# Number System

Numbers are the building blocks of mathematics, and the Number System is the bedrock of your CAT exam preparation. At Quantifiers, we’re here to guide you through this fascinating world, making it not only understandable but also engaging. Join us on an adventure to master the Number System and find your way to CAT exam success!

## Understanding Number System

Before we dive into CAT exam specifics, let’s get comfortable with the Number System. It is like a language of mathematics that encompasses all types of numbers: integers, fractions, decimals, and more. It’s the universal code that allows us to represent and manipulate quantities. So, how does the Number System play into the CAT exam? Here’s why it’s a crucial topic:
• Foundation of Quantitative Aptitude: It is the cornerstone of the Quantitative Aptitude section. It’s the lens through which you’ll view all things numerical in the CAT exam.
• Prime for Problem Solving: Many problem-solving questions involve the Number System. To tackle these efficiently, you need to understand the nuances of different types of numbers.
• Logical Reasoning: The Number System also appears in logical reasoning questions, testing your ability to work with numerical data and draw logical conclusions.
Mastering the Number System isn’t just about passing the CAT exam; it’s about honing your critical thinking and analytical skills, which are invaluable in numerous aspects of life. So, don’t let Quantitative Aptitude be a puzzle; let it be your guide in your journey to CAT success.

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## Practice Questions for CAT with Solutions

#### 1. CAT - Number System

When 1313 is divided by a positive integer x, the remainder is 17. How many values of x are possible?

16

#### 2. CAT - Number System

N is a number having exactly 4 factors and is not a perfect cube. Sum of all it’s factors excluding the number itself is 2014. Find N.

4022

#### 3. CAT - Number System

Using all the digits 0,1,2,3,4,5,6 exactly once, Find the greatest number divisible by 55

6431205

#### 4. CAT - Number System

If a,b,c and d are integers, where a+b+c+d=4 then find the minimum value of 1/a+1/b+1/c+1/d.

-20/7

#### 5. CAT - Number System

If N = 364 x n, where N is a positive integer, has 182 factors, how many possible values N can assume?

2 Possibilities

### 6. CAT - Number System

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

70

#### 7. CAT - Number System

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4- digit number satisfying the above conditions is:

4195

### 8. CAT - Number System

For all possible integers n satisfying 2.25 ≤ 2 + 2n+2 ≤ 202, the number of integer values of 3 + 3n+1 is:

7

#### 9. CAT - Number System

If n is a positive integer such that (7√10) (7√10)2…… (7√10)n  is greater than 999, then the smallest value of n is

6

#### 10. CAT - Number System

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

6

### 11. CAT - Number System

If a, b, c are non-zero and 14a = 36b = 84c, then 6b(1/c – 1/a) is equal to:

3

#### 12. CAT - Number System

Let m and n be natural numbers such that n is even and 0, 2 less than m/20, n/m, n/11 less than 0.5.

Then m – 2n equals:

1. 2

2. 4

3. 3

4. 1

4. 1

#### 13. CAT - Number System

How many of the integers 1, 2, ….., 120, are divisible by none of 2, 5 and 7?

1. 40

2. 42

3. 41

4. 43

3. 41

#### 14. CAT - Number System

2521 – 921 is not divisible by which one of the following :

1. 16

2. 98

3. 544

4. 14896

3. 544

#### 15. CAT - Number System

ABCD is a 4 digit number having all distinct digits such that AB is a 2 digit prime number, CD is also a 2 digit -prime number and BC is a 2 digit perfect square. How many such numbers are possible?

12

### 16. CAT - Number System

Let X be a four-digit number with exactly three consecutive digits being the same and is a multiple of 9. How many such values of X are possible?