −3, 1 − 4ω, 1 − 4ω2

CAT Exam Important Topic: Strategy to Prepare “Complex Numbers” for CAT exam 2023 ( important complex number questions).

Find the CAT tips and tricks for complex numbers Questions below:

  1. i4k = 1 (where k is a positive integer)

  1. Learn algebra of complex numbers

Addition: N1= a1+ ib1; N2 = a2+ ib2; N1+ N2 = (a1+a2) +i(b1+ b2)

Subtraction: N1= a1+ ib1; N2 = a2+ ib2; N1- N2 = (a1-a2) +i(b1- b2)

Multiplication: N1 x N2 = (a1a2 + b1b2) + i(a1b2 + b1a2)

Division: N1/ N2 = (a1+ ib1)/(a2+ ib2)

  1. Less frequently asked in the CAT Exam. Do not waste much time. Keep this topic for last.

  1. Practice Previous years questions to get familiar with the types of questions being asked.

CAT entrance exam: Prerequisite to complex numbers questions

  1. Basics of the number system

  2. Imaginary Numbers

References to Study (Theory) complex numbers

  1. NCERT Class 11

  2. TriOsEducate: YouTube (https://www.youtube.com/watch?v=CwxDoiXb1D0)

References to Practice complex numbers questions for CAT exam

Study sources of Complex Numbers Questions for CAT Exam are given below:

  1. How to Prepare Quantitative Aptitude by Arun Sharma (7th Edition)

  2. ( https://www.youtube.com/watch?v=VlEwd_dq-9s&t=2920s)

  3. Practice Sample Papers

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

All the important tips of the calendar should be covered by the aspirants and for the aspirants Calendar reasoning questions with solutions are given below. Aspirants can also download calendar questions pdf and calendar reasoning questions pdf for more practice and references

CAT 2023 Syllabus Topic: Strategy to prepare “Concept of Calendar” and Calendar Aptitude Questions for CAT Exam

Important Concept/Formula Used in Calendar Questions for CAT Preparation

The concepts used in CAT calendar questions are given below:

  1. Concept of odd days Number of days divided by 7 and the remainder is odd days.

XAT- Xavier Aptitude Test 2026

75+ years of legacy | #1 Entrance Exam | Score accepted by 250+ BSchools | Apply now

Symbiosis MBA - SNAP 2025

1 Exam accepted by 17 Top Symbiosis Institutes for 29 MBA programmes.

  1. Concept of leap year

  • Any year (Not multiple of 100) divisible by 4

  • Any year (multiple of 100) divisible by 400

  1. Concept of finding a day on a given date.

  1. Repetition of Calendar

  • Ordinary year after every 11 years (few exceptions)

  • Leap year after every 28 years (few exceptions)

CAT Calendar questions From CAT Previous Years Papers

Q1. CAT calendar questions are given below:

Given that 27th February 2003 is Thursday. What was the day on 27th February 1603? [CAT 2016]

  1. Monday

  2. Thursday

  3. Sunday

  4. Tuesday

Answer: [2]

After every 400 years, the calendar repeats itself. So, the answer is Thursday.

Q2. Calendar aptitude questions are given below:

Today is Monday. After 73 days, it will be [SNAP Sample Question]

  1. Thursday

  2. Friday

  3. Saturday

  4. Sunday

Calender reasoning questions with solutions are given below:

Ans: [1]

Divide 73 by 7, then odd days are 3.

So, 3 days after Monday will be Thursday.

Tips/Tricks for CAT on calendar based CAT questions

Tips and tricks: Calendar Questions for CAT Preparation are given below:

  1. An ordinary year starts with and end on the same day.

  2. A leap year-end with a day after it starts.

  3. Odd days in a week is ‘0’.

  4. A century can not end on Tuesday, Thursday or Saturday.

  5. After every 400 years the calendar repeats.

  6. Practice separately each kind of question.

  7. Practice previous years questions from various MBA entrance Exams to get an idea of the pattern of questions being asked.

