Number System Questions for Banking Exams

Many aspirants while preparing for the banking exams struggle with the quantitative aptitude section. This is the reason we have been keeping up with the trend of explaining each and every concept along with some practice questions with it. Today, we are explaining the concept of the number system and how to go about solving these types of problems. Number system in simple terms is a systematic way of expressing numbers and it even helps to understand the basics of quantitative ability. Mentioned below are the types and few practice questions on the number system.

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Number system:

Natural numbers:

Natural numbers are counting numbers starting with ‘1’. The set of natural numbers is usually denoted by ‘N’ i.e. {1, 2 , 3…….}

Whole numbers:

Whole numbers comprise natural numbers and the number zero. The set of whole numbers is usually denoted by ‘W’ i.e. {0, 1, 2, 3…….}

Integers:

An Integer is any number in the set {….,-1, 0, 1, 2, ………}.

Integers comprise natural numbers (1, 2 , 3………..), their negatives (-1, -2, -3………..) and the number zero.

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Consecutive integers:

Integers that occur in a sequence and where the difference between two successive integers is ‘1’, are consecutive integers.

Consecutive integers can be expressed in the form: ‘n’, (n + 1), (n + 2), (n + 3), ……….. where ‘n’ is an integer.

Even numbers: 

All natural numbers that are divisible by ‘2’ are called even numbers.

Consecutive even numbers can be expressed in the form ‘2n’, (2n + 2), (2n + 4), (2n + 6)……., where ‘n’ is a natural number.

Odd numbers:

All natural numbers that are not divisible by ‘2’ are called odd numbers.

Consecutive odd numbers can be expressed in the form (2n + 1), (2n + 3), (2n + 5), (2n + 7)……., where ‘n’ is a whole number.

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Prime numbers:

A natural number greater than ‘1’, that has exactly two factors, i.e., 1 and the number itself, is called a prime number. e.g. 2, 3, 5, 7, etc. Any prime number greater than 3 can be expressed as (6n + 1) or (6n – 1) (where ‘n’ is a positive integer).

Note: All the numbers in the form (6n + 1) and (6n – 1) are not necessarily prime numbers.

Composite numbers:

Any number that has more than two factors (i.e. other than itself and ‘1’) is called a composite number. e.g. 4, 6, 8 etc.

Note: Except ‘1’, every other integer can be classified as either a prime or a composite number.

HCF (Highest Common Factor):

HCF is the largest integer that perfectly divides two or more given integers. It is also known as the GCD (Greatest Common Divisor).

Example: Find the HCF of 9 and 18.

The factors or divisors of ‘9’ are: 1, 3 and 9

The factors or divisors of ‘18’ are: 1, 2, 3, 6, 9 and 18  

So, the HCF of 9 and 18 is ‘9’ (Since, highest factor common to both ‘9’ and ‘18’ is ‘9’).

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LCM (Lowest Common Multiple):

LCM is the smallest integer that is perfectly divisible by two or more given integers.

Example:

Find the LCM of 9 and 18

The multiples of 9 are: 9, 18, 27, ……………..

The multiples of 18 are: 18, 36, 54,  ……………………….  the LCM of 18 and 9 is ‘18’. (Since, the least multiple that is common to both ‘9’ and ‘18’ is ‘36’)

Also, Product of two numbers = LCM of the same two numbers × HCF of the same two numbers

Co-Prime or Relatively prime numbers:

If two numbers have no factor common other than ‘1’, then the numbers are co-prime to each other. For example, ‘5’ and ‘6’ are co-prime to each other.

Note: LCM of two prime or co-prime numbers is the product of the two numbers and the HCF of two prime or co-prime numbers is ‘1’.

Factorial:

A factorial is a number obtained by multiplying all the positive integers less than or equal to a given positive integer. The factorial of a given integer ‘n’ is usually written as ‘n!’.  

And, n! = n × (n – 1) × (n – 2) × (n – 3) × ……………..× 3 × 2 × 1

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Some other important formulas associated with numbers:

I. Number of factors of a number:

The number of factors of a number written in the form a^x × b^y × c^z × ……. (Where ‘a’, ‘b’ and ‘c’ are prime numbers) are (x + 1) × (y + 1) × (z + 1) × …..

