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CAT 2024 Slot 1 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2024 Slot 1 (IIM Calcutta, Morning Session (8:30 AM – 10:30 AM IST); 22 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2024 Slot 1 Quantitative Aptitude (QA) was conducted by IIM Calcutta during the Morning Session (8:30 AM – 10:30 AM 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 2024 Slot 1 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 1QANumber Systems • RemainderEasy
When 1010010^{100} is divided by 7, the remainder is
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Question 2 of 22
CAT 2024 Slot 1QAArithmetic • Time, Speed & DistanceHard
Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
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Question 3 of 22
CAT 2024 Slot 1QAArithmetic • Mean, Median & ModeModerate
There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is
TITA Answer:
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Question 4 of 22
CAT 2024 Slot 1QAModern Math • Permutation & CombinationModerate
The sum of all four-digit numbers that can be formed with the distinct non-zero digits a,b,c,a, b, c, and dd , with each digit appearing exactly once in every number, is 153310+n153310 + n , where nn is a single digit natural number. Then, the value of (a+b+c+d+n)(a + b + c + d + n) is
TITA Answer:
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Question 5 of 22
CAT 2024 Slot 1QAArithmetic • Ratio, Proportion & VariationEasy
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8:6:58 : 6 : 5. They rent a house together, and Kamal pays 15%15\% , Amal pays 12%12\% and Vimal pays 18%18\% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%,12%10\% , 12\% and 15%15\% , respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to
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Question 6 of 22
CAT 2024 Slot 1QAArithmetic • Simple & Compound InterestModerate
An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
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Question 7 of 22
CAT 2024 Slot 1QAAlgebra • PolynomialsModerate
If the equations x2+mx+9=0,x2+nx+17=0x^2 + mx + 9 = 0 , x^2 + nx + 17 = 0 , and x2+(m+n)x+35=0x^2 + (m + n)x + 35 = 0 have a common negative root, then the value of 2m+3n2m + 3n is
TITA Answer:
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Question 8 of 22
CAT 2024 Slot 1QAModern Math • LogarithmsModerate
If xx is a positive real number such that 4log⁡10x+4log⁡100x+8log⁡1000x=134 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13 , t hen greatest integer not exceeding x , is
TITA Answer:
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Question 9 of 22
CAT 2024 Slot 1QAAlgebra • IdentitiesHard
Let x, y, and z be real numbers satisfying 4(x2+y2+z2)=a4(x−y−z)=3+a4(x^2 + y^2 + z^2) = a 4(x - y - z) = 3+ a Then a equals
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Question 10 of 22
CAT 2024 Slot 1QAGeometry • CirclesHard
In the XY-plane, the area, in sq. units, of the region defined by the inequalities y≥x+4y \geq x+4 and −4≤- 4 \leq x2+y2+4(x−y)≤0x^{2} + y^{2} + 4(x-y) \leq 0 is
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Question 11 of 22
CAT 2024 Slot 1QAArithmetic • Mixture & AlligationEasy
A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is
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Question 12 of 22
CAT 2024 Slot 1QAAlgebra • FunctionsModerate
Consider two sets A={2,3,5,7,11,13}A = \{2, 3, 5, 7, 11, 13\} and B={1,8,27}B = \{1, 8, 27\}. Let ff be a function from AA to BB such that for every element bb in BB , there is at least one element aa in AA such that f(a)=bf(a) = b. Then, the total number of such functions ff is
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Question 13 of 22
CAT 2024 Slot 1QAGeometry • SolidsHard
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is
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Question 14 of 22
CAT 2024 Slot 1QAArithmetic • Profit & LossModerate
The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
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Question 15 of 22
CAT 2024 Slot 1QAAlgebra • Linear EquationEasy
A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
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Question 16 of 22
CAT 2024 Slot 1QAAlgebra • IdentitiesHard
If (a+bn)(a+b\sqrt{n}) is the positive square root of (29−125)(29-12\sqrt{5}) , where aa and bb are integers, and nn is a natural number, then the maximum possible value of (a+b+n)(a+b+n) is
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Question 17 of 22
CAT 2024 Slot 1QAGeometry • TrianglesModerate
ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of in circle of △\triangleADE is
TITA Answer:
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Question 18 of 22
CAT 2024 Slot 1QAArithmetic • Ratio, Proportion & VariationModerate
A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 :
2
After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3:
2
The total number of unsold fruits is
TITA Answer:
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Question 19 of 22
CAT 2024 Slot 1QAAlgebra • IndicesModerate
The sum of all real values of kk for which (18)k×(132768)13=(18)×(132768)1k\small \left( \dfrac{1}{8} \right)^k \times \left( \dfrac{1}{32768} \right)^{\frac{1}{3}} = \left( \dfrac{1}{8} \right) \times \left( \dfrac{1}{32768} \right)^{\frac{1}{k}} is
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Question 20 of 22
CAT 2024 Slot 1QAAlgebra • Progression & SeriesModerate
Suppose x1,x2,x3,…,x100x_{1}, x_{2}, x_{3}, \ldots, x_{100} are in arithmetic progression such that x5=−4x_{5}=-4 and 2x6+2x9=x11+x132 x_{6}+2 x_{9}=x_{11}+x_{13} , Then, x100x_{100} equals
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Question 21 of 22
CAT 2024 Slot 1QAArithmetic • Time & WorkModerate
Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
TITA Answer:
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Question 22 of 22
CAT 2024 Slot 1QANumber Systems • MiscellaneousModerate
For any natural number nn , let ana_{n} be the largest integer not exceeding n\sqrt{n}. Then the value of a1+a2+….+a50a_{1}+a_{2}+\ldots .+a_{50} is
TITA Answer:
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Frequently Asked Questions about CAT 2024 Slot 1 QA Questions & Answer Key

How many questions were asked in CAT 2024 Slot 1 QA?

CAT 2024 Slot 1 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 1 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the moderate difficulty (straightforward algebra, standard dilr grids).

Can I practice other sections of CAT 2024 Slot 1?

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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