Number System Mock Test for CUET UG GAT 2026 (Based on Latest Exam Pattern)

Introduction: Number System Mock Test for CUET UG GAT 2026

Preparing for the Number System Mock Test CUET UG GAT 2026 exam requires strong conceptual clarity and consistent practice. Among all quantitative topics, the Number System plays a crucial role because it forms the foundation of arithmetic and logical reasoning questions frequently asked in the exam.

A well-structured Number System Mock Test for CUET UG GAT 2026 helps students evaluate their preparation level, improve speed and accuracy, and identify weak areas before the final examination. Regular mock practice also builds confidence and reduces exam anxiety.

This CUET Number System Mock Test is carefully designed according to the latest CUET UG exam pattern, covering important concepts such as:

• Divisibility Rules
• Factors and Multiples
• HCF and LCM
• Remainders
• Prime Numbers
• Even and Odd Numbers
• Simplification
• Number Properties

Whether you are targeting top CUET colleges or aiming to score high percentile in GAT, practicing this mock test will significantly boost your performance.

Start practicing now and move one step closer to your dream university admission.

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Why Number System Mock Tests Are Important for CUET UG GAT 2026

• Improves problem-solving speed
• Enhances accuracy in calculations
• Builds exam confidence
• Identifies weak topics quickly
• Helps understand the latest CUET question pattern
• Boosts chances of scoring high marks in Quantitative Aptitude

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Key Features of This Number System Mock Test

• Based on CUET UG GAT 2026 syllabus
• Includes exam-level MCQs
• Detailed step-by-step solutions
• Covers most expected questions
• Ideal for last-minute revision
• 100% free practice material

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Who Should Practice This Mock Test?

This mock test is perfect for:

• CUET UG 2026 aspirants
• Class 12 students preparing for entrance exams
• Students weak in basic mathematics
• Candidates targeting high scores in GAT
• Beginners who want to strengthen fundamentals

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Exam-Oriented Important Number System MCQs Word Problems (with Step-By-Step Solutions)

Q 4522) The sum of two numbers is 84, and their HCF is 12. How many such pairs are possible?

A. 1
B. 2
C. 3
D. 4

Answer

B. 2

Step-by-Step Solution

Let numbers be:

12x and 12y

So:

12x + 12y = 84

x + y = 7

Possible co-prime pairs:

1 and 6
2 and 5

Total pairs:

2

Q 4523) Find the smallest number that must be added to 156 to make it divisible by 11.

A. 6
B. 7
C. 8
D. 9

Answer

D. 9

Step-by-Step Solution

156 ÷ 11

= 14 remainder 2

Required addition:

11 − 2

= 9

Q 4524) A number when divided by 6 leaves remainder 4. What will be the remainder when the same number is divided by 3?

A. 0
B. 1
C. 2
D. 4

Answer

B. 1

Step-by-Step Solution

Number:

6k + 4

Divide by 3:

6k divisible by 3

So remainder:

4 ÷ 3

= 1

Q 4525) Find the smallest number that must be multiplied by 18 to make it a perfect cube.

A. 3
B. 6
C. 9
D. 12

Answer

D. 12

Step-by-Step Solution

18 = 2¹ × 3²

For cube:

Exponents multiple of 3

Need:

2² × 3¹

= 12

Q 4526) A two-digit number is such that the sum of its digits is 12 and the number formed by reversing the digits is 18 less than the original number. Find the number.

A. 60

B. 65

C. 70

D. 75

Answer: D. 75

Solution

Let digits be:

x (tens)
y (units)

Number:

10x + y

Reversed number:

10y + x

Condition 1:

x + y = 12

Condition 2:

10y + x = 10x + y − 18

9y − 9x = −18

y − x = −2

So:

y = x − 2

Substitute into first equation:

x + (x − 2) = 12

2x − 2 = 12

2x = 14

x = 7

Then:

y = 5

Number:

75

Q 4527) Find the smallest number that must be multiplied by 45 to make it a perfect square.