CAT entrance exam: Prerequisite to calendar reasoning questions

  1. Knowledge of reading a calendar

  2. Basics Calculations

CAT study material: References to Study (Theory) Concept of Calendar

  1. R S Agrawal

  2. Rodha

  3. (https://www.youtube.com/watch?v=fnGRCej5qUw)

CAT study material: References to Practice ( calendar questions for CAT preparation)

Study sources of calendar aptitude questions for CAT exam are given below:

  1. MBA Entrance Previous years Papers and Sample Papers.

  2. Unacademy CAT

  3. (https://www.youtube.com/results?search_query=calendars+for+CAT+Exam)

Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Statement and Conclusions” (Critical Reasoning) for CAT-2023

Important Concept of CAT Statement and Conclusions questions

The concepts used in Statement and Conclusions CAT questions are given below:

The question has three parts

Statement + Question+ Options (Conclusions)

Statement: A statement is a formal account of certain facts, views or situations in words.

Conclusions:

  • No degree of assumptions
  • It is derived
  • It is not an opinion
  • It should not be forced

CAT Practice Questions on Statements and Conclusions (critical reasoning questions for CAT)

Question 1: Statements and Conclusions (critical reasoning questions for CAT) are given below:

Read the passage and answer the questions based on it. (CAT 2017)

Typewriters are the epitome of a technology that has been comprehensively rendered obsolete by the digital age. The ink comes off the ribbon, they weigh a ton, and second thoughts are a disaster. But they are also personal, portable and, above all, private. Type a document and lock it away and more or less the only way anyone else can get it is if you give it to them. That is why the Russians have decided to go back to typewriters in some government offices, and why in the US, some departments have never abandoned them. Yet it is not just their resistance to algorithms and secret surveillance that keeps typewriter production lines - well one, at least - in business (the last British one closed a year ago). Nor is it only the nostalgic appeal of the metal body and the stout well-defined keys that make them popular on eBay. A typewriter demands something particular: attentiveness. By the time the paper is loaded, the ribbon tightened, the carriage returned, the spacing and the margins set, there's a big premium on hitting the right key. That means sorting out ideas, pulling together a kind of order and organising details before actually striking off. There can be no thinking on screen with a typewriter. Nor are there any easy distractions. No online shopping. No urgent emails. No Twitter. No need even for electricity - perfect for writing in a remote hideaway. The thinking process is accompanied by the encouraging clack of keys, and the ratchet of the carriage return. Ping!

Question. Which one of the following best describes what the passage is trying to do?

  1. It describes why people continue to use typewriters even in the digital age.

  2. It argues that typewriters will continue to be used even though they are an obsolete technology.

  3. It highlights the personal benefits of using typewriters.

  4. It shows that computers offer fewer options than typewriters.

Ans: [1]

Explanation:

The author is trying to explain:

why the typewriter continues to be used even in today's digital age. For this, he has given reasons that typewriters are personal and private and cannot be hacked. These can be used anywhere without the requirement of electricity.

Q2. CAT exam 2023 statements and Conclusions questions with solutions are given below:

Comprehension: [CAT 2018]

[The] Indian government [has] announced an international competition to design a National War Memorial in New Delhi, to honour all of the Indian soldiers who served in the various wars and counter-insurgency campaigns from 1947 onwards. The terms of the competition also specified that the new structure would be built adjacent to the India Gate – a memorial to the Indian soldiers who died in the First World War. Between the old imperialist memorial and the proposed nationalist one, India’s contribution to the Second World War is airbrushed out of existence.

The Indian government’s conception of the war memorial was not merely absent-minded. Rather, it accurately reflected the fact that both academic history and popular memory have yet to come to terms with India’s Second World War, which continues to be seen as little more than mood music in the drama of India’s advance towards independence and partition in 1947. Further, the political trajectory of the postwar subcontinent has militated against popular remembrance of the war. With partition and the onset of the India-Pakistan rivalry, both of the new nations needed fresh stories for self-legitimisation rather than focusing on shared wartime experiences.

