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CAT 2024 Slot 2 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2024 Slot 2 (IIM Calcutta, 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 2024 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Calcutta 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: 14 (+3 / -1)
TITA: 8 (0 Negative Penalty)
Attempt QA Section in Timed 40-Min ModeSolve Questions on this Page

CAT Direct Answer Fact Sheet & Citation Summary

Structured Knowledge Graph • Verified Academic Analysis
Updated for CAT 2026: 31 October 2026
Verified Questions
22 Qs
14 MCQ + 8 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.
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Editorial & Academic Authority: Verified by ThinkCAT Academic & Editorial Council.
Citation Format: ThinkCAT Academic Archive (thinkcat.in)

CAT 2024 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.

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Official Exam Questions & Explanations (22 of 22)

Sorted in official convenor sequence

Most-searched questions here

Question 1 of 22
CAT 2024 Slot 2QAArithmetic • Mean, Median & ModeHard
A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs.
50000
Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was
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Question 2 of 22
CAT 2024 Slot 2QANumber Systems • RemainderEasy
When 33333^{333} is divide by 11, the remainder is
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Question 3 of 22
CAT 2024 Slot 2QANumber Systems • FactorisationModerate
If mm and nn are natural numbers such that n>1n > 1 , and mn=225m^{n}= 2^{25} ×340\times 3^{40} , then m−nm-n equals
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Question 4 of 22
CAT 2024 Slot 2QAArithmetic • Mixture & AlligationEasy
A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
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Question 5 of 22
CAT 2024 Slot 2QAAlgebra • IndicesModerate
If (x+62)12−(x−62)12=22(x+6\sqrt{2})^{\frac{1}{2}} - (x-6\sqrt{2})^{\frac{1}{2}} = 2\sqrt{2}, then xx equals
TITA Answer:
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Question 6 of 22
CAT 2024 Slot 2QAArithmetic • Simple & Compound InterestModerate
Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
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Question 7 of 22
CAT 2024 Slot 2QAArithmetic • Time & WorkHard
Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
TITA Answer:
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Question 8 of 22
CAT 2024 Slot 2QAArithmetic • Time, Speed & DistanceModerate
A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is
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Question 9 of 22
CAT 2024 Slot 2QAAlgebra • FunctionsHard
A function ff maps the set of natural numbers to whole numbers, such that f(xy)=f(x)f(y)+f(x)+f(y)f (xy) = f (x) f (y) + f (x) + f (y) for all x,yx, y and f(p)=1f (p) = 1 for every prime number pp. Then, the value of f(160000)f (160000) is
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Question 10 of 22
CAT 2024 Slot 2QAAlgebra • Progression & SeriesModerate
The sum of the infinite series is 15(15−17)+(15)2((15)2−(17)2)+(15)3((15)3−(17)3)+…\frac{1}{5}\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{5}\right)^{2}\left(\left(\frac{1}{5}\right)^{2}-\left(\frac{1}{7}\right)^{2}\right)+\left(\frac{1}{5}\right)^{3}\left(\left(\frac{1}{5}\right)^{3}-\left(\frac{1}{7}\right)^{3}\right)+\ldots equal to
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Question 11 of 22
CAT 2024 Slot 2QAArithmetic • Profit & LossHard
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
TITA Answer:
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Question 12 of 22
CAT 2024 Slot 2QAArithmetic • Profit & LossModerate
Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is
TITA Answer:
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Question 13 of 22
CAT 2024 Slot 2QAGeometry • CirclesHard
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
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Question 14 of 22
CAT 2024 Slot 2QAAlgebra • ModulusModerate
If x and y are real numbers such that ∣x∣+x+y=15|x| + x + y = 15 and x+∣y∣−y=20x + |y| - y = 20 , then (x−y)(x - y) equals
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Question 15 of 22
CAT 2024 Slot 2QAAlgebra • PolynomialsModerate
The roots α,β\alpha, \beta of the equation 3x2+λx−1=03x^{2} + \lambda x-1=0 , satisfy 1α2+1β2=15\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}=15. The value of (α3+β3)2\left(\alpha^{3} + \beta^{3}\right)^{2} , is
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Question 16 of 22
CAT 2024 Slot 2QAAlgebra • InequalitiesModerate
All the values of x satisfying the inequality 1x+5≤12x−3\frac{1}{x+5} \leq \frac{1}{2 x-3} are
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Question 17 of 22
CAT 2024 Slot 2QAArithmetic • Ratio, Proportion & VariationModerate
When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3:
2
When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
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Question 18 of 22
CAT 2024 Slot 2QAModern Math • Permutation & CombinationHard
P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is
TITA Answer:
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Question 19 of 22
CAT 2024 Slot 2QAGeometry • TrianglesEasy
The coordinates of the three vertices of a triangle are: (1,2),(7,2)(1, 2) , (7, 2) , and (1,10)(1, 10). Then the radius of the in circle of the triangle is
TITA Answer:
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Question 20 of 22
CAT 2024 Slot 2QAModern Math • LogarithmsHard
If a, b and c are positive real numbers such that a>10≥b≥ca > 10 \ge b \ge c and log⁡8(a+b)log⁡2c+log⁡27(a−b)log⁡3c=23\frac{\log_8(a+b)}{\log_2 c} + \frac{\log_{27}(a - b)}{\log_3 c} = \frac{2}{3} , then the greatest possible integer value of a is
TITA Answer:
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Question 21 of 22
CAT 2024 Slot 2QAAlgebra • PolynomialsModerate
If xx and yy are real numbers such that 4x2+4y2−4xy−6y+3=04x^2 + 4y^2 - 4xy - 6y + 3 = 0 , then the value of (4x+5y)(4x + 5y) is
TITA Answer:
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Question 22 of 22
CAT 2024 Slot 2QAGeometry • TrianglesModerate
ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of △AEB\triangle AEB is
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Frequently Asked Questions about CAT 2024 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2024 Slot 2 QA?

CAT 2024 Slot 2 QA contained 22 questions convened by IIM Calcutta. 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 2024 Slot 2 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the moderate to high difficulty (arithmetic heavy, missing-data tables).

Can I practice other sections of CAT 2024 Slot 2?

Yes! You can explore the full paper or switch directly to DILR, VARC, or QA using the related sectional links below.

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Topics in this paper

CAT Arithmetic PYQs 8 QsCAT Algebra PYQs 7 QsCAT Geometry PYQs 3 QsCAT Modern Math PYQs 2 QsCAT Polynomials & Roots of Equations Questions 2 QsCAT Profit, Loss & Discount Questions 2 Qs