Question 1 of 22
Any non-zero real numbers such that and , Will satisfy the condition.
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Official Convenor Paper• Convenor Master Key Verified
CAT 2023 Slot 2 QA Questions & Answer Key
Quantitative Aptitude questions from CAT 2023 Slot 2 (IIM Lucknow, Afternoon Session (12:30 PM – 2:30 PM IST); 22 in the exam) with the answer key and step-by-step solutions
Executive Answer & Section Summary
CAT 2023 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Lucknow during the Afternoon Session (12:30 PM – 2:30 PM IST). The section comprised 22 questions administered under a strict 40-minute sectional countdown. Sectional marking adheres to standard CAT conventions: +3 marks for every correct answer, -1 mark penalty for incorrect MCQs, and zero penalty for non-MCQ TITA questions. Securing a 99.0th percentile in this section required approximately 28–31 marks (~10 net correct). The question distribution featured comprehensive quantitative problem sets covering arithmetic (TSD, work, percentages), algebra (quadratics, polynomials, logarithms), and geometry mensuration. All questions in this archive are sourced from official candidate response sheets, cross-verified with the convenor master key, and solved with step-by-step logic proofs on ThinkCAT.
22 Total Questions
MCQ: 15 (+3 / -1)
TITA: 7 (0 Negative Penalty)
CAT Direct Answer Fact Sheet & Citation Summary
Structured Knowledge Graph • Verified Academic Analysis
Updated for CAT 2026: 1 November 2026
Verified Questions
22 Qs
15 MCQ + 7 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)
CAT 2023 Slot 2 QA Answer Key
Correct option (MCQ) or value (TITA) for every question, numbered as in the exam. Full solutions are in the questions below.
Exam Hall Replica
Attempt under official TCS iON 40-Min countdown timer
Experience real test pressure with on-screen virtual calculator, section lockouts, 5-color question palette, and percentile estimation curve.
Official Exam Questions & Explanations (22 of 22)
Sorted in official convenor sequenceMost-searched questions here
- CAT 2023 Slot 2 QA Q1: Any non-zero real numbers x, y such that y \neq 3 and \frac{x}{y}<\fra…
- CAT 2023 Slot 2 QA Q2: For any natural numbers m, n , and k , such that k divides both m+2 n…
- CAT 2023 Slot 2 QA Q3: The sum of all possible values of x satisfying the equations 2^{4x^{2}…
- CAT 2023 Slot 2 QA Q4: Let a , b , m and n be natural numbers such that a > 1 and b > 1. If a…
- CAT 2023 Slot 2 QA Q5: Let k be the largest integer such that the equation (x - 1)^2 + 2kx +…
- CAT 2023 Slot 2 QA Q6: The number of positive integers less than 50 , having exactly two dist…
- CAT 2023 Slot 2 QA Q7: For some positive real number x , if \log_{\sqrt{3}}(x) + \frac{\log_x…
- CAT 2023 Slot 2 QA Q8: Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. P…
- CAT 2023 Slot 2 QA Q9: Minu purchases a pair of sunglasses at Rs. 1000 and sells to Kanu at 2…
- CAT 2023 Slot 2 QA Q10: In a company, 20\% of the employees work in the manufacturing departme…
- CAT 2023 Slot 2 QA Q11: Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters be…
- CAT 2023 Slot 2 QA Q12: The price of a precious stone is directly proportional to the square o…
- CAT 2023 Slot 2 QA Q13: Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounde…
- CAT 2023 Slot 2 QA Q14: Jayant bought a certain number of white shirts at the rate of Rs 1000…
- CAT 2023 Slot 2 QA Q15: If certain amount of money is divided equally among n person, each one…
- CAT 2023 Slot 2 QA Q16: A container has 40 liters of milk. Then, 4 liters are removed from the…
- CAT 2023 Slot 2 QA Q17: A triangle is drawn with its vertices on the circle C such that one of…
- CAT 2023 Slot 2 QA Q18: In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points o…
- CAT 2023 Slot 2 QA Q19: The area of the quadrilateral bounded by the Y - axis, the line x=5 ,…
- CAT 2023 Slot 2 QA Q20: Let both the series a_1, a_2, a_3, \dots and b_1, b_2, b_3 \dots be in…
- CAT 2023 Slot 2 QA Q21: If p^{2}+ q^{2} - 29=2 p q-20=52-2 p q , then the difference between t…
- CAT 2023 Slot 2 QA Q22: Let a_n and b_n be two sequences such that a_n = 13 + 6 (n - 1) and b_…
Question 2 of 22
For any natural numbers , n , and , such that divides both and + 4 must be a common divisor of
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 3 of 22
The sum of all possible values of satisfying the equations , is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 4 of 22
Let and be natural numbers such that and . If , then the largest possible value of is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 5 of 22
Let k be the largest integer such that the equation has no real roots. If y is a positive real number, then the least possible value of is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 6 of 22
The number of positive integers less than , having exactly two distinct factors other than 1 and itself, is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 7 of 22
For some positive real number \log_{ $}(x) + = , then the value of is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 8 of 22
Pipes and are fill pipes while Pipe is a drain pipe of a tank. Pipe empties the full tank in one hour less than the time taken by Pipe to fill the empty tank. When pipes and are turned on together, the empty tank is filled in two hours. If pipes and are turned on together when the tank is empty and Pipe is turned off after one hour, then Pipe takes another one hour and 15 minutes to fill the remaining tank. If Pipe can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe to fill the empty tank is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 9 of 22
Minu purchases a pair of sunglasses at Rs. 1000 and sells to Kanu at profit. Then, Kanu sells it back to Minu at loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs. , then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 10 of 22
In a company, of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 11 of 22
Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 12 of 22
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be . Then, the price of the original precious stone is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 13 of 22
Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 14 of 22
Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was higher than the average cost of all the shirts. He sold all the shirts at a discount of and made a total profit of Rs . If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 15 of 22
If certain amount of money is divided equally among n person, each one receives Rs . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them received less than or equal to Rs . Then, the maximum possible value of is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 16 of 22
A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 17 of 22
A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio . If the radius of the circle is , then the area of the triangle is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 18 of 22
In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 19 of 22
The area of the quadrilateral bounded by the - axis, the line , and the lines , is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 20 of 22
Let both the series and be in arithmetic progression such that the common differences of both the series are prime numbers. If and , then equals
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 21 of 22
If p q , then the difference between the maximum and minimum possible value of is
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
Question 22 of 22
Let and be two sequences such that and for all natural numbers . Then, the largest three digit integer that is common to both these sequences, is
TITA Answer:
⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution
ThinkCAT Pro Season PassFull Exam Access
Unlock All 24 Full-Length Official Mocks & 6,000+ Questions
Get lifetime access to all 2017–2025 past papers in timed exam mode, 3,400+ topic drills, 30 sectional sprints, and predicted IIM cutoffs.
Frequently Asked Questions about CAT 2023 Slot 2 QA Questions & Answer Key
How many questions were asked in CAT 2023 Slot 2 QA?
CAT 2023 Slot 2 QA contained 22 questions convened by IIM Lucknow. Marking was +3 marks for correct answers, -1 for incorrect MCQs, and zero penalty for TITA questions.
What score was required for a 99th percentile in CAT 2023 Slot 2 QA?
Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the high difficulty (heavy number systems, grid logic dilr).
Can I practice other sections of CAT 2023 Slot 2?
Yes! You can explore the full paper or switch directly to DILR, VARC, or QA using the related sectional links below.
Related CAT Papers & Topic Mastery Hubs
Explore other slots, sections, and high-weightage topic collections