Introduction: The Strategic Importance of Quantitative Ability in NIFT 2027
For aspiring designers aiming for the prestigious National Institute of Fashion Technology (NIFT), the General Ability Test (GAT) serves as a critical differentiator. While your creative skills are tested in the CAT, your logical rigor and mathematical precision are evaluated in the GAT. This mock test focuses on Ratio and Proportion, Average, Algebra, and Linear Equations—four pillars that constitute a significant portion of the Quantitative section. Mastering these topics is not just about solving numbers; it is about developing the analytical mindset required for inventory management, scaling designs, and budgeting in the fashion industry. A high score in these sections can drastically improve your overall rank, securing your seat in the top campuses. Let us dive into this challenging mock test designed specifically for the 2027 NIFT pattern.
💡 Pro-Tip for NIFT GAT
Always try to eliminate options first. In NIFT GAT, many algebra and ratio questions can be solved by plugging in the options into the equation rather than solving the full step-by-step method. This saves precious seconds!
Section 1: Ratio and Proportion
1. If A:B = 3:4 and B:C = 8:9, then what is the ratio of A:C?
A) 1:2
B) 2:3
C) 3:2
D) 1:3
2. A sum of Rs. 391 is divided among A, B, and C in the ratio 1/2 : 2/3 : 3/4. What is the share of B?
A) Rs. 102
B) Rs. 136
C) Rs. 153
D) Rs. 120
3. Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new ratio becomes 12:23. What is the smaller number?
A) 27
B) 33
C) 49
D) 55
4. In a mixture of 60 liters, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is:
A) 20 Liters
B) 30 Liters
C) 40 Liters
D) 60 Liters
5. The mean proportional between 0.32 and 0.02 is:
A) 0.08
B) 0.04
C) 0.4
D) 0.8
💡 Ratio Shortcut
When converting fractional ratios to whole numbers, multiply each term by the LCM (Least Common Multiple) of the denominators to simplify the calculation instantly.
Section 2: Averages
6. The average age of a class of 30 students is 15 years. If the age of the teacher is included, the average increases by 1 year. The age of the teacher is:
A) 31 years
B) 46 years
C) 45 years
D) 40 years
7. The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?
A) 2
B) 5
C) 8
D) 10
8. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. What is his average after the 17th inning?
A) 36
B) 39
C) 42
D) 45
9. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
A) 75 kg
B) 85 kg
C) 80 kg
D) 90 kg
10. The average of first five multiples of 3 is:
A) 3
B) 9
C) 12
D) 15
Section 3: Algebra and Polynomials
11. If x + 1/x = 5, then the value of x² + 1/x² is:
A) 25
B) 27
C) 23
D) 20
12. Find the value of k for which the expression x³ + 3x² + 3x + k is exactly divisible by (x + 1).
A) 1
B) -1
C) 0
D) 2
13. If (a – b) = 3 and (a² + b²) = 29, find the value of ab.
A) 10
B) 12
C) 15
D) 18
14. Factorize: x² – 5x + 6. The factors are:
A) (x-1)(x-6)
B) (x-2)(x-3)
C) (x+2)(x+3)
D) (x-5)(x+1)
15. If 2^x = 32, then what is the value of x?
A) 4
B) 5
C) 6
D) 7
Section 4: Linear Equations
16. Five years ago, the age of a father was three times the age of his son. Ten years later, the father will be twice as old as his son. The current age of the father is:
A) 45
B) 50
C) 35
D) 40
17. The sum of two numbers is 45 and their difference is 15. The numbers are:
A) 25, 20
B) 30, 15
C) 35, 10
D) 40, 5
18. In a library, there are two types of books: fiction and non-fiction. The total number of books is 120. If non-fiction books are 20 more than fiction books, how many fiction books are there?
A) 50
B) 70
C) 60
D) 40
19. If 3x + 2y = 13 and 2x + 3y = 12, find the value of x + y.
A) 5
B) 6
C) 4
D) 7
20. The cost of 3 pens and 2 pencils is Rs. 80. If the cost of a pen is Rs. 20, what is the cost of a pencil?
A) Rs. 5
B) Rs. 10
C) Rs. 15
D) Rs. 20
Answer Key & Detailed Explanations
To find A:C when A:B and B:C are given, we multiply the ratios. (A/B) * (B/C) = (3/4) * (8/9). The B’s cancel out. 3/4 * 8/9 = (3*8)/(4*9) = 24/36. Simplifying 24/36 by dividing both by 12 gives us 2/3. Therefore, A:C is 2:3. This method is the fastest way to link chained ratios in GAT exams.
2. Answer: B (Rs. 136)First, find the LCM of the denominators (2, 3, 4), which is 12. Multiply each term by 12: (1/2)*12 : (2/3)*12 : (3/4)*12 = 6 : 8 : 9. The total parts are 6 + 8 + 9 = 23. B’s share is (8/23) * 391. 391 divided by 23 is 17. So, 8 * 17 = 136. This technique of clearing fractions is essential for NIFT math questions involving complex ratios.
3. Answer: B (33)Let the numbers be 3x and 5x. According to the problem, (3x – 9) / (5x – 9) = 12/23. Cross-multiplying: 23(3x – 9) = 12(5x – 9) => 69x – 207 = 60x – 108. Subtracting 60x from both sides gives 9x = 207 – 108 = 99. Thus, x = 11. The smaller number is 3x = 3 * 11 = 33. Many students forget to multiply by ‘x’ at the end; always re-read the final question.
4. Answer: D (60 Liters)Initially, 60 liters is divided in 2:1. Milk = (2/3)*60 = 40L, Water = (1/3)*60 = 20L. Let ‘w’ be the water added. The new ratio is 40 / (20 + w) = 1/2. Cross-multiplying: 80 = 20 + w, so w = 60. You must add 60 liters of water. Mixture problems are common in design exams as they relate to color pigment mixing ratios.