A. 5
B. 7
C. 9
D. 11

Answer

A. 5

Step-by-Step Solution

45 = 3² × 5¹

Exponent of 5 is odd

Multiply by:

5

Result becomes perfect square.

Q 4528) How many multiples of 7 are there between 50 and 150?

A. 11
B. 13
C. 14
D. 16

Answer

C. 14

Step-by-Step Solution

First multiple:

56

Last multiple:

147

Count:

(147 − 56) ÷ 7 + 1

= 14

Q 4529) Find the greatest three-digit number divisible by 9.

A. 969
B. 979
C. 989
D. 999

Answer

D. 999

Step-by-Step Solution

999 ÷ 9

= 111

So divisible.

Q 4530) Find the smallest number divisible by 15 and 20.

A. 50
B. 60
C. 70
D. 80

Answer

B. 60

Step-by-Step Solution

LCM of:

15 and 20

= 60

Q 4531) A number leaves remainder 5 when divided by 12. What remainder will it leave when divided by 6?

A. 5
B. 9
C. 7
D. 3

Answer

A. 5

Step-by-Step Solution

Number:

12k + 5

Divide by 6:

5 remains remainder.

Q 4532) Find the smallest number divisible by 3, 4, and 5.

A. 58
B. 60
C. 62
D. 70

Answer

B. 60

Q 4533) Which number when divided by 8 gives remainder 7?

A. 63
B. 64
C. 65
D. 66

Answer

A. 63

Step-by-Step Solution

63 ÷ 8

= remainder 7

Q 4534) Find the smallest number divisible by 7 greater than 200.

A. 153
B. 168
C. 198
D. 203

Answer

D. 203

Step-by-Step Solution

200 ÷ 7

= remainder 4

Need:

7 − 4

= 3

200 + 3

= 203

Q 4535) How many factors does 81 have?

A. 2
B. 3
C. 4
D. 5

Answer

D. 5

Step-by-Step Solution

81 = 3⁴

Using formula:

If N=pa, then Number of Factors=(a+1)\text{If } N = p^{a}, \text{ then Number of Factors} = (a+1)If N=pa, then Number of Factors=(a+1)

4 + 1

= 5

Q 4536) Find the smallest number divisible by 11 and 13.

A. 121
B. 132
C. 143
D. 156

Answer

C. 143

Step-by-Step Solution

LCM:

11 × 13

= 143

Q 4537) Find the remainder when 250 is divided by 12.

A. 7
B. 8
C. 9
D. 10

Answer

D. 10

Step-by-Step Solution

12 × 20 = 240

Remainder:

10

Q 4538) Find the smallest number that must be added to 999 to make it divisible by 8.

A. 1
B. 3
C. 5
D. 7

Answer

A. 1

Step-by-Step Solution

999 ÷ 8

= remainder 7

Needed:

1

Q 4539) Problem based on Three Consecutive Even Numbers

The sum of three consecutive even numbers is 84. Find the numbers.

Solution

Let numbers be:

x
x + 2
x + 4

Sum:

x + (x + 2) + (x + 4) = 84

3x + 6 = 84

3x = 78

x = 26

Numbers:

26, 28, 30

Final Answer:

26, 28, and 30

Q 4540) Problem based on Remainder

When a number is divided by 7, the remainder is 3.
What will be the remainder when the same number is divided by 14?

Solution

Let number be:

7k + 3

Divide by 14:

14 = 7 × 2

So:

7k + 3 = 14m + remainder

Since:

3 < 14

Remainder remains:

3

Final Answer:

3

Q 4541) Problem based on: Greatest Three-Digit Number.

Find the greatest three-digit number that is divisible by 8.

Solution

Largest three-digit number:

999

Divide:

999 ÷ 8

= 124 remainder 7

Subtract remainder:

999 − 7

= 992

Final Answer:

992

Q 4542) Problem based on: Perfect Square Condition

Find the smallest number that must be multiplied by 72 to make it a perfect square.