However, the Second World War played a crucial role in both the independence and partition of India. . . . The Indian army recruited, trained and deployed some 2.5 million men, almost 90,000 of which were killed and many more injured. Even at the time, it was recognised as the largest volunteer force in the war. . . .

India’s material and financial contribution to the war was equally significant. India emerged as a major military-industrial and logistical base for Allied operations in Southeast Asia and the Middle East. This led the United States to take considerable interest in the country’s future and ensured that this was no longer the preserve of the British government.

Other wartime developments pointed in the direction of India’s independence. In a stunning reversal of its long-standing financial relationship with Britain, India finished the war as one of the largest creditors to the imperial power.

Such extraordinary mobilization for war was achieved at a great human cost, with the Bengal famine the most extreme manifestation of widespread wartime deprivation. The costs on India’s home front must be counted in millions of lives.

Indians signed up to serve on the war and home fronts for a variety of reasons. . . . [M]any were convinced that their contribution would open the doors to India’s freedom. . . . The political and social churn triggered by the war was evident in the massive waves of popular protest and unrest that washed over rural and urban India in the aftermath of the conflict. This turmoil was crucial in persuading the Attlee government to rid itself of the incubus of ruling India. . . .

Seventy years on, it is time that India engaged with the complex legacies of the Second World War. Bringing the war into the ambit of the new national memorial would be a fitting – if not overdue – recognition that this was India’s War.

Question: In the first paragraph, the author laments the fact that

  1. the new war memorial will be built right next to India Gate.
  2. there is no recognition of the Indian soldiers who served in the Second World War.
  3. funds will be wasted on another war memorial when we already have the India Gate memorial.
  4. India lost thousands of human lives during the Second World War

Ans: [2]

In the first paragraph, the author says that ‘India’s contribution to the second world war is airbrushed out of existence.’ This means, there is no recognition of the Indian soldiers’ contribution to the second world war.

Tips and Tricks for Statement and Conclusions questions for CAT exam 2023

  1. Conclusions are not generalised.

  2. Conclusions have to be “No exception at all”.

  3. Understand the difference between Inference and Conclusion

  4. Rephrase the question in your words.

  5. Generally, indirect questions are asked in CAT Exam (generally in the RCs). So, Practice different RCs appeared in CAT Exam.

  6. Practice questions daily (Fewer questions but daily)

CAT 2023: Prerequisite to Statement and Conclusions

  1. Knowledge of basic components of statements and arguments.

  2. Reading Skills.

References to Study (Theory) Statement and Conclusions for CAT

  1. How to Prepare for Verbal Ability and Reading Comprehension for CAT | 9th Edition Book by Arun Sharma and Meenakshi Upadhyay

  2. Rodha (YouTube: https://www.youtube.com/watch?v=EL9hYXQteUU)

References to Practise CAT Questions on Statement and Conclusions

  1. Verbal Reasoning by Disha Experts (kindle)

  2. Unacademy CAT4MBA

  3. (https://www.youtube.com/watch?v=p1KwwOjk-zI)


Short Tricks to Solve Complex Number Questions in CAT

Complex number questions in the CAT exam often appear in the Quantitative Aptitude section and can be solved quickly with the right approach. Here are six effective tricks to simplify your preparation:

1. Use i2=−1i^2 = -1i2=−1 Efficiently
Always reduce powers of iii using:

  • i1=ii^1 = ii1=i,

  • i2=−1i^2 = -1i2=−1,

  • i3=−ii^3 = -ii3=−i,

  • i4=1i^4 = 1i4=1.

Repeat this cycle to simplify powers of iii instantly.