II. Sum of first ‘n’ natural numbers:

= {n(n + 1)}/2

III. Sum of first ‘n’ odd natural numbers:

= n²

IV. Sum of first ‘n’ even natural numbers:

= n(n + 1)

V. Sum of squares of first ‘n’ natural numbers:

= {n(n + 1)(2n + 1)} ÷ 6

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Number System Questions for Banking Exams

Question 1: Product of digits at unit place and tens place is 18, when its digits are interchanged then the number is increased by 27. Find the square of the number.

A) 841

B) 256

C) 324

D) 729

E) None of these

Question 2: LCM of two numbers is 15 times of their HCF. The product of numbers is 15360. What will be the maximum possible difference between the numbers?

A) 448

B) 512

C) 416

D) 544

E) None of these

Question 3: The largest 2-digit prime number is subtracted from the LCM of all single digit prime numbers to obtain a number ‘X’. Find the unit digit of ‘X’.

A) 3

B) 5

C) 7

D) 8

E) 2

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Question 4: 1/5^th of a number ‘x’ is 20% more than 2/5^th of another number ‘y’. ‘x’ is how much percent more/less than ‘y’?

A) 80%

B) 115%

C) 220%

D) 140%

E) 100%

Question 5: When a least four digit number ‘x’ is divided by 96, 64 and 72, then it leaves a remainder 9 in each case. What least number must be added to ‘x’ so that it becomes a perfect square?

A) 12

B) 64

C) 75

D) 48

E) None of these

Question 6: If a number is increased by x% and then by 25%, the resultant number is 945 which is 135 less than the double of the original number, find the value of ‘x’.

A) 20

B) 30

C) 40

D) 50

E) 55

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Question 7: Find the largest three-digit number that leave 3 as remainder when divided by 4, 5 and 12.

A) 907

B) 987

C) 903

D) 993

E) 963

Question 8: When a number is decreased by 25%, then the number obtained is 36 more than 60% of the original number. Find the original number.

A) 200

B) 220

C) 240

D) 260

E) 280

Question 9: Find the largest 3-digit number that is divisible by both 13 and 37.

A) 962

B) 982

C) 989

D) 481

E) 491

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Question 10: The LCM of two numbers is 186 while their product is 5766. Find the HCF of the two numbers.

A) 62

B) 31

C) 93

D) 186

E) None of these

प्रश्न 1: इकाई और दहाई के अंकों का गुणनफल 18 है, जब इसके अंकों को आपस में बदल दिया जाता है तो संख्या 27 बढ़ जाती है। संख्या का वर्ग ज्ञात कीजिए।

A) 841

B) 256

C) 324

D) 729

E) इनमें से कोई नहीं

प्रश्न 2: दो संख्याओं का लघुत्तम उनके महत्तम का 15 गुना है।संख्याओं का गुणनफल 15360 है।संख्याओं के बीच अधिकतम संभव अंतर कितना होगा?

A) 448

B) 512

C) 416

D) 544

E) इनमें से कोई नहीं

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प्रश्न 3: संख्या ‘X’ प्राप्त करने के लिए सभी एकल अंक वाली अभाज्य संख्याओं के LCM से सबसे बड़ी 2-अंकीय अभाज्य संख्या घटा दी जाती है। ‘X’ का इकाई अंक ज्ञात कीजिए।

A) 3

B) 5

C) 7

D) 8

E) 2

प्रश्न 4: एक संख्या ’x ‘ का 1 / 5th, दूसरी संख्या ‘y’ के 2/5th से 20% अधिक है। ‘x’,‘y’ से कितना प्रतिशत अधिक / कम है?

A) 80%

B) 115%

C) 220%

D) 140%

E) 100%

प्रश्न 5: जब एक न्यूनतम चार अंकीय संख्या ‘x’ को 96, 64 और 72 से विभाजित किया जाता है, तो प्रत्येक मामले में शेष 9 बचता है। ‘x’ में कौन सी न्यूनतम संख्या जोड़ी जाए ताकि वह एक शुद्ध वर्ग बन जाए?

