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CAT 2025 Slot 2 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2025 Slot 2 (IIM Kozhikode, 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 2025 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Kozhikode 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: 1 November 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 2025 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 2025 Slot 2QAGeometry • CirclesHard
Two tangents drawn from a point PP touch a circle with center OO at points QQ and RR. Points AA and BB lie on PQPQ and PRPR , respectively, such that ABAB is also a tangent to the same circle. If ∠\angle AOB = 50∘50^\circ , then ∠\angle APB , in degrees, equals
TITA Answer:
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Question 2 of 22
CAT 2025 Slot 2QANumber Systems • Integral SolutionsHard
Suppose a,b,ca,b,c are three distinct natural numbers, such that 3ac=8(a+b)3ac = 8(a+b). Then, the smallest possible value of 3a+2b+c3a+2b+c is
TITA Answer:
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Question 3 of 22
CAT 2025 Slot 2QAAlgebra • Progression & SeriesModerate
Let ana_n be the nthn^{th} term of a decreasing infinite geometric progression. If a1+a2+a3=52a_1+a_2+a_3 = 52 and a1a2+a2a3+a3a1=624a_1a_2+a_2a_3+a_3a_1 = 624 , then the sum of this geometric progression is
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Question 4 of 22
CAT 2025 Slot 2QAArithmetic • Mean, Median & ModeModerate
The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is
TITA Answer:
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Question 5 of 22
CAT 2025 Slot 2QANumber Systems • Integral SolutionsHard
If mm and nn are integers such that (m+2n)(2m+n)=27(m+2n)(2m+n) = 27 , then the maximum possible value of 2m−3n2m-3n is
TITA Answer:
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Question 6 of 22
CAT 2025 Slot 2QAArithmetic • Ratio, Proportion & VariationModerate
The ratio of expenditures of Lakshmi and Meenakshi is 2:32:3 , and the ratio of income of Lakshmi to expenditure of Meenakshi is 6:76:7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4:94:9 , then the ratio of their incomes is
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Question 7 of 22
CAT 2025 Slot 2QAArithmetic • Time, Speed & DistanceModerate
Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is
TITA Answer:
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Question 8 of 22
CAT 2025 Slot 2QAGeometry • PolygonsModerate
Let ABCDEFABCDEF be a regular hexagon and PP and QQ be the midpoints of ABAB and CDCD , respectively. Then, the ratio of the areas of trapezium PBCQPBCQ and hexagon ABCDEFABCDEF is
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Question 9 of 22
CAT 2025 Slot 2QANumber Systems • MiscellaneousModerate
The sum of digits of the number (625)65×(128)36(625)^{65} \times (128)^{36} , is
TITA Answer:
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Question 10 of 22
CAT 2025 Slot 2QAArithmetic • Time & WorkModerate
Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is
TITA Answer:
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Question 11 of 22
CAT 2025 Slot 2QAAlgebra • IndicesModerate
If 9x2+2x−3−4(3x2+2x−2)+27=09^{x^2+2x-3} - 4\left(3^{x^2+2x-2}\right) + 27 = 0 , then the product of all possible values of xx is
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Question 12 of 22
CAT 2025 Slot 2QANumber Systems • FactorisationHard
The number of divisors of (26×35×53×72)(2^6 \times 3^5 \times 5^3 \times 7^2) , which are of the form (3r+1)(3r+1) , where rr is a non-negative integer, is
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Question 13 of 22
CAT 2025 Slot 2QAModern Math • LogarithmsHard
If log⁡64x2+log⁡8y+3log⁡512(y z)=4\log_{64} x^2 + \log_8 \sqrt{y} + 3\log_{512}\left(\sqrt{y}\,z\right) = 4 , where x,yx, y and zz are positive real numbers, then the minimum possible value of (x+y+z)(x+y+z) is
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Question 14 of 22
CAT 2025 Slot 2QAAlgebra • Minima & MaximaModerate
If a,b,ca,b,c and dd are integers such that their sum is 46, then the minimum possible value of (a−b)2+(a−c)2+(a−d)2(a-b)^2 + (a-c)^2 + (a-d)^2 is
TITA Answer:
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Question 15 of 22
CAT 2025 Slot 2QAArithmetic • Mixture & AlligationModerate
A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is
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Question 16 of 22
CAT 2025 Slot 2QAArithmetic • Profit & LossHard
An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs.
110
The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to
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Question 17 of 22
CAT 2025 Slot 2QAArithmetic • PercentagesEasy
A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is
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Question 18 of 22
CAT 2025 Slot 2QAAlgebra • PolynomialsHard
The equations 3x2−5x+p=03x^2 - 5x + p = 0 and 2x2−2x+q=02x^2 - 2x + q = 0 have one common root. The sum of the other roots of these two equations is
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Question 19 of 22
CAT 2025 Slot 2QAArithmetic • Simple & Compound InterestModerate
A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is
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Question 20 of 22
CAT 2025 Slot 2QAAlgebra • ModulusModerate
The set of all real values of xx for which (x2−∣x+9∣+x)>0(x^2 - |x + 9| + x) > 0 , is
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Question 21 of 22
CAT 2025 Slot 2QAAlgebra • FunctionsModerate
Let f(x)=x(2x−1)f(x) = \dfrac{x}{(2x-1)} and g(x)=x(x−1)g(x) = \dfrac{x}{(x-1)}. Then, the domain of the function h(x)=f(g(x))+g(f(x))h(x) = f(g(x)) + g(f(x)) is all real numbers except
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Question 22 of 22
CAT 2025 Slot 2QAGeometry • TrianglesHard
In a △\triangle ABC , points DD and EE are on the sides BCBC and ACAC , respectively. BEBE and ADAD intersect at point TT such that AD:AT=4:3AD:AT = 4:3 , and BE:BT=5:4BE:BT = 5:4. Point FF lies on ACAC such that DFDF is parallel to BEBE. Then, BD:CDBD:CD is
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Frequently Asked Questions about CAT 2025 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2025 Slot 2 QA?

CAT 2025 Slot 2 QA contained 22 questions convened by IIM Kozhikode. 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 2025 Slot 2 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the high difficulty (calculation-intensive dilr, complex modern math).

Can I practice other sections of CAT 2025 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 6 QsCAT Number Systems PYQs 4 QsCAT Geometry PYQs 3 QsCAT Circles Geometry & Tangents Questions 1 QCAT Logarithms & Exponential Equations Questions 1 Q