Question 1 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationEasy
If $2x + 3 = 7 , what is the value of $x$?
Official Correct Answer: A. Subtract 3 from both sides: $2x = 4$. Divide both sides by 2: $x = 2$. The correct answer is A.
Algebra Practice Hub (QA) • 626 Qs• Official Answer Keys
CAT Algebra Practice Questions & Drills
Extensive Algebra Practice Covering Quadratics, Linear Equations, Functions, Logarithms, Polynomials, and Inequalities with Verified Solutions
626 Total Questions
MCQ: 490 (+3 / -1)
TITA: 136 (0 Negative Penalty)
Core Formulas & Shortcut Matrix: Algebra
Vieta Formulas for QuadraticsFormula #1
\alpha + \beta = - , \quad \alpha \beta = $
Roots of ax^2 + bx + c = 0.
Logarithm Base ChangeFormula #2
\log_b a = $
Crucial for multi-base CAT exponential equations.
Sum of First n Terms of APFormula #3
S_n = $[2a + (n-1)d] = n × \text{Middle Term}
Fastest evaluation using arithmetic symmetry.
Sum of Infinite GP (|r| < 1)Formula #4
S_∞ = $
Standard convergence condition.
Exam Hall Traps & Speedbreakers to Avoid
- •Extraneous roots: Squaring both sides of an equation can introduce false solutions; always substitute back.
- •Modulus boundary points: Forgetting that |x - a| changes signs at x = a.
- •Logarithm Domain restrictions: Ensuring arguments strictly satisfy x > 0 and base b > 0, b \neq 1.
Bite-Sized Practice Sets (28 Modules Available)
Authentic CAT BlueprintSolve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.
24 QuestionsFree Pass
Set 01: Linear Equation
Difficulty: Easy
12 QuestionsFree Pass
Set 02: Inequalities
Difficulty: Easy
24 QuestionsPro Pass
Set 03: Polynomials
Difficulty: Easy
23 QuestionsPro Pass
Set 04: Indices
Difficulty: Easy
25 QuestionsPro Pass
Set 05: Progression & Series
Difficulty: Easy
17 QuestionsPro Pass
Set 06: Functions
Difficulty: Hard
25 QuestionsPro Pass
Set 07: Linear Equation
Difficulty: Moderate
24 QuestionsPro Pass
Set 08: Progression & Series
Difficulty: Hard
22 QuestionsPro Pass
Set 09: Functions
Difficulty: Hard
22 QuestionsPro Pass
Set 10: Quadratic Equations
Difficulty: Easy
24 QuestionsPro Pass
Set 11: Linear Equation
Difficulty: Moderate
21 QuestionsPro Pass
Set 12: Polynomials
Difficulty: Hard
25 QuestionsPro Pass
Set 13: Indices
Difficulty: Easy
22 QuestionsPro Pass
Set 14: Quadratic Equations
Difficulty: Hard
25 QuestionsPro Pass
Set 15: Progression & Series
Difficulty: Easy
25 QuestionsPro Pass
Set 16: Linear Equation
Difficulty: Easy
25 QuestionsPro Pass
Set 17: Indices
Difficulty: Moderate
18 QuestionsPro Pass
Set 18: Quadratic Equations
Difficulty: Hard
25 QuestionsPro Pass
Set 19: Linear Equation
Difficulty: Easy
19 QuestionsPro Pass
Set 20: Polynomials
Difficulty: Hard
20 QuestionsPro Pass
Set 21: Modulus
Difficulty: Easy
18 QuestionsPro Pass
Set 22: Functions
Difficulty: Hard
24 QuestionsPro Pass
Set 23: Progression & Series
Difficulty: Hard
25 QuestionsPro Pass
Set 24: Linear Equation
Difficulty: Easy
19 QuestionsPro Pass
Set 25: Inequalities
Difficulty: Moderate
25 QuestionsPro Pass
Set 26: Quadratic Equations
Difficulty: Moderate
24 QuestionsPro Pass
Set 27: Progression & Series
Difficulty: Easy
24 QuestionsPro Pass
Set 28: Integral Solutions
Difficulty: Hard
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Official Exam Questions & Explanations (25 of 626)
Sorted in official convenor sequenceQuestion 2 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What are the roots of the equation ?
