Number system comprises of 10 digits (0, 1, 2,3,4,5,6,7,8,9 ).  When these digits are grouped together it becomes a number.

When the value of the digits varies according to their placements it is termed as Place Value, however, when the value of digit remains the same irrespective of its place, it is termed Face Value.  

In the CLAT exam, you can expect 2-3 questions based on this topic. Though it has the least weightage in the exam if prepared well you can get complete marks.

This post shall guide you through different types of numbers, sample number system questions for CLAT 2023, and more.

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Different Types of Numbers

The number system is the easiest topic among others as it includes basic operations and problems. With the help of these basics, you can solve a higher level of application-based problems. 

The following are different types of numbers where you can expect questions in the upcoming exam.

1. Natural Numbers: Positive numbers (1,2,3,4,5,6……) beginning from 1 that can be counted are known as Natural Numbers. These numbers are also known as Positive Integers.
2. Whole Numbers: All the numbers that can be counted including zero ( 0,1,2,3,4….) are known as Whole Numbers.
3. Integers: All the numbers that can be counted (positive and negative) and 0 are Integers. …-3,-2,-1,0,1,2,3…. Positive Integers: Positive numbers including zero 0,1,2,…. Negative Integers: Negative numbers ….-4,-3,-2,-1
4. Rational Number: Number that can be expressed in the format of (a/b) where b≠0 is a rational number. This includes all integers, zero or fraction.
5. Irrational Numbers: Numbers that cannot be expressed in proper (a/b) format are irrational numbers. For eg: π = 1415926535897932384626433832795028… And this value of pi never terminates and we use 3.14 or 22/7 (where 22/7 is an irrational number). That’s why irrational numbers are also known for their recurring property.
6. Even Numbers: Integers (+ve & -ve) that can be divided by 2 are even numbers
7. Odd Numbers: Integers that cannot be divided by 2 are odd numbers
8. Prime Numbers: Positive Integers that have only two factors 1 and itself are Prime numbers. It is advisable to know all 25 prime numbers below 100 i.e., 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 & 97.
9. Composite Number: All the numbers that are not prime are Composite Numbers.
10. Co- Prime Numbers: Two numbers that have HCF as 1 i.e, no other common factor exists between them are called Co- Prime Numbers. Ex: 5 and 24
11. Real Number: All the numbers discussed above come under the umbrella of Real numbers. These numbers can be represented in the number line. 

How to Approach Number System Questions in CLAT 2023?

Most of you might be wondering how can you can solve number system questions quickly in the exam.

Here are a few tips that help you better understand how to solve CLAT Maths Questions in a matter of seconds.

•  The entire question paper includes passages and questions. Hence, it is essential to read the complete passage thoroughly.
• Make sure to understand each and every line before proceeding with answering any question.
• As the question paper trend is changing each year, the exam conducting authority is testing your ability in solving logical questions rather than just formula-based questions. Hence, it is essential to spare at least 1 hour daily for CLAT Maths preparation.
• While doing any calculations in the rough sheet during the exam, make sure to retain them.
• You may require the previous solution to answer the next question since the questions are comprehension-based.

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Sample Number Systems Questions for CLAT 2023

To help you get an idea about the type of questions asked from the number system, we have provided a few questions from the previous year's question papers for CLAT.

Try to practice these regularly to enhance your speed and accuracy in the final exam.

Q. 476 ** 0 is divisible by both 3 and 11. The non zero digits in the hundred's and ten's places are respectively:

1. 7 and 5
2. 8 and 5
3. 4 and 7
4. 7 and 4

Q. What least digit should come in place of # in the 9 digit number 15549#325, for which the number is divisible by 3?

1. 0
2. 1
3. 2
4. Any of these

Q. A 107 digit number is formed by writing first 58 natural numbers next to each other. Find the remainder when number is divided by 8.

1. 6
2. 10
3. 4
4. 9

Q. What is the sum of this series 1 + 1 + 2 + 8 + 3+ 27 + 4 + 64 +_______10 + 1000?

1. 308
2. 3008
3. 3800
4. 3080

Q. What is the sum of first 10 perfect cubes?

1. 3025
2. 5625
3. 1225
4. None of these

Q. If n is a natural number, then the largest number dividing (n³ - n) is:

1. 2
2. 3
3. 6
4. 12

Q. Which temperature is warmer -3°C or 0°C?

1. 0°
2. -3°
3. both (a) and (b)
4. none of these

Q. If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

1. 0
2. 2
3. 1
4. 3

Q. In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:

1. 4236
2. 4306
3. 4336
4. 5336

Q.  Evaluate: 0.54 x 0.54 - 0.46 x 0.46.

1. 0.8
2. .8
3. 0.08
4. 8.08

Q. In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:

1. 4236
2. 4306
3. 4336
4. 5336

Q. The largest four-digit number exactly divisible by each of 12, 15, 18, and 27 is:

1. 9660
2. 9720
3. 9930
4. 9960

Q. Which of the following numbers are divisible by 9?

1. 5016
2. 7954
3. 61853
4. 53024

More Questions on Number System for CLAT 2023

To ease out your preparation, we have provided a few questions on the number system here. Along with these questions, try to solve CLAT Mathematics Quiz every week to test your preparation levels.

1. What should be subtracted from 2016 to make it completely divisible by 19?
2. Find the unit digit of the product (463 * 756 * 414 * 679).
3. Find out the smallest 4 digit number which is divisible by 31?
4. What is the total number of Prime factors in (4⁷ * 7⁵ *11¹¹)
5. What is the nearest natural number to 8488, which is completely divisible by 77?
6. Find out the smallest number to be subtracted from 13501, so that the remainder is divisible by 87.
7. Find out the largest 6 digit number which is divisible by 91?
8. Find out how many numbers between 100 to 1000 are divisible by 6.
9. Find out the value of x for which 7396×51 is divisible by 11? 9?
10. If a number is divided by 56 then the remainder is 29. Find out the remainder if the same number is divided by 8.