Solution

Prime factorization:

72 = 2³ × 3²

For perfect square:

Exponents must be even

2³ → need one more 2

So multiply by:

2

New number:

72 × 2 = 144

144 = 12²

Final Answer:

2

Q 4543) Problem based on: Digit Sum Divisibility

Find the smallest number that should be added to 785 to make it divisible by 9.

Solution

Sum of digits:

7 + 8 + 5

= 20

Next multiple of 9:

27

Difference:

27 − 20

= 7

Final Answer:

7

Q 4544) Problem based on: Consecutive Numbers with Product

The product of three consecutive numbers is 210.
Find the numbers.

Solution

Prime factorization:

210 = 5 × 6 × 7

These are consecutive numbers.

Final Answer:

5, 6, and 7

Common Word Problem Patterns in Number System

Most exam questions come from:

1. Consecutive numbers
2. Digit reversal problems
3. Remainder problems
4. LCM and HCF applications
5. Perfect square and cube
6. Divisibility conditions
7. Number of factors
8. Greatest or smallest number

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Short Tricks for Number System Problems

Trick 1: Greatest Divisible Number

Greatest number divisible by n:

Largest number − remainder

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Trick 2: Perfect Square Trick

All prime exponents must be even.

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Trick 3: Remainder Shortcut

If:

Number = divisor × quotient + remainder

Then:

Remainder < divisor

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Tips to Score High in Number System for CUET UG

• Learn and revise divisibility rules
• Practice mental math shortcuts
• Focus on remainders and LCM/HCF
• Solve previous year questions regularly
• Attempt mock tests under timed conditions
• Analyze mistakes after every test

Conclusion: Number System Mock Test for CUET UG GAT 2026

The Number System is one of the most scoring and fundamental topics in the CUET UG GAT 2026 examination. Mastering this topic can significantly improve your overall performance in the quantitative section.

By regularly practicing the Number System Mock Test, students can strengthen their mathematical foundation, enhance calculation speed, and gain confidence before the actual exam. Consistent practice not only helps in understanding concepts but also improves time management during the exam.

If you aim to secure admission into a top university through CUET UG 2026, make mock tests a regular part of your preparation strategy. Start practicing today, track your progress, and move closer to achieving your academic goals.

Practice daily, analyze mistakes, and success will follow.

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Frequently Asked Questions (FAQs) – Number System Mock Test for CUET UG GAT 2026

1. Is Number System important for CUET UG GAT 2026?

Yes, the Number System is one of the most important topics in the CUET UG GAT exam. Many quantitative aptitude questions are directly or indirectly based on number system concepts.

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2. How many questions from Number System are asked in CUET UG?

Typically, 2 to 3 questions from the Number System topic can appear in the CUET UG GAT exam, depending on the paper pattern.

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3. What topics are covered in the Number System mock test?

The mock test covers:

• Divisibility rules
• Prime numbers
• Factors and multiples
• HCF and LCM
• Remainders
• Even and odd numbers
• Simplification
• Number properties

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4. How can I improve my score in Number System for CUET?

You can improve your score by:

• Practicing mock tests regularly
• Learning shortcuts and tricks
• Revising formulas frequently
• Solving previous year questions
• Managing time effectively

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5. Are mock tests necessary for CUET UG preparation?

Yes, mock tests are essential because they simulate the real exam environment, improve speed and accuracy, and help identify weak areas before the actual exam.

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6. Where can I practice Number System mock tests for CUET UG 2026?

You can practice free Number System mock tests on educational platforms, coaching websites, and dedicated CUET preparation portals like your own CUET NOW website.

These problems:

• Improve logical reasoning
• Strengthen conceptual clarity
• Prepare for moderate-level CUET questions
• Increase exam confidence
• Help score faster

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