A) 12

B) 64

C) 75

D) 48

E) इनमें से कोई नहीं

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प्रश्न 6: यदि एक संख्या में x% और फिर 25% की वृद्धि की जाती है, तो परिणामी संख्या 945 है जो वास्तविक संख्या के दोगुने से 135 कम है, ‘x’ का मान ज्ञात कीजिए।

A) 20

B) 30

C) 40

D) 50

E) 55

प्रश्न 7: वह तीन अंकों की सबसे बड़ी संख्या ज्ञात कीजिए जिसे 4, 5 और 12 से विभाजित करने पर शेषफल 3 बचता है।

A) 907

B) 987

C) 903

D) 993

E) 963

प्रश्न 8: जब किसी संख्या में 25% की कमी की जाती है, तो प्राप्त संख्या वास्तविक संख्या के 60% से 36 अधिक होती है। वास्तविक संख्या ज्ञात कीजिए।

A) 200

B) 220

C) 240

D) 260

E) 280

प्रश्न 9: तीन अंकों की सबसे बड़ी संख्या ज्ञात कीजिए जो 13 और 37 दोनों से विभाज्य हो।

A) 962

B) 982

C) 989

D) 481

E) 491

प्रश्न 10: दो संख्याओं का महत्तम 186 है जबकि उनका गुणनफल 5766 है। दोनों संख्याओं का महत्तम ज्ञात कीजिए।

A) 62

B) 31

C) 93

D) 186

E) इनमे से कोई नही

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ANSWER KEYS and SOLUTIONS:

Solution 1: E)

Let the number be ‘10x + y’

So, x × y = 18

And, (10y + x) – (10x + y) = 27

Or, 9(y – x) = 27

Or, y – x = 3

Or, y – (18/y) = 3

Or, y² – 3y – 18 = 0

Or, y² – 6y + 3y – 18 = 0

Or, y(y – 6) + 3(y – 6) = 0

Or, (y + 3)(y – 6) = 0

Or, y = 6 or y = -3 (not possible)

So, x = 18/6 = 3

So, the number = 10 × 3 + 6 = 36

And, 36 × 36 = 1296

Hence, option e.

Solution 2: A)

Let HCF of two numbers be ‘x’

So, LCM of two numbers = 15 × x = 15x

Or, x × 15x = 15360

Or, 15x² = 15360

Or, x² = 1024

Or, x = 32

LCM of two numbers = 32 × 15 = 480

Let two number be ‘32a’ and ‘32b’, where ‘a’ and ‘b’ are co-prime numbers.

So, 32ab = 480

Or, a × b = 15

So, when a = 1 and b = 15, then difference will be maximum

Desired difference = 32 × 15 – 32 × 1 = 448

Hence, option a.

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Solution 3: A)

LCM of all single digit prime numbers = (2 × 3 × 5 × 7) = 210

So, ‘X’ = 210 – 97 = 113

Unit digit of ‘X’ = 3

Hence, option a.

Solution 4: D)

According to the question,

(x/) = 1.2 × (2y/5)

Or, x/y = 12/5

Required percentage = {(12 – 5)/5} × 100 = 140%

Hence, option d.

Solution 5: B)

LCM of 96, 64 and 72 = 576

Since, least 4-digit number = 576 × 2 = 1152

So, x = 1152 + 9 = 1161

Least number added = 1225 – 1161 = 64

Hence, option b.

Solution 6: C)

ATQ,

945 + 135 = 2 × original number

Original number = 1080/2 = 540

Now,

540 × [(100 + x)/100] × 1.25 = 945

Or, (5400 + 54x) = 9450/1.25

Or, 54x = 7560 – 5400

Or, x = 2160/54 = 40

Hence, option c.

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Solution 7: E)

Required number = largest three-digit multiple of LCM (4, 5 and 12) + 3

So, LCM (4, 5 and 12) = 60

So, largest three-digit multiple of 60 = 960

So, required number = 960 + 3 = 963

Hence, option e.

Solution 8: C)

Let the original number be ‘x’.

According to the question,

x × 0.75 = 36 + 0.60 × x

Or, 0.75x – 0.6x = 36

Or, 0.15x = 36

Or, x = 240

So, the original number = 240

Hence, option c.

Solution 9: A)

LCM (13 and 37) = 481

Largest 3-digit multiple of 481 = 962

Therefore, required number = 962

Hence, option a.

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Solution 10: B)

For two numbers;

LCM × HFC = Product of the two numbers

So, HCF = Product of the two numbers ÷ LCM

Required HCF = 5766 ÷ 186 = 31

Hence, option b.

This brings us to the end of the article. Candidates can prepare really well the concept of Number System from here and can practice questions as well. Meanwhile attempt SBI Clerk prelims free mock test to know your initial exam preparation level.

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