NMAT Algebra Questions with Solutions PDF Download Here Section Wise

Overview: Boost your preparation for the NMAT exam with 25+ high-level NMAT algebra questions. Check out the key tips and strategies to solve them easily!

Algebra accounts for approximately 15-20% of the NMAT and typically includes 3-5 questions covering topics such as linear equations, quadratic equations, inequalities, logarithms, sequences, and series. 

Understanding NMAT algebra questions is essential for securing a competitive score and gaining admission to premier B-schools like NMIMS and other top institutions accepting NMAT scores.

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This comprehensive guide provides you with 30 high-difficulty NMAT algebra questions with complete solutions, expert tips to solve algebra problems efficiently, common mistakes to avoid, and proven strategies to maximise your score in this section. 

What are NMAT Algebra Questions?

Algebra is an integral part of the NMAT Quantitative Skills section, which consists of 36 questions to be solved in 52 minutes. 

The algebra component tests your ability to manipulate equations, understand mathematical relationships, and apply logical reasoning to solve complex problems. 

Unlike other MBA entrance exams like CAT or XAT, NMAT algebra questions are considered moderate in difficulty but require speed and accuracy due to the computer-adaptive nature of the exam.

The NMAT exam follows a computer-adaptive pattern, meaning the difficulty of subsequent questions adjusts based on your previous responses. 

Key Features of NMAT Algebra Section 2025

• Weightage: 15-20% of Quantitative Skills section (approximately 3-5 questions out of 36)
• Difficulty Level: Moderate, focusing on application rather than complex computation
• Topics Covered: Linear equations, quadratic equations, inequalities, logarithms, sequences & series (AP/GP), surds and indices, functions, and absolute value
• Time Management: Average 1.44 minutes per question in the Quantitative Skills section
• Scoring: No negative marking; each correct answer contributes to your scaled score (12-120 per section)

25+ High-Difficulty NMAT Algebra Questions with Solutions

Below are 30 carefully crafted high-difficulty algebra questions that mirror the style and complexity of actual NMAT exam questions. These questions cover all major algebra topics tested in NMAT and will help you assess your preparation level.

Question 1: If 3(2x - 5) - 2(3x - 7) = 5x - 1, then find the value of x.

A) 2

B) 3

C) 4

D) 5

Correct Answer: C) 4

Question 2:  The sum of two numbers is 45. If one-third of the first number exceeds one-seventh of the second number by 5, find the larger number.

A) 27

B) 30

C) 33

D) 36
 

Correct Answer: C) 33

Question 3: If (5x - 3)/4 - (3x - 5)/6 = 2x/3 + 1, then x equals:

A) -6

B) -4

C) 4

D) 6

Correct Answer: A) -6

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Question 4: A number consists of two digits whose sum is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.

A) 36

B) 45

C) 54

D) 63
 

Correct Answer: D) 63

Question 5: If 2x + 3y = 12 and 3x + 2y = 13, then find the value of x² + y².

A) 10

B) 13

C) 17

D) 25

Correct Answer: B) 13

Question 6: If one root of the equation x² - 7x + k = 0 is 5, then find the value of k and the other root.

A) k = 10, root = 2

B) k = 12, root = 3

C) k = 10, root = 3

D) k = 12, root = 2

Correct Answer: A) k = 10, root = 2

Question 7: The sum of the roots of the equation 3x² - 9x + 5 = 0 is:

A) 3

B) 9

C) -3

D) 5/3

Correct Answer: A) 3

Question 8: If α and β are roots of x² + 5x + 3 = 0, then find the value of α² + β².

A) 19

B) 21

C) 25

D) 31

Correct Answer: A) 19

Question 9: For what value of k will the equation kx² - 5x + k = 0 have equal roots?

