Algebra

Are you ready to tackle the Algebra section of the Common Admission Test (CAT) with confidence? Welcome to Quantifiers, your one-stop destination for comprehensive CAT exam preparation. In this section, we’ll delve into the concept of Algebra, its pivotal role in the Quantitative Aptitude aspect of the CAT exam, and how our expert guidance can lead you to success.

Understanding Algebra

Algebra may seem like a daunting word, but at its core, it’s all about using symbols and letters to represent numbers and express relationships between them. In the context of the CAT exam, algebraic concepts are applied to solve a variety of quantitative problems, making it an integral part of the test. By mastering algebra, you’ll gain the ability to solve complex equations, inequalities, and word problems efficiently.

Algebra is the backbone of the Quantitative Aptitude section in the CAT exam. You can expect a significant portion of your test to be devoted to algebraic concepts and problem-solving. At Quantifiers, we recognize the importance of algebra in the CAT exam. Our approach to algebraic concepts is geared towards simplifying the learning process and making it accessible to all.

Take our free tests to evaluate your progress in algebra and fine-tune your skills.

Prepare for the CAT exam with Quantifiers, and conquer the algebra section with confidence. Whether you’re a beginner or looking to refine your algebraic skills, we have the resources and support you need to excel in the Quantitative Aptitude segment. Your CAT success story begins here.

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Practice Questions for CAT Algebra with Solutions

1. CAT - Functions

If x is a positive real number then the minimum value of (x + 7) (x + 19)/(x + 3) is:

36

2. CAT - Functions

If f(x) = x– 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. -16

3. CAT - Functions

If 3x + 2 |y| + y = 7 and x + |x| + 3y = 1, then x + 2y is:

(CAT 2021)

1. 8/3

2. -4/3

3. 1

4. 0

4. 0

4. CAT - Functions

Find the range of (x2 + 4x + 8)/(x2 + 4x + 5)

(1,4]

5. CAT - Inequalities

Find the sum of all negative integral values of x where |x – | x – 2 | + 3 | – 4 < 3

-5

6. CAT - Inequalities

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:

24

7. CAT - Inequalities

How many integer values of x will satisfy this (x² – 16|x| + 60) / (x² – 14x + 49) < 0

2 integer value of x

8. CAT - Inequalities

For how many positive integral values of k is (k-11)(k-15)(k − 19)… (k – 99) < 0?

43

9. CAT - Inequalities

The number of integers n that satisfy the inequalities |n -60| < |n-100| < |n-20| is:

(CAT 2021)

19

10. CAT - Inequalities

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

1. 8

11. CAT - Inequalities

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

2. -5 < x < -2 or 3 < x < 9

12. CAT - Inequalities

Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if (CAT 2020)

1. k ≠ 2
2. |k| = 2
3. k = 2
4. |k| ≠ 2

4. |k| ≠ 2

13. CAT - Series (AP & GP)

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?

186

14. CAT - Series (AP & GP)

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

1. 14

15. CAT - Series (AP & GP)

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

-20/7

16. CAT - Series (AP & GP)

If x, y and z are non – zero real numbers and 9x = 16y = 36z Find the value of 5[xz/(xy -yz) ]

10

17. CAT - Series (AP & GP)

If a, b, c are non-zero and 14a = 36b = 84c, then 6b(1/c – 1/a) is equal to:

3

18. CAT - Series (AP & GP)

How many 3 term geometric progressions can be made from the series 1, 3, 32, 33, …… 348?

1152

19. CAT - Logs

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

2.  2 / (A + B - 3)

20. CAT - Logs

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

3. 4 < a < 5

21. CAT - Logs

If log2 [3 + log2 {4 + log4 (x – 1)}] – 2 = 0, then 4x equals: (CAT 2021)

5

22. CAT - Logs

If 5 – log10 √(1 + x) + 4 log10 √(1 – x) = log10 (1/√(1 – x²), then 100x equals

99

23. CAT - Logs

Log (x+3) (x² – x ) < 1

(-3, -2) ∪ (-1, 0) ∪ (1, 3)

24. CAT - Equations

x² + 9x + |K| = 0, roots of this quadratic are integers. How many integral values of K are possible?

9 integral values

25. CAT - Equations

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

90°

26. CAT - Equations

If r a constant such that |x² – 4x – 13| = r has exactly three distinct real roots, then the value of r is
(CAT 2021)

1. 17

2. 18

3. 15

4. 21

1. 17

27. CAT - Equations

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

2. 2

28. CAT - Equations

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

4. 6

29. CAT - Equations

For natural numbers x, y and z, if xy + yz = 19 and yz + xz = 51, then how many such solutions are possible?

30. CAT - Equations

Given that three roots of f(x) = x4 + ax2 + bx + c are 2, – 3 and 5, what is the value of a + b + c?

79

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