CAT 2024 Slot 2 Quantitative Aptitude Questions with Video Solutions [Complete Analysis]
- Anshu Agarwal
- 4 days ago
- 7 min read
Updated: 9 hours ago
CAT 2024 Slot 2 Quantitative Aptitude: Full Questions + Video Solutions
If you’re preparing for CAT 2025, there’s no better way to strengthen your concepts than by solving actual CAT questions. In this blog, we bring you the complete list of questions from CAT 2024 Slot 02 Quantitative Aptitude section, along with video solutions by Anshu Agarwal Sir — known for his 99.97%ile in CAT QA and XAT QA Topper.
Whether you struggled with arithmetic, algebra, geometry, or modern math, this post has you covered!
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📌 What You’ll Find in This Blog:
✅ All 22 questions from CAT 2024 Slot 2 QA
📹 HD Video Solutions by Anshu Sir
📈 Strategy to handle tricky CAT QA questions
⏱️ Time-saving tips and alternate methods
👉 Anshu Agarwal Sir’s teaching combines deep conceptual clarity with real CAT strategy, trusted by toppers and beginners alike.
🔢 CAT 2024 Slot 2 QA Questions with Solutions
Each question is followed by a detailed YouTube video explanation.
1. The roots α, β of the equation 3x² + λx − 1 = 0, satisfy 1/α² + 1/β² = 15.
The value of (α³ + β³)² is:
(a) 1
(b) 4
(c) 9
(d) 16
Short Explanation [If required]
2. A function f maps the set of natural numbers to whole numbers, such that:
f(xy) = f(x)f(y) + f(x) + f(y) for all x, y,
and f(p) = 1 for every prime number p.
Then, the value of f(160000) is:
(a) 8191
(b) 2047
(c) 4095
(d) 1023
Short Explanation [If required]
3. If a, b, c are positive real numbers such that:
a > 10 ≥ b ≥ c,
and
[log₈(a + b)] / [log₂(c)] + [log₂₇(a − b)] / [log₃(c)] = 2/3,
then the greatest possible integer value of a is:
Short Explanation [If required]
4. If x and y are real numbers such that:
4x² + 4y² − 4xy − 6y + 3 = 0,
then the value of (4x + 5y) is:
Short Explanation [If required]
5. Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch 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:
(a) 4 + 2√3 : 1
(b) 4 + √3 : 1
(c) 2 + √3 : 1
(d) 7 + 4√3 : 1
Short Explanation [If required]
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6. The sum of the infinite series
[1/5 × (1/5 − 1/7)] + (1/5)² × [(1/5)² − (1/7)²] + (1/5)³ × [(1/5)³ − (1/7)³] + ⋯ is equal to:
(a) 5/408
(b) 5/816
(c) 7/408
(d) 7/816
7. 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:
(a) 4 : 5
(b) 5 : 3
(c) 5 : 4
(d) 3 : 5
Short Explanation [If required]
8. If m and n are natural numbers such that n > 1, and mⁿ = 2²⁵ × 3⁴⁰, then the value of
m − n equals:
(a) 209942
(b) 209947
(c) 209932
(d) 209937
9. 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 the perimeter of ABCD is 6 cm, then the perimeter (in cm) of ∆AEB is:
(a) 8
(b) 9
(c) 7
(d) 10
10. The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10).
Then the radius of the incircle of the triangle is:
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11. 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:
(a) 5 : 4
(b) 4 : 3
(c) 2 : 1
(d) 3 : 2
12. 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:
Short Explanation [If required]
13. When 3³³³ is divided by 11, the remainder is:
(a) 5
(b) 6
(c) 1
(d) 10
14. Bina incurs 19% loss when she sells a product at ₹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:
15. All the values of x satisfying the inequality:
1⁄(x + 5) ≤ 1⁄(2x − 3) are:
(a) −5 < x < 3⁄2 or 3⁄2 < x ≤ 8
(b) x < −5 or x > 3⁄2
(c) x < −5 or 3⁄2 < x ≤ 8
(d) −5 < x < 3⁄2 or x > 3⁄2
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16. 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 ₹ 40000, of the last 30 employees was ₹ 60000, and of the first 10 and last 10 employees together was ₹ 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
(a) ₹95000
(b) ₹85000
(c) ₹80000
(d) ₹90000
Short Explanation [If required]
17. If √(x + 6√2) ¹ᐟ² − √(x − 6√2) ¹ᐟ² = 2√2 then x equals:
18. 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:
(a) 7:00 pm
(b) 9:00 pm
(c) 10:30 pm
(d) 7:30 pm
Short Explanation [If required]
19. 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
Short Explanation [If required]
20. Anil invests ₹ 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
(a) 20808
(b) 20860
(c) 20480
(d) 20640
Short Explanation [If required]
21. 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:
Short Explanation [If required]
22. If x and y satisfy the equations |x| + x + y = 15 and x + |y| − y = 20, then (x − y) equals:
(a) 15
(b) 10
(c) 20
(d) 5
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