What are Algebra CAT Questions?
These questions are the most important part of CAT Quant Questions. Considering the previous years' analysis, Algebra CAT Questions carry a good amount of weightage in the CAT Exam. Last year, it was seen that the maximum number of questions were asked from Arithmetic and Algebra topics. The topics for CAT Algebra Questions consist of various sub-topics. Algebra CAT Questions comprise both MCQ as well as Non-MCQ questions. Go through the detailed CAT Syllabus to understand the topics to be covered.
The topics covered in Algebra CAT Questions are mentioned below:
- Inequalities and Modulus
- Functions and Graphs
- Linear and Quadratic Equations
- Algebraic Entities
- Maxima and Minima
The candidates should thoroughly practise the above topics to solve the Algebra CAT Questions.
Weightage of CAT Algebra Questions
The candidates must know how many questions they should practice from each topic under Algebra. The candidates will get an idea about how many questions can be asked from each topic under the Algebra Section. According to CAT Exam Analysis, the weightage of Algebra CAT Questions is given below.
Number Of Questions (Approx)
☛ Also Check: CAT Preparation Strategy for Working Professionals
Algebra Questions for CAT PDF
The Algebra CAT Questions carry maximum weightage under the Quantitative Ability of CAT; therefore, the candidates are suggested to practice as many questions as possible on this topic. The candidates are advised to solve CAT Previous Year Papers and mocks so that they are well-versed with the different patterns of questions asked in this section. Candidates can download the Algebra CAT Questions PDF given below:
Algebra CAT Questions Types
Given below are some of the sample CAT Algebra Questions. The candidates can go through the below given Algebra CAT Questions to score well in the QA. Quant Questions will help you practice and improve the accuracy and speed of solving questions.
The CAT Algebra Questions will give an overview of the type of questions asked on this topic.
Question: For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
X2 – y2 = 0
(x-k)2 + y2 = 1
Given: x ² = y ² and (x − k) ² + y ² = 1
Solving the two equations simultaneously, we get
(x – k) ² + x ² = 1
∴x ² – 2kx + k ² + x ² = 1
∴2x ² – 2kx + (k ² – 1) = 0
If this equation has a unique solution for x, then discriminant = 0
∴4k ² – 8(k ² – 1) = 0
∴8 – 4k ² = 0
∴k ² = 2
Since k is positive, the other solution is ruled out.
Hence k = √2
Question: The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n on the nth day of 2007 (n = 1, 2, 3,…., 100) and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n on the nth day of 2007 (n = 1, 2,…., 365). On which date in 2007 will be prices of these two varieties of tea be equal?
Answer: 20th May
Explanation: Note that the price of Darjeeling tea remains constant after the 100th day (n=100)
If the prices of the two varieties of tea become equal before n=100, then 100 + 0.1 = 89 + 0.15 n
∴n =220, which is not possible. (since n is assumed to be less than 100)
∴The prices of the two varieties will be equal after n =100,
i.e., when the price of Darjeeling tea = 100 + 0.1 x 100 =110
∴ 89 + 0.15 n = 110
∴ n= 140
2007 is not a leap year. Number of days till 30th April 31+ 28 + 31 + 30 = 120
The prices of the two varieties will be equal on 20th May
Question: If a + b + c = 9, a3 + b3 + c3 – 3abc = 1026, then what is the value of ab + bc + ca?
Explanation: Given, a3 + b3 + c3 – 3abc = 1026
We know that x3 + y3 + z3 – 3xyz = (x + y + z)[(x + y + z)2 – 3(xy + yz + zx)]
So, (a + b + c)[(a + b + c)2 – 3(ab + bc +ca)] = 1026
⇒ 9 × [(9)2 – 3(ab + bc + ca)] = 1026
⇒ 81 – 3(ab + bc + ca) = 1029/9
⇒ 3(ab + bc + ca) = 81 – 114 = -33
⇒ ab + bc + ca = -33/3 = -11
Question: If xy = 96 and x2 + y2 = 208, then the value of (x + y) is:
Explanation: xy = 96 and x2 + y2 = 208
We know that (x+y)2 = x2 + y2 + 2xy
(x+y)2 = 208 + 192 = 400
x+y = ±20
How to Solve Algebra Questions for CAT?
To solve Algebra CAT Questions, the candidates must have good knowledge of Arithmetic. Knowledge of basic arithmetic will help the candidates to solve CAT Algebra Questions accurately. Following are some of the tips to prepare for Algebra CAT Questions:
- The candidates can solve Algebra questions perfectly if they have a clear concept of Algebraic Identities.
- The candidates should regularly practice and analyse mocks and previous year's question papers. This will help them to solve Algebra CAT Questions accurately.
- Candidates should have good knowledge of graphs to solve the questions on functions and graphs under Algebra CAT Questions.
Best Books to Prepare Algebra CAT Questions
The candidates often get confused about which books to choose to practice the CAT Algebra Questions. There are a variety of CAT Books available in the market for aspirants who wish to prepare for the Quantitative Ability section of the CAT. The candidates can refer to BYJU'S Exam Prep study notes available on the App for Algebra CAT Questions.