Algebra plays a pivotal role in the CAT exam, as it is both foundational and versatile. The questions test your ability to work with variables and equations, which are critical for solving real-world problems. Topics such as linear equations, quadratic equations, inequalities, logarithms, polynomials, and progressions are frequently covered in the exam.
A typical CAT Algebra problem might involve solving systems of equations, simplifying expressions, or analyzing the behavior of functions and graphs. These problems require not just mathematical proficiency but also logical reasoning and time management skills. For instance, quadratic equations often appear with a twist, demanding innovative approaches like factorization or completing the square. Similarly, understanding arithmetic and geometric progressions can help solve pattern-based problems quickly and accurately.
Moreover, Algebra is often integrated with other topics in the Quantitative Ability section. Questions may combine concepts from Geometry, Number Systems, or Probability, testing your ability to link different mathematical ideas. Familiarity with concepts like maxima, minima, and logarithmic relationships can also be advantageous, especially in higher-difficulty questions.
Developing a strategic approach to Algebra involves consistent practice with varied problems and understanding shortcuts or tricks to save time during the exam. As a key area of focus in CAT preparation, mastering Algebra ensures you’re well-equipped to handle its challenges with confidence.
If x is a positive real number then the minimum value of (x + 7) (x + 19)/(x + 3) is:
If f(x) = x2 – 7x and g(x) = x + 3, then the minimum value of f(g(x)) – 3x is
(CAT 2021)
1. -16
2. -15
3. -12
4. -20
1. 8/3
2. -4/3
3. 1
4. 0
Find the range of (x2 + 4x + 8)/(x2 + 4x + 5)
Find the sum of all negative integral values of x where |x – | x – 2 | + 3 | – 4 < 3
Consider the function f(x) = (x + 4) (x + 6) (x + 8) ………….. (x + 98). The number of integers x for which f(x) is less than 0 are:
How many integer values of x will satisfy this (x² – 16|x| + 60) / (x² – 14x + 49) < 0
For how many positive integral values of k is (k-11)(k-15)(k − 19)… (k – 99) < 0?
The number of integers n that satisfy the inequalities |n -60| < |n-100| < |n-20| is:
(CAT 2021)
Consider the pair of equations: x² – xy – x = 22 and y² – xy + y = 34. If x > y, then x – y equals (CAT 2021)
1. 8
2. 6
3. 4
4. 7
f(x) = (x² + 2x -15) /(x² – 7x – 18) is negative if and only if (CAT 2021)
1. x < -5 or 3 < x < 9
2. -5 < x < -2 or 3 < x < 9
3. x < -5 or -2 < x < 3
4. -2 < x < 3 or x > 9
Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if (CAT 2020)
Consider 2 APs 2,6,10……. and 5,12,19………….If S is a set containing the first 100 members of each progression then how many distinct elements are there in S?
Three positive integers x, y and z are in arithmetic progression. If y − x greater than 2 and xyz = 5 (x + y + z), then z − x equals: (CAT 2021)
1. 14
2. 10
3. 8
4. 12
a + b + c + d = 4 All a,b,c,d are integers Find minimum possible value of 1/a + 1/b + 1/c + 1/d
If x, y and z are non – zero real numbers and 9x = 16y = 36z Find the value of 5[xz/(xy -yz) ]
If a, b, c are non-zero and 14a = 36b = 84c, then 6b(1/c – 1/a) is equal to:
How many 3 term geometric progressions can be made from the series 1, 3, 32, 33, …… 348?
If loga30 = A, loga(5/3) = – B and log2 a = 1 /3, then log3 a equals: (CAT 2020)
1. 2/(A + B) – 3
2. 2/(A + B – 3)
3. (A + B)/2 – 3
4. (A + B – 3)/2
For a real number a , if (log15 a + log32 a) / [(log15 a)(log32 a)] = 4 then a must lie in range
1. 3 < a < 4
2. 2 < a < 3
3. 4 < a < 5
4. a > 5
If log2 [3 + log2 {4 + log4 (x – 1)}] – 2 = 0, then 4x equals: (CAT 2021)
If 5 – log10 √(1 + x) + 4 log10 √(1 – x) = log10 (1/√(1 – x²), then 100x equals
Log (x+3) (x² – x ) < 1
x² + 9x + |K| = 0, roots of this quadratic are integers. How many integral values of K are possible?
The equation ax²+bx+c = 0 and 5x²+12x+13 = 0 have a common root where a,b,c are the side lengths of triangles ABC then find Angle C
1. 17
2. 18
3. 15
4. 21
Suppose one of the roots of the equation ax² – bx + c = 0 is 2 + root13, where a, b and c are rational numbers and a is not equal to zero. If b = c³, then |a| equals to: (CAT 2021)
1. 4
2. 2
3. 1
4. 3
Let m and n be positive integers, If x² + mx + 2n = 0 and x² + 2nx + m = 0 have real roots, then the smallest possible value of m+ n is: (CAT 2020)
1. 5
2. 8
3. 7
4. 6
For natural numbers x, y and z, if xy + yz = 19 and yz + xz = 51, then how many such solutions are possible?
Given that three roots of f(x) = x4 + ax2 + bx + c are 2, – 3 and 5, what is the value of a + b + c?
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