A) ±5/2

B) ±5/3

C) ±5/4

D) ±25/4

Correct Answer: A) ±5/2

Question 10: If one root of x² - kx + 12 = 0 is double the other, then k equals:

A) ±6

B) ±9

C) ±6√2

D) ±3√6

Correct Answer: C) ±6√2

Question 11: Solve: (x - 3)/(x + 2) < 0. The solution set is:

A) x < -2

B) -2 < x < 3

C) x > 3

D) x < -2 or x > 3

Correct Answer: B) -2 < x < 3

Question 12: If 2x - 3 < 5 and 3x + 4 > -5, then x lies in the interval:

A) (-3, 4)

B) (-5, 3)

C) (-3, 5)

D) (-5, 4)

Correct Answer: A) (-3, 4)

Question 14: If x² - 5x + 6 > 0, then:

A) x < 2 or x > 3

B) 2 < x < 3

C) x ≤ 2 or x ≥ 3

D) 2 ≤ x ≤ 3

Correct Answer: A) x < 2 or x > 3

Question 15: If |x - 2| + |x + 3| = 7, then the number of integral values of x is:

A) 5

B) 6

C) 7

D) 8

Correct Answer: C) 7

Question 16: If log₂(x - 3) + log₂(x + 1) = 3, then x equals:

A) 4

B) 5

C) 6

D) 7

Correct Answer: B) 5

Question 17: If log₃x = 2 and log₃y = 4, then log₃(x²y³) equals:

A) 10

B) 14

C) 16

D) 18

Correct Answer: C) 16

Question 18: If logₐb = 2 and logᵦc = 3, then logₐc equals:

A) 5

B) 6

C) 8

D) 9

Correct Answer: B) 6

Question 19: If log₁₀x + log₁₀(x - 3) = 1, then x equals:

A) 3

B) 4

C) 5

D) 6

Correct Answer: C) 5

Question 20: The value of log₅125 + log₅(1/25) is:

A) 0

B) 1

C) 2

D) 3

Correct Answer: B) 1

Question 21: The 10th term of an AP is 52 and the 16th term is 82. Find the 32nd term.

A) 142

B) 152

C) 162

D) 172

Correct Answer: C) 162

Question 22: If the sum of first n terms of an AP is 3n² + 5n, then the common difference is:

A) 3

B) 5

C) 6

D) 8

Correct Answer: C) 6

Question 23: In a GP, if the 3rd term is 24 and the 6th term is 192, then the first term is:

A) 3

B) 4

C) 6

D) 8

Correct Answer: C) 6

Question 24: The sum of an infinite GP with first term 8 and common ratio 1/2 is:

A) 12

B) 14

C) 16

D) 18

Correct Answer: C) 16

Question 25: If the arithmetic mean of two numbers is 13 and their geometric mean is 12, then the numbers are:

A) 8, 18

B) 9, 16

C) 10, 16

D) 12, 14

Correct Answer: A) 8, 18

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Question 26: If f(x) = 2x + 3 and g(x) = x² - 1, then f(g(2)) equals:

A) 7

B) 9

C) 11

D) 13

Correct Answer: B) 9

Question 27: Simplify: √(5 + 2√6) + √(5 - 2√6)

A) 2√2

B) 2√3

C) 2√5

D) 2√6
 

Correct Answer: B) 2√3

Question 28: If 3^(x+2) = 9^(2x-1), then x equals:

A) 2

B) 3

C) 4

D) 5

Correct Answer: A) 2

Question 29: If |x| + x + y = 10 and |y| - y + x = 12, then (x, y) equals:

A) (7, 3)

B) (8, 2)

C) (9, 1)

D) (11, -1)

Correct Answer: D) (11, -1)

Question 30: The number of real solutions of the equation |x² - 4x + 3| = x - 1 is:

A) 0

B) 1

C) 2

D) 3

Correct Answer: C) 2

Tips to Solve NMAT Algebra Questions 2025

Mastering NMAT algebra questions requires more than just knowing formulas—it demands strategic thinking, efficient problem-solving techniques, and consistent practice. Here are expert tips to help you excel in the algebra section:

Master the Fundamentals

Before attempting complex problems, ensure you have a solid grasp of basic algebraic concepts. This includes understanding variables, coefficients, constants, and the properties of equality and inequality. Many students jump to advanced topics without strengthening their foundations, which leads to conceptual gaps.