5. Answer: A (0.08)The mean proportional between ‘a’ and ‘b’ is calculated as sqrt(a*b). Here, mean proportional = sqrt(0.32 * 0.02) = sqrt(0.0064). The square root of 64 is 8, and the square root of 0.0064 is 0.08. Mastery of decimals is vital since NIFT often uses them to increase the difficulty level of simple concepts.
6. Answer: B (46 years)Total age of 30 students = 30 * 15 = 450 years. When the teacher is added, there are 31 people and the average is 16. Total age = 31 * 16 = 496 years. Teacher’s age = 496 – 450 = 46 years. A quick shortcut: Teacher’s age = New Average + (Old Count * Change in Average) = 16 + (30 * 1) = 46.
7. Answer: C (8)For any set of ‘n’ consecutive odd or even numbers, the difference between the highest and lowest is always 2(n-1). Here, n=5, so the difference is 2(5-1) = 8. To verify: if the average of 5 numbers is 61, the numbers are 57, 59, 61, 63, 65. 65 – 57 = 8. Using the formula saves significant time during the exam.
8. Answer: B (39)Let the average of 16 innings be ‘x’. Total runs after 16 innings = 16x. Total runs after 17th inning = 16x + 87. New average = (16x + 87)/17 = x + 3. Solving: 16x + 87 = 17x + 51 => x = 36. New average = x + 3 = 39. This type of problem tests your ability to translate verbal scenarios into algebraic expressions.
9. Answer: B (85 kg)Total weight increase = 8 persons * 2.5 kg/person = 20 kg. Since the new person replaced someone weighing 65 kg and increased the total by 20 kg, the new person’s weight = 65 + 20 = 85 kg. Logical deduction is often faster than setting up full algebraic equations for replacement problems.
10. Answer: B (9)The first five multiples of 3 are 3, 6, 9, 12, 15. Average = (3 + 6 + 9 + 12 + 15) / 5 = 45 / 5 = 9. Shortcut: For numbers in an Arithmetic Progression (like multiples), the average is simply the middle term. Here, the middle term is 9.
11. Answer: C (23)Using the identity (x + 1/x)² = x² + 1/x² + 2. Substituting the known value: 5² = x² + 1/x² + 2 => 25 = x² + 1/x² + 2. Therefore, x² + 1/x² = 23. This is a classic algebraic identity question that appears frequently in competitive exams.
12. Answer: A (1)According to the Remainder Theorem, if f(x) is divisible by (x + 1), then f(-1) must be 0. Let f(x) = x³ + 3x² + 3x + k. f(-1) = (-1)³ + 3(-1)² + 3(-1) + k = -1 + 3 – 3 + k = -1 + k. For f(-1) = 0, k must be 1. Understanding polynomials is key for higher-level quantitative logic.
13. Answer: A (10)We know (a – b)² = a² + b² – 2ab. Substituting values: 3² = 29 – 2ab => 9 = 29 – 2ab. Rearranging: 2ab = 29 – 9 = 20. Thus, ab = 10. Manipulating standard identities is a required skill for the NIFT Algebra section.
14. Answer: B (x-2)(x-3)To factorize x² – 5x + 6, we need two numbers that multiply to 6 and add up to -5. These numbers are -2 and -3. So, x² – 2x – 3x + 6 = x(x – 2) – 3(x – 2) = (x – 2)(x – 3). This is a fundamental skill for solving quadratic equations.
15. Answer: B (5)32 can be written as a power of 2: 2 * 2 * 2 * 2 * 2 = 32, which is 2^5. If the bases are the same (2^x = 2^5), then the exponents must be equal. Therefore, x = 5. Index and surd problems test your basic numerical comfort.
16. Answer: B (50)Let current ages of Father and Son be F and S. 5 years ago: (F-5) = 3(S-5) => F – 3S = -10. 10 years later: (F+10) = 2(S+10) => F – 2S = 10. Subtracting the first equation from the second: (F – 2S) – (F – 3S) = 10 – (-10) => S = 20. Plugging S=20 into F – 2S = 10: F – 40 = 10, so F = 50. Age problems are staples of linear equation testing.
17. Answer: B (30, 15)Let the numbers be x and y. x + y = 45 and x – y = 15. Adding the two equations: 2x = 60, so x = 30. Substituting x=30 in x+y=45 gives y=15. You can also verify this by checking which option fits both conditions (summing to 45 and having a gap of 15).
18. Answer: A (50)Let fiction be ‘f’ and non-fiction be ‘n’. n + f = 120 and n = f + 20. Substitute the second into the first: (f + 20) + f = 120 => 2f + 20 = 120 => 2f = 100, so f = 50. Non-fiction would be 70. Always ensure you are solving for the correct variable requested in the question.
19. Answer: A (5)Add the two equations: (3x + 2y) + (2x + 3y) = 13 + 12 => 5x + 5y = 25. Divide the entire equation by 5: x + y = 5. This is a common pattern where adding equations yields the answer directly without needing to find individual values for x and y.
20. Answer: B (Rs. 10)Let pen be ‘x’ and pencil be ‘y’. 3x + 2y = 80. Since x = 20, 3(20) + 2y = 80 => 60 + 2y = 80 => 2y = 20, so y = 10. Simple substitution is a frequent task in the arithmetic section of the GAT.
Need More Guidance for NIFT 2027?
Preparing for NIFT requires more than just solving questions; it requires a strategy. If you have doubts about these problems or need personalized mentoring for your entrance journey, our experts are here to help!
💬 Chat with our Experts on WhatsApp (+91 9526806124)
