Algebra Marathon: Every CAT Algebra Question Solved | CAT 2025 | 2IIM

Описание: Algebra Marathon: Every CAT Algebra Question Solved | 2IIM

Watch us solve every single Algebra question that appeared in CAT 2024 in one continuous marathon. This session is a deep dive into how to approach Algebra inside the Quant section — from spotting patterns to handling tough questions under time pressure.

If you are preparing for CAT 2025 or CAT 2026, this video will give you a clear picture of how Algebra appears in the exam and how to tackle it effectively. Learn the methods, mindset, and strategies that can push your percentile higher.

Algebra is a crucial part of CAT Quant, and going through past year questions is one of the most effective ways to prepare. This marathon is designed to make you exam-ready.
0:00 – Introduction
0:06 – CAT 2024 – Slot 1
0:17 – Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A with f(a) = b. Find the total number of such functions.
5:19 – If x is a positive real number such that 4 log base 10 of x + 4 log base 100 of x + 8 log base 1000 of x = 13, then find the greatest integer not exceeding x.
7:18 – Find the sum of all real values of k for which (18)^k × (132768)^(13) = 18 × (132768)^(1/k).
9:52 – Suppose x1, x2, x3, …, x100 are in arithmetic progression such that x5 = −4 and 2x6 + 2x9 = x11 + x13. Find the value of x100.
11:44 – For any natural number n, let An be the largest integer not exceeding the square root of n. Find the value of A1 + A2 + ⋯ + A50.
14:26 – Let x, y, and z be real numbers satisfying 4(x² + y² + z²) = a and 4(x − y − z) = 3 + a. Find the value of a.
19:50 – If the equations x² + mx + 9 = 0, x² + nx + 17 = 0 and x² + (m + n)x + 35 = 0 have a common negative root, then find the value of (2m + 3n).
22:53 – If (a + b√n) is the positive square root of (29 − 12√5), where a and b are integers, and n is a natural number, then find the maximum possible value of (a + b + n).
28:47 – A shop sells grains as follows: It sells half the quantity plus an additional three kilograms to the first customer. Then it sells half of the remaining quantity plus three kilograms to the second customer. Finally, it sells half of what is left plus three kilograms to the third customer, leaving nothing.
Find the initial quantity of grains in kilograms.
30:55 – In the XY-plane, find the area of the region defined by the inequalities y greater than or equal to x + 4 and −4 less than or equal to x² + y² + 4(x − y) less than or equal to 0.
35:42 – CAT 2024 – Slot 2
35:45 – If x and y satisfy |x| + x + y = 15 and x + |y| − y = 20, then find (x − y).
38:45 – Find all values of x that satisfy the inequality 1/x + 5 less than or equal to 1/(2x) − 3.
40:51 – If a, b and c are positive real numbers such that a greater than 10, b less than or equal to 10, and b greater than or equal to c, and [log base 8 of (a + b)] / [log base 2 of c] + [log base 27 of (a − b)] / [log base 3 of c] = 2/3, then find the greatest possible integer value of a.
44:16 – If √(x + 6√2) − √(x − 6√2) = 2√2, then find x.
46:12 – A function f maps 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. Find f(160000).
52:09 – The roots α and β of 3x² + λx − 1 = 0 satisfy (1/α² + 1/β²) = 15. Find the value of (α³ + β³)².
57:29 – If x and y are real numbers such that 4x² + 4y² − 4xy − 6y + 3 = 0, then find the value of (4x + 5y).
1:00:26 – If m and n are natural numbers such that n greater than 1 and m^n = 2^25 × 3^40, then find m − n.
1:02:07 – When Rajesh’s age was equal to Garima’s present age, their age ratio was 3 : 2. When Garima’s age becomes equal to Rajesh’s present age, what will be the ratio of their ages?
1:03:44 – Evaluate 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
1:05:44 – CAT 2024 – Slot 3
1:05:48 – For constants p, k and a, consider the system of linear equations: px − 4y = 2 and 3x + ky = a. Find the necessary condition for the system to have no solution.
1:07:11 – Consider the sequence t1 = 1, t2 = −1, and tn = ((n − 3)/(n − 1)) × tn−2 for n ≥ 3. Find the value of 1/t2 + 1/t4 + 1/t6 + ⋯ + 1/t2022 + 1/t2024.
1:10:26 – If (a + b√3)² = 52 + 30√3, where a and b are natural numbers, then find a + b.
1:11:58 – Find the number of distinct real values of x satisfying max{x, 2} − min{x, 2} = |x + 2| − |x − 2|.
1:15:56 – If 3^a = 4, 4^b = 5, 5^c = 6, 6^d = 7, 7^e = 8 and 8^f = 9, then find the value of the product abcdef.
1:18:24 – For any non-zero real number x, let f(x) + 2f(1/x) = 3x. Find the sum of all possible values of x for which f(x) = 3.
1:21:57 – Find the sum of all distinct real values of x that satisfy the equation 10^x + 4^(10x) = 8^(1/2).
1:24:37 – Find the number of distinct integer solutions (x, y) of the equation |x + y| + |x − y| = 2. (edited)