The CAT 2023 QA Slot 3 question paper was part of the third and final slot held on November 26, 2023, conducted by IIM Lucknow, with the evening session running from 4:30 PM to 6:30 PM. The Quantitative Aptitude section carried 22 questions to be solved in a 40-minute sectional window for a total of 66 marks, with each question worth 3 marks. Of the 22 questions, 14 were MCQs (+3 for a correct answer, -1 for a wrong one) and around 8 were TITA questions (+3 for a correct answer, with no negative marking). On this page you can download the full Slot 3 QA paper and work through detailed, step-by-step solutions for every question to see exactly how each answer is reached.
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CAT 2023 Slot 3 QA Questions with Solutions
For a real number \(x\) , if \(\frac{1}{2},\frac{log_3(2^x-9)}{log_34}\), and \(\frac{log_5\bigg(2^x+\frac{17}{2}\bigg)}{log_54}\) are in an arithmetic progression, then the common difference is
Let \(n\) and \(m\) be two positive integers such that there are exactly \(41\) integers greater than \(8^m\) and less than \(8^n\) , which can be expressed as powers of \(2\) . Then, the smallest possible value of \(n +m\) is
For some real numbers \(a\) and \(b\) , the system of equations \(x + y = 4\) and \((a+5)x+(b^2-15)y = 8b\) has infinitely many solutions for \(x\) and \(y\). Then, the maximum possible value of \(ab\) is
If \(x\) is a positive real number such that \(x^8+\bigg(\frac{1}{x}\bigg)^8=47\) , then the value of \(x^9+\bigg(\frac{1}{x}\bigg)^9\) is
A quadratic equation \(x^2+bx+c=0\) has two real roots. If the difference between the reciprocals of the roots is \(\frac{1}{3}\) , and the sum of the reciprocals of the squares of the roots is \(\frac{5}{9}\) , then the largest possible value of \((b+c)\) is
Let n be any natural number such that \(5^{n-1} < 3^{n+1}\) . Then, the least integer value of m that satisfies \(3^{n+1} < 2^{n+m}\) for each such \(n\) , is
The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
A merchant purchases a cloth at a rate of Rs. 100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B . If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is
There are three persons A B, and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg . Instead of D , if person E joins the room, the average weight of the persons in the room increases by 2 kg x . If the weight of E is 12 kg more than that of D , then the value of x is
In 2021, the population was 100000. In 2022 it is decreased by x%. In 2023, it will increase by y%. The population in 2023 is more than that of 2021 and difference between x and y is 10. Minimum population in 2021 was?
Anil mixes cocoa with sugar in the ratio 3: 2 to prepare mixture A , and coffee with sugar in the ratio 7: 3 to prepare mixture B . He combines mixtures A and B in the ratio 2: 3 to make a new mixture C . If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be
Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be
The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is
Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
Let \(ΔABC\) be an isosceles triangle such that \(AB\) and \(AC\) are of equal length. \(AD\) is the altitude from \(A\) on \(BC\) and \(BE\) is the altitude from \(B\) on \(AC\) . If \(AD\) and \(BE\) intersect at \(O\) such that \(∠AOB =105\degree\) , then \(\frac{AD}{BE}\) equals
A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is
In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
The value of \(1+\bigg(1+\frac{1}{3}\bigg)\frac{1}{4}+\bigg(1+\frac{1}{3}+\frac{1}{9}\bigg)\frac{1}{16}+\bigg(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\bigg)\frac{1}{64}+....\),is
Let \(a_n=46+8n\) and \(b_n=98+4n\) be two sequences for natural numbers \(n ≤ 100\) . Then, the sum of all terms common to both the sequences is
Suppose \(f(x,y)\) is a real-valued function such that \(f(3x+2y,2x-5y)=19x\), for all real numbers \(x\) and \(y\) . The value of x for which \(f(x,2x) = 27\) , is
CAT 2023 QA Slot 3 Exam Pattern and Marking Scheme
The QA section in Slot 3 followed the standard CAT 2023 structure: 22 questions, a 40-minute sectional time limit, and 3 marks per question for a maximum of 66 marks. About 8 of the 22 questions were TITA (type-in-the-answer) and the remaining 14 were MCQs, so getting comfortable with both formats is essential before you attempt the paper.