2. Convert to Polar Form When Multiplying
For multiplication or division of complex numbers, convert them to polar form:
z=r(cos⁡θ+isin⁡θ)z = r(\cos \theta + i \sin \theta)z=r(cosθ+isinθ).
Use De Moivre’s Theorem to handle powers and roots easily.

3. Use Conjugates to Simplify Divisions
To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator to eliminate the imaginary part from the denominator.

4. Apply Modulus for Distance-Based Questions
Use modulus ∣z∣=x2+y2|z| = \sqrt{x^2 + y^2}∣z∣=x2+y2 for any complex number z=x+iyz = x + iyz=x+iy. This is helpful in geometry-based or coordinate format questions.

5. Visualise on the Argand Plane
Plotting complex numbers on the Argand plane (real vs. imaginary axes) can simplify addition, subtraction, and understanding geometrical relationships like collinearity or symmetry.

6. Use Properties of Roots of Quadratic Equations
If a quadratic equation has complex roots, use the identity:
If zzz is a root, the conjugate zˉ\bar{z}zˉ is also a root. This helps in quickly identifying missing roots or verifying options.

CAT Syllabus: Subjects & Chapters
Select your preferred subject to view the chapters

Short Tricks to Solve Calendar Puzzles Questions in CAT

Calendar-based puzzles in CAT test logical reasoning and date-based calculations. With smart shortcuts, you can solve them quickly and accurately. Here are six effective tricks to tackle calendar questions with ease:

1. Memorise Odd Days of Each Month
Know how many odd days each month contributes:

Jan: 3, Feb: 0/1 (non-leap/leap), Mar: 3, Apr: 2, etc.
Use this to calculate the day of the week efficiently.

2. Use the “Odd Days” Concept for Day Calculations
Total days ÷ 7 = Quotient + Remainder
The remainder gives the odd days, which determine the day of the week. For example, 3 odd days after Sunday means Wednesday.

3. Learn Century Code Tricks
Each century has a fixed code:

  • 1600s: 6, 1700s: 4, 1800s: 2, 1900s: 0, 2000s: 6.
    This helps in quickly determining the base weekday for any date.

4. Zeller’s Rule Shortcut
Use Zeller’s Congruence Formula for exact day calculation, or its simplified version if you're comfortable with modular arithmetic.

5. Check Leap Year Pattern
A year is a leap year if divisible by 4 (but not 100 unless also divisible by 400). This affects February and must be considered in day calculations.

6. Use Date Reversal Logic
Some puzzles ask about days like “what day is it 100 days from now?” Quickly find the remainder when divided by 7 and count forward using odd days logic.


Practice, stay focused, and we'll be back tomorrow with Day 55 CAT Preparation Tips.

Thank You. All the Best!

Frequently Asked Questions (FAQs)

Q: Why are complex numbers important for CAT preparation?
A:

Complex numbers are frequently tested in the Quantitative Aptitude section. Questions may involve basic properties, powers of i, conjugates, and modulus

Q: How can previous year's questions (PYQs) help me with the reasoning section of CAT?
A:

PYQs help you understand the sorts of questions that have previously been asked, as well as their degree of complexity. Solving these will give you an idea of what to anticipate and help you prepare for similar critical thinking questions on the CAT Exam.

Q: How can I answer the complex number and Calendar Questions quickly?
A:

Here are some useful tips. For complex numbers, concentrate on learning crucial formulae and learning shortcuts to save time. For calendar questions, master particular strategies such as determining the day of the week for a given date. Regular practice will help you become more efficient and accurate.

Q: How can I distinguish between Complex Numbers and Quadratic Equations?
A:

Many candidates mix up complex numbers with quadratic equations. To prevent misunderstanding, review each subject independently and understand their distinct features. Practice answering a lot of questions for more clarity.

Q: Why is this topic important for the CAT exam?
A:

Complex numbers are those that have both real and imaginary parts. Complex number problems on the CAT examine your knowledge of equations and mathematics. Knowing this subject may help you answer difficult problems quickly, which is critical for scoring well.

