CAT 2022 Slot 2 Quantitative Aptitude Full Paper Solutions | Easy Explanations & Video Tutorials
- Anshu Agarwal
- Sep 15
- 6 min read
📌 Introduction
Preparing for CAT is never just about solving questions—it’s about solving them fast and smart. In this blog, I have provided the complete solutions for CAT 2022 Slot 2 Quantitative Aptitude section, explained in the simplest possible way.
Along with written explanations, you’ll also find exclusive video tutorials for each question, so you can learn the concepts more deeply and master the shortcuts.
👉 Whether you are targeting CAT 2025 or CAT 2026, going through these questions will help you understand the exam pattern, improve accuracy, and build confidence.
🎯 Why These Solutions Are Helpful?
Step-by-Step Clarity – Each question is broken down into easy steps.
Shortcut Methods – Learn how to solve in seconds during the actual exam.
Video Tutorials – Visual explanation for better understanding.
Exam Relevance – Designed for future aspirants (CAT 2025, CAT 2026).
📝 CAT 2022 Slot 2 Quantitative Aptitude – Question-wise Solutions
Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is:
(a) 12
(b) 18
(c) 20
(d) 24
On day one, there are 100 particles in a laboratory. On day n, where n ≥ 2, one out of every n particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals:
(a) 16
(b) 18
(c) 19
(d) 17
The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is:
(a) √8
(b) √6
(c) √7
(d) √5
The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is:
(a) 1200
(b) 1420
(c) 1480
(d) 1440
Let f(x) be a quadratic polynomial in x such that f(x) ≥ 0, for all real numbers x. If f(2) = 0 and f(4) = 6, then f(−2) is equal to:
(a) 12
(b) 24
(c) 36
(d) 6
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For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is:
(a) 7
(b) 4
(c) 8
(d) 9
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is:
Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is:
(a) 24
(b) 22
(c) 20
(d) 21
There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is:
(a) 4:5
(b) 5:4
(c) 5:6
(d) 6:5
In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is:
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If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is:
(a) 3
(b) 4.5
(c) 4
(d) 3.5
The number of integer solutions of the equation
Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals:
Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be:
(a) 4300
(b) 4400
(c) 4350
(d) 4200
The number of distinct integer values of n satisfying
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Let r and c be real numbers. If r and −r are roots of 5x³ + cx² − 10x + 9 = 0, then c equals:
(a) −9/2
(b) −4
(c) 4
(d) 9/2
The average of a non-decreasing sequence of N numbers a₁, a₂, …, aₙ is 300. If a₁ is replaced by 6a₁, the new average becomes 400. Then, the number of possible values of a₁ is:
Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) − 1 = 0 and g(x) = x². If f(x² − x) = 5, then the value of the sum f(g(5)) + g(f(5)) is:
Consider the arithmetic progression 3, 7, 11, … and Aₙ denote the sum of the first n terms of this progression. Then the value of
(a) 415
(b) 455
(c) 404
(d) 442
Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is:
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In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC = 45° and ∠ABC = θ, then AD/BE equals:
(a) (sinθ + cosθ)/√2
(b) 1
(c) √2 cosθ
(d) √2 sinθ
In an election, there were four candidates and 80% of the registered voters cast their votes. One of the candidates received 30% of the cast votes while the other three candidates received the remaining cast votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was:
(a) 50240
(b) 60288
(c) 40192
(d) 62800
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📚 Related Resources
🙋 About Me
I’m Anshu Agarwal, a 99.97%iler in CAT QA and XAT QA Topper.
Over the years, I have guided thousands of students to crack CAT, XAT, IPMAT, CMAT, and other exams through my video courses, test series, and mentorship programs.
My goal is to make Quant & DILR easy, logical, and exam-focused.
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