Official Correct Answer: B. Factorize the equation: $(x - 2)(x - 3) = 0$. Roots are $x = 2$ and $x = 3$. The correct answer is B.
Question 3 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationModerate
If and $x - 2y = -4 , what is the value of $x$?
Official Correct Answer: C. Add the equations: $4x = 18$. Divide both sides by 4: $x = 4.5$. The correct answer is C.
Question 4 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
Find the roots of the equation .
Official Correct Answer: D. Simplify the equation: $x^2 - 5x + 6 = 0$. Factorize: $(x - 2)(x - 3) = 0$. Roots are $x = 2$ and $x = 3$. The correct answer is D.
Question 5 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
Find the sum and product of the roots of the equation .
Official Correct Answer: A. Sum of roots = - \frac{b}{a} = - \frac{-7}{3} = \frac{7}{3}$. Product of roots = \frac{c}{a} = \frac{2}{3}$. The correct answer is A.
Question 6 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationEasy
If $2x + 3 = 9 , what is the value of $x$?
TITA Answer:
Official Correct Answer: 3. Subtract 3 from both sides: $2x = 6$. Divide both sides by 2: $x = 3$.
Question 7 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What are the roots of the equation ?
TITA Answer:
Official Correct Answer: 2. Factorize the equation: $(x - 2)^2 = 0$. Root is $x = 2$.
Question 8 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationModerate
If $5x - 7 = 3x + 11 , what is the value of $x$?
TITA Answer:
Official Correct Answer: 9. Subtract $3x$ and add 7 to both sides: $2x = 18$. Divide both sides by 2: $x = 9$.
Question 9 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
Find the roots of the equation .
TITA Answer:
Official Correct Answer: 5, -2. Factorize the equation: $(x - 5)(x + 2) = 0$. Roots are $x = 5$ and $x = -2$.
Question 10 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationHard
If and $x + y = 5 , find the value of $x$.
Official Correct Answer: C. Multiply the second equation by 2: $2x + 2y = 10$. Add this to the first equation: $5x = 24$. So, $x = \frac{24}{5} = 4.8$. The correct answer is C.
Question 11 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
Find the sum and product of the roots of the equation .
Official Correct Answer: A. Sum of roots = - \frac{b}{a} = - \frac{-8}{1} = 8$. Product of roots = \frac{c}{a} = \frac{15}{1} = 15$. The correct answer is A.
Question 12 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationEasy
If $4x + 5 = 21 , what is the value of $x$?
Official Correct Answer: A. Subtract 5 from both sides: $4x = 16$. Divide both sides by 4: $x = 4$. The correct answer is A.
Question 13 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationEasy
If $3x - 5 = 10 , what is the value of $x$?
Official Correct Answer: A. Add 5 to both sides to get $3x = 15$. Then, divide both sides by 3 to get $x = 5$. Therefore, the correct answer is A)
Question 14 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
Which of the following is a solution to the equation ?
Official Correct Answer: A. Factorize the quadratic equation to get $(x-1)(x-3) = 0$. Therefore, $x = 1$ or $x = 3$. The correct answer is A) 1.
Question 15 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationModerate
If and $x + y = 7 , what is the value of $x$?
Official Correct Answer: B. From $x + y = 7 , we get $y = 7 - x$. Substitute $y$ in the first equation to get $2x - 3(7 - x) = 12$. Simplify to get $5x - 21 = 12$ or $5x = 33$. Therefore, $x = 6.6$. The closest integer is 6, hence B) 6.
Question 16 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What is the sum of the roots of the equation ?
Official Correct Answer: D. The sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is - b/a$. Here, $a = 1$ and $b = -8$. Therefore, the sum of the roots is $8$. The correct answer is D) 8.
Question 17 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationHard
If and $5x - 4y = 7 , what is the value of $x + y$?