Q: What are Complex Numbers?
A:

In mathematics, a complex number is an element of a number system that extends the real numbers with a particular element labeled i, known as the imaginary unit, and satisfies the equation; every complex number may be represented in the form a+bi, where a, and b are real numbers.   

Articles
|
Certifications By Top Providers
Online MBA Business Analytics
Via Centre for Distance and Online Education, Anna University, Chennai
Corporate Law
Via National Law University, New Delhi
The Science and Business of Biotechnology
Via Massachusetts Institute of Technology, Cambridge
Online MBA
Via Centre for Distance and Online Education, Anna University, Chennai
Management of Commercial Banking
Via Indian Institute of Technology Kharagpur
Strategic Management
Via Indian Institute of Management Bangalore
Udemy
 703 courses
Edx
 467 courses
Swayam
 236 courses
Emeritus
 231 courses
Explore Top Universities Across Globe
University of Essex, Colchester
Wivenhoe Park Colchester CO4 3SQ
Oxford Brookes University, Oxford
Headington Campus Oxford OX3 0BP UK
Northumbria University, Newcastle City Campus
Sutherland Building, Northumberland Road, Newcastle-upon-Tyne, NE1 8ST
Cardiff Metropolitan University, Cardiff
Llandaff Campus, Western Avenue, Cardiff, CF5 2YB
University of Reading, Reading
Whiteknights PO Box 217 Reading Berkshire RG6 6AH
Bristol Baptist College, Bristol
The Promenade, Clifton Down, Bristol BS8 3NJ

Questions related to CAT

On Question asked by student community

Have a question related to CAT ?

Hello Aspirant,

Since your payment status shows "S" , it means your payment is successful. The "payment unsuccessful" message on the form is likely a temporary system error or a delay in updating.

Do not make another payment.

Making a second payment could cause a double debit, which is difficult to get a refund for. You should:

  1. Wait 24-48 hours for the status to update automatically.

  2. Download and save a copy of your form and a screenshot of the "S" payment status as proof.

  3. Check your bank statement to confirm the money has been debited.

  4. If the issue is not fixed after 48 hours, contact the official CAT helpdesk immediately with your transaction details.

Hello

The CAT 2025 exam is a national-level MBA entrance test for IIMs and top B-schools in India. It will be held on 30th November 2025 in computer-based mode across ~170 cities.
The registration is open from 1st August to 13th September 2025 on iimcat.ac.in .
Admit cards will be available from 5th November 2025 onward.
Graduates with at least 50 marks (45 for SC/ST/PwD) are eligible to apply.
The exam tests English, Reasoning, and Quantitative Aptitude in three timed sections.

Yes, you can pursue an MBA at Babasaheb Bhimrao Ambedkar University (BBAU), Lucknow, through the CAT exam.

Eligibility Criteria:

  • Educational Qualification: A bachelor's degree with at least 50% marks (45% for SC/ST/PwD candidates) from a recognized university.

  • Entrance Exam: A valid CAT score is required for admission.

Admission Process:

  1. Application: Register online through the BBAU admission portal.

  2. Entrance Exam: Appear for the CAT exam and obtain a valid score.

  3. Counseling: Shortlisted candidates will be called for counseling based on their CAT scores.

  4. Document Verification: Submit necessary documents for verification.

  5. Fee Payment: Complete the fee payment to confirm admission.

Course Details:

  • Duration: 2 years (full-time).

  • Specializations: Finance, Marketing, Human Resource Management, among others.

Placement Opportunities:
BBAU has a strong placement record, with top companies recruiting MBA graduates.

For more details and to apply, visit the  official BBAU MBA admission page

Hello Amgothu

With 305 marks in ICAR PG and being from ST category, your chances of getting an AIEEA (CAT) seat is good, especially in plant sciences and less competitive subjects