The CAT 2023 QA Slot 2 question paper was part of the exam conducted by IIM Lucknow on November 26, 2023, with the afternoon slot running from 12:30 PM to 2:30 PM. The Quantitative Aptitude (QA) section carried 22 questions to be solved in a 40-minute sectional limit, for a total of 66 marks at 3 marks per question. Around 8 of the 22 questions were TITA (type-in-the-answer), so you faced no negative marking on those, while the 14 MCQs followed +3/-1 scoring. As per the official Collegedunia note, this QA section was rated moderate to difficult, with lengthier and more calculation-heavy questions than the previous year. On this page you can read every question with a fully worked solution and download the complete solved paper PDF.
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CAT 2023 Slot 2 QA Questions with Solutions
For any natural numbers \(m\), \(n\), and \(k\), such that \(k\) divides both \(m + 2n\) and \(3m + 4n\), \(k\) must be a common divisor of
The sum of all possible values of \(x\) satisfying the equation \(2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0\), is
Any non-zero real numbers \(x, y\) such that \(y ≠ 3\) and \(\frac{x}{y}<\frac{x+3}{y-3}\), will satisfy the condition
Let \(a, b, m\) and \(n\) be natural numbers such that \(a >1\) and \(b >1\) . If \(a^m+b^n = 144^{145}\) , then the largest possible value of \(n − m\) is
Let \(k\) be the largest integer such that the equation \((x-1)^2+2kx+11=0\) has no real roots. If \(y\) is a positive real number, then the least possible value of \(\frac{k}{4y}+9y\) is
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
For some positive real number \(x\) , if \(log_{\sqrt 3}(x)+\frac{log_x(25)}{log_x(0.008)}=\frac{16}{3}\), then the value of \(log_3(3x^2)\) is
Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is
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
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
Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
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 288000. Then, the price of the original precious stone is
In a company, 20% 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
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
If a certain amount of money is divided equally among n persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of n is
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 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
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 a:b. If the radius of the circle is r, then the area of the triangle is
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
The area of the quadrilateral bounded by the \(Y\) -axis, the line \(x = 5\) , and the lines \(|x-y|-|x-5|=2\), is
If \(p^2+q^2-29=2pq-20=52-2pq\) , then the difference between the maximum and minimum possible value of \((p^3-q^3 ) \)is
Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) be in arithmetic progression such that the common differences of both the series are prime numbers. If \(a_5=b_9,a_{19}=b_{19}\) and \(b_2=0\) , then \(a_{11}\) equals
Let \(a_n\) and \(b_n\) be two sequences such that \(a_n=13+6(n-1)\) and \(b_n=15+7(n-1)\) for all natural numbers \(n\) . Then, the largest three digit integer that is common to both these sequences, is
CAT 2023 QA Slot 2 Exam Pattern and Marking Scheme
The QA section in CAT 2023 Slot 2 held 22 questions that you had to clear within a 40-minute sectional time limit, carrying a maximum of 66 marks. Each question was worth 3 marks, and the question types were split between MCQs and TITA questions.
- 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: Of the 22 questions, 14 were multiple-choice questions (MCQs) carrying +3/-1 marking, while around 8 were TITA (type-in-the-answer) questions with +3 and no negative marking, so guessing on TITA questions carried no risk.
CAT 2023 QA Slot 2 Area-Wise Weightage
The 22 questions in CAT 2023 Slot 2 QA were spread across five areas, with Algebra and Arithmetic together accounting for 15 of the 22 questions. The breakdown below shows you where the marks were concentrated so you know which areas to prioritise.
- Algebra: 8 questions, the single largest area, covering quadratic equations, linear equations, modulus, maxima-minima, inequalities and polynomials.
- Arithmetic: 7 questions on simple and compound interest, time and work, time-speed-distance, averages, mixtures and alligations, and profit and loss.
- Geometry and Mensuration: 3 questions drawn from triangles, rectangles, coordinate geometry and parallelograms.
- Modern Maths: 2 questions, mainly on logarithms and sequences and series.
- Number System: 2 questions, focused on indices and the number of factors.
CAT 2023 Slot 2 QA Question Paper Solutions Video
Source: Hritik Raj
How to Use the CAT 2023 QA Slot 2 Solved Paper
This solved paper helps you benchmark your speed and accuracy against the actual CAT 2023 Slot 2 standard. Since only 9 to 10 of the 22 questions were genuinely doable in the time available, smart selection mattered as much as solving ability.
- Attempt all 22 questions in a timed 40-minute sitting before you look at any solution, so you replicate real sectional pressure.
- Prioritise Arithmetic and Algebra first, since these two areas alone offered 15 of the 22 questions and the bulk of the easy marks.
- Use the no-negative TITA questions (around 8 of them) to attempt freely, since a wrong answer costs you nothing.
- Review every worked solution to spot faster methods, because the paper was flagged as lengthy and calculation-heavy.
Good Attempts and Percentile Benchmark
- A good attempt was 10 to 12 questions at roughly 75 to 80 percent accuracy.
- A raw score in the range of 36 to 38 marks was enough to reach around the 99 percentile in QA.
- Clearing 9 to 10 questions accurately put you in a strong position given the moderate-to-difficult rating.
QA Slot 2 Question Paper FAQs
Ques. How many questions were there in the CAT 2023 QA Slot 2 section?
Ans. The QA section in CAT 2023 Slot 2 had 22 questions, to be solved within a 40-minute sectional time limit for a total of 66 marks at 3 marks per question.
Ques. How difficult was the CAT 2023 QA Slot 2 paper?
Ans. As per the official Collegedunia note, the CAT 2023 Slot 2 QA section was rated moderate to difficult. It was tougher than CAT 2022 and a slight step up from Slot 1, with lengthier and more calculation-heavy questions.
Ques. What was the area-wise weightage in CAT 2023 QA Slot 2?
Ans. Algebra led with 8 questions, followed by Arithmetic with 7, Geometry and Mensuration with 3, and Modern Maths and Number System with 2 each, adding up to all 22 questions.
Ques. What is a good score and attempt in CAT 2023 QA Slot 2?
Ans. A good attempt was 10 to 12 questions at about 75 to 80 percent accuracy. A raw score of 36 to 38 marks was enough to reach roughly the 99 percentile in the QA section.
Ques. How is the CAT QA section marked?
Ans. Each question carries 3 marks. MCQs award +3 for a correct answer and deduct 1 for a wrong one, while TITA questions award +3 for a correct answer with no negative marking. Around 8 of the 22 questions were TITA.
Ques. Where can you find official CAT exam information?
Ans. You can check official details about the CAT exam, including the pattern and notifications, on the official website iimcat.ac.in.
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