2. Practice Mental Math and Quick Calculations

The NMAT Quantitative Skills section requires you to solve 36 questions in 52 minutes, giving you an average of less than 1.5 minutes per question. Developing mental math skills can save precious seconds.

3. Use the "Plug-In" Method for Complex Equations

When faced with algebraic word problems or equations with multiple variables, the plug-in method (substituting answer choices) can be highly effective. This approach is particularly useful in NMAT because:

• It saves time on complex algebraic manipulations
• It works well with a multiple-choice format

4. Recognise Common Algebraic Patterns

NMAT frequently tests standard algebraic identities and patterns. Recognising these patterns instantly can significantly reduce solving time

5. Break Down Word Problems Systematically

Algebra word problems are common in NMAT and test your ability to translate verbal statements into mathematical equations. Follow this systematic approach

6. Master Quadratic Equation Shortcuts

Quadratic equations are high-frequency topics in NMAT algebra. Instead of always using the quadratic formula, develop faster approaches

7. Handle Inequalities with Care

Inequality questions require special attention because the rules differ from equations. Common mistakes include forgetting to flip the inequality sign when multiplying or dividing by negative numbers.

Check Now: NMAT 2025 Syllabus in Detail

8. Leverage Logarithm Properties

Logarithm questions appear regularly in NMAT and can be solved quickly if you know the properties.

9. Practice Sequences and Series Formulas

Arithmetic and geometric progressions are moderate-difficulty topics that can yield quick marks if you know the formulas.

10. Time Management Strategy

Given the computer-adaptive nature of NMAT and sectional time limits, effective time management is crucial.

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Mistakes to Avoid While Solving NMAT Algebra Questions 2025

Understanding common mistakes is as important as learning the right techniques. Here are the most frequent errors NMAT aspirants make in the algebra section, as outlined in the NMAT syllabus, along with strategies to avoid them.

1. Sign Errors in Algebraic Manipulation

Incorrectly handling negative signs, especially during distribution or when dealing with subtraction.

2. Misapplying Distributive Property

Assuming that operations distribute over addition/subtraction when they don't.

3. Dividing by Variables Without Considering Zero

Dividing both sides of an equation by a variable expression without checking if it could be zero.

4. Incorrect Handling of Absolute Value

Not considering both positive and negative cases when solving absolute value equations or inequalities.

Read More: NMAT 2025 Admit Card Download Link

5. Forgetting Domain Restrictions

Arriving at solutions that are mathematically invalid due to domain restrictions.

6. Misinterpreting Quadratic Equation Questions

Not understanding what the question asks whether it's the roots themselves, the sum of roots, the product of roots, or the properties of roots

7. Rushing Through Word Problems

Misreading the problem statement or mistranslating verbal relationships into equations

8. Calculation Errors Under Time Pressure

Making arithmetic mistakes when rushing to beat the clock.

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Key Takeaways:

• Focus on high-weightage topics like linear equations, quadratic equations, and logarithms.
• Practice mental math and quick calculations to save time.
• Learn to identify patterns and shortcuts that reduce the time required to solve.
• Analyse your mistakes from mock tests and create an error log
• Maintain a study schedule that covers all algebra topics systematically

Conclusion

Mastering NMAT algebra questions 2025 is a critical component of achieving a competitive score in the Quantitative Skills section.

With algebra comprising 15-20% of the section and covering diverse topics like linear equations, quadratic equations, inequalities, logarithms, and sequences, a strategic and comprehensive approach to preparation is essential.

This guide provides 30 high-difficulty practice questions that mirror the actual NMAT exam format, along with detailed solutions to help you understand the problem-solving process.

Take regular mock tests to familiarise yourself with exam patterns and time management