Official Correct Answer: B. Multiply the first equation by 2 and the second by 1 to get $6x + 4y = 22$ and $5x - 4y = 7$. Add both equations to get $11x = 29$ or $x = 2.636$. Substitute $x$ in the first equation to get $y = 1.364$. Therefore, $x + y = 4$. The closest integer is 4, hence C) 4.
Question 18 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
If the roots of the equation are in the ratio 2:3, what is the value of ?
Official Correct Answer: B. Let the roots be $2a$ and $3a$. By Vieta's formulas, the sum of the roots is $2a + 3a = 5a = 7$. Therefore, $a = 1.4$. The product of the roots is $2a \cdot 3a = 6a^2 = k$. Substitute $a = 1.4$ to get $k = 6 \cdot 1.96 = 11.76$. The closest integer is 12, hence B) 12.
Question 19 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationEasy
If $4x - 5 = 11 , what is the value of $x$?
TITA Answer:
Official Correct Answer: 4. Add 5 to both sides to get $4x = 16$. Then, divide both sides by 4 to get $x = 4$. Therefore, the correct answer is 4.
Question 20 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
If $x^2 - 9 = 0 , what is the value of $x$?
TITA Answer:
Official Correct Answer: -3, 3. Factorize the equation to get $(x - 3)(x + 3) = 0$. Therefore, $x = 3$ or $x = -3$. Hence, the correct answer is -3, 3.
Question 21 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationModerate
If $5x - 7 = 3x + 11 , what is the value of $x$?
Official Correct Answer: A. Subtract $3x$ from both sides to get $2x - 7 = 11$. Add 7 to both sides to get $2x = 18$. Divide both sides by 2 to get $x = 9$. The closest integer is 4, hence A) 4.
Question 22 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What is the product of the roots of the equation ?
Official Correct Answer: D. The product of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $c/a$. Here, $a = 1$ and $c = 21$. Therefore, the product of the roots is $21$. The correct answer is D) 21.
Question 23 of 626
ThinkCAT Practice SetQAAlgebra • Linear EquationHard
If and $5x - 2y = 18 , what is the value of $x + y$?
Official Correct Answer: B. Multiply the first equation by 2 and the second by 4 to get $6x + 8y = 44$ and $20x - 8y = 72$. Add both equations to get $26x = 116$ or $x = 4.46$. Substitute $x$ in the first equation to get $4y = 10$ or $y = 2.5$. Therefore, $x + y = 6.96$. The closest integer is 7, hence B) 7.
Question 24 of 626
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
If the roots of the equation are in the ratio 1:2, what is the value of ?
Official Correct Answer: B. Let the roots be $a$ and $2a$. By Vieta's formulas, the sum of the roots is $a + 2a = 3a = 6$. Therefore, $a = 2$. The product of the roots is $a \cdot 2a = 2a^2 = k$. Substitute $a = 2$ to get $k = 2 \cdot 4 = 8$. The closest integer is 9, hence B) 9.
Question 25 of 626
ThinkCAT Practice SetQAAlgebra • InequalitiesEasy
If $2x - 3 > 5 , what is the minimum possible integer value of $x$?
Official Correct Answer: B. Step 1: Add 3 to both sides to get $2x > 8$. Step 2: Divide both sides by 2 to get $x > 4$. Step 3: The smallest integer greater than 4 is 5, but since the question asks for the minimum possible integer, we choose the next smallest integer, which is 2.
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Frequently Asked Questions about CAT Algebra Practice Questions & Drills
How many Algebra practice questions are in this collection?
This repository contains 626 curated CAT Algebra practice questions organized by subtopic and difficulty (Easy, Moderate, Hard).
What is the historical weightage of Algebra in the CAT exam?
6 to 8 Questions in QA Section (~25–35% of QA weightage). Excelling in Algebra is critical for securing a 99.0+ percentile.
Are these practice questions accompanied by past year CAT questions?
Yes! You can explore verified official past year questions for this section in our dedicated CAT Algebra Previous Year Questions (2017–2025) archive.
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