- Total questions: 22 in the Quantitative Ability section
- Section duration: 40 minutes (sectional time limit)
- Total marks: 66 (3 marks per question)
- Marking (MCQ): +3 for a correct answer, -1 for a wrong one
- Marking (TITA): +3 for a correct answer, no negative marking
- Question types: 14 MCQs with four options each and around 8 TITA (non-MCQ) questions where you type the numeric answer; only MCQs carry the -1 negative marking, so the 8 TITA questions are risk-free attempts.
CAT 2023 QA Slot 3 Area-Wise Weightage
The 22 questions in Slot 3 QA were spread across five areas, with Arithmetic carrying the single largest share at 8 questions. Knowing this split helps you decide where to invest your 40 minutes, since clearing the Arithmetic and Algebra blocks alone covered 12 of the 22 questions.
- Arithmetic: 8 questions, the heaviest block, covering Time and Work, Time-Speed-Distance, Averages, Mixtures and Alligations, Percentages, and Profit and Loss.
- Algebra: 4 questions on Quadratic Equations, Linear Equations, Modulus, Maxima-Minima, Inequalities, and Polynomials.
- Modern Maths: 4 questions drawn from Progressions, Permutations and Combinations, and related topics.
- Geometry and Mensuration: 3 questions based on Triangles, Rectangles, and Polygons.
- Number System: 3 questions testing properties of numbers and related fundamentals.
CAT 2023 Slot 3 QA Question Paper Solutions Video
Source: GP Ka Funda
How to Use the CAT 2023 QA Slot 3 Paper
Slot 3 QA was the toughest QA section of CAT 2023, harder than both Slot 1 and Slot 2, with several lengthy, calculation-heavy questions. Treat this paper as a timed mock first and only then study the solutions, so you experience the same pressure that test-takers faced in the 40-minute window.
- Attempt all 22 questions in a single 40-minute sitting before opening any solution, mirroring the real sectional limit.
- Start with the 8 TITA questions, since they carry no negative marking and are free to attempt even if you are unsure.
- Prioritise the 8 Arithmetic questions, the largest block, to lock in marks early before moving to Algebra and Modern Maths.
- After the timed attempt, read the step-by-step solution for every question you skipped or got wrong, and note the exact concept being tested.
Good Attempts and Percentile Benchmark
- Because Slot 3 QA ran tough, solving 9 to 11 questions accurately (around 75-80% accuracy) was considered a strong performance.
- A QA sectional score in the low-to-mid 20s on a 66-mark scale was enough to clear roughly the 90-95 percentile band in this slot.
- Across all three sections, an overall attempt of about 40-48 questions with high accuracy was the typical benchmark for a 99 percentile in CAT 2023.
QA Slot 3 Question Paper FAQs
Ques. How many questions were there in CAT 2023 QA Slot 3 and what was the time limit?
Ans. The QA section in CAT 2023 Slot 3 had 22 questions with a 40-minute sectional time limit. Each question carried 3 marks, for a total of 66 marks.
Ques. What was the marking scheme for the CAT 2023 QA Slot 3 section?
Ans. Every question was worth 3 marks. For the 14 MCQs you got +3 for a correct answer and -1 for a wrong one, while the roughly 8 TITA questions gave +3 for a correct answer with no negative marking.
Ques. How difficult was the QA section in CAT 2023 Slot 3?
Ans. Slot 3 QA was the most difficult QA section across the three CAT 2023 slots, tougher than both Slot 1 and Slot 2, largely because of several lengthy, calculation-heavy questions. Many students found Arithmetic and Algebra the most demanding areas.
Ques. What was a good number of attempts in CAT 2023 QA Slot 3?
Ans. Given the difficulty, attempting 9 to 11 questions with about 75-80% accuracy was considered a good performance in QA Slot 3. A QA score in the low-to-mid 20s out of 66 was generally enough to reach the 90-95 percentile range.
Ques. Which topics had the highest weightage in CAT 2023 QA Slot 3?
Ans. Arithmetic was the heaviest area with 8 of the 22 questions, followed by 4 questions each in Algebra and Modern Maths, and 3 questions each in Geometry and Mensuration and Number System.
Ques. Where can I find the official CAT exam pattern and updates?
Ans. You can check the official exam pattern, notifications, and registration details on the official CAT website at iimcat.ac.in. The page below also lets you download the CAT 2023 QA Slot 3 paper with full solutions for practice.
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