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## Number System problems with solutions

Nov 17 • Bank, Maths Notes • 1487 Views • No Comments on Number System problems with solutions

# Number System problems with solutions for goverment exam like Bank,SSC,IBPS

Number System problems with solutions for Bank Exam

Natural numbers 1, 2, 3, 4, 5, …………………………….. are called natural numbers

Whole numbers  0,1, 2, 3, 4, 5, 6, …………………………   are called whole numbers

Integers  0, ± 1, ± 2, ± 3, ± 4,………………………… are called integers .

Rational numbers  Numbers which can be written in the form of p/q, where p and q are integers and q ≠ 0 are called  rational numbers.

A number whose decimal expansion is terminating or recurring (recurring means repetition of a set of digits)

Irrational numbers  Numbers whose decimal expression is non recurring or non terminating are called  irrational numbers.

## Number System Question and Solution for  Bank Exam like IBPS and SBI PO

Real numbers : Real number contains all the rational numbers and all the irrational numbers.

Fraction A fraction is a rational number written in the form of a/b, where a and b are integers and b ≠ 0.

Proper fraction if the denominator of a fraction is greater than the numerator then the fraction is called a proper fraction

Example : ¼, ⅔, ⅓

Improper fraction if the numerator of a fraction is greater than the denominator then the fraction is called a improper fraction

Example 3/2, 17/5, 9/2

Divisor, Dividend, Quotient and Remainder

Suppose we have to divide 17 by 3

Then 3 is the divisor, 17 is the dividend

5 is the quotient and 2 is the remainder

There is a important formula about divisor, dividend, quotient and remainder

Dividend = divisor quotient+ remainder

Modulus value or absolute value : The modulus value of a number is equal to that number with positive sign or (positive value of that number). The symbol of modulus is x.

Example : Ι5Ι = 5, Ι-5.4 Ι = 5.4,Ι  Ι-6 Ι= 6

Some important tricks

• If a/c/d, then a + c/b + d lies between a/and c/d
• If a and b are two rational numbers such that a < b, then a + b/lies between a and b
• The sum of first n natural numbers i.e. 1 +2 + 3 +………+ n = n (n+1)/2

Example : 1 + 2 + 3 + ………+ 12 = 12 × 13/2 = 78

• The sum of squares of first n natural numbers i.e.12+22+….+n2 = n(n+1)(2n+1)/6

Example : 122 +….+ 152 = 15 × 16 × 31/6= 1240

• The sum of cubes of first  n natural numbers i.e. 12+…….+nn(n+1)2/4

Example : 12+…….+12= 12× 133/4= 6084

• The sum of first n odd natural numbers  =  n^2

Example : 1 + 3 + 5 + ………+ 19 = 10= 100

• The sum of first n even natural numbers = n+ n

Example : 2 + 4 + 6 + …….. + 40 = 20+ 20 = 400 + 20 = 420

• The sum of squares of even natural numbers upto n2= n(n+1)(n+2)/6

Example : 2+ 4+……….+ 10= 10 × 11 × 12/= 220

• The sum of squares of odd natural numbers up to n^2= n(n+1)(n+2)/6

Example : 1+ 3+………… + 9= 9 × 10 × 11/= 165

1 The unit digit of 7254 is

1. 7
2. 9
3. 3
4. 1

Solution The unit digit of 71= 7

The unit digit of 7= 9

The unit digit of 7= 3

The unit digit of 74= 1

The next 4 consecutive power of 7 gives the unit digit 7, 9, 3 and 1 respectively

When we divide 254 by 4, the remainder is 2

And the unit digit of 72= 9

So, the unit digit of 7^254 is 9

2 The decimal expression 2.23 is equal to

1. 22/9
2. 223/99
3. 221/99
4. 222/99

Solution Let x = 2.23

Then, x = 2.232323…………                                                                   (1)

Multiply by 100 in equation (1)

100x = 223.232323……..                                                                        (2)

Subtract (1) from (2)

99x = 221

x = 221/99

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3 Find the remainder when 230 + 330 430 530 divided by 7

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

Solution when 2divided by 7, the remainder is 2

When 22 divided by 7, the remainder is 4

When 23 divided by 7, the remainder is 1

230 = (23)10

When  230 divided by 7 the remainder is same as the remainder when 1^10 divided by 7

230/7, remainder = 1

Similarly 330/7, remainder = 1

430/7, remainder = 1

530/7, remainder = 1

230 + 330 30 +530/7, remainder is same as the remainder when 1 + 1 + 1  + 1 divided by 7

Remainder = 4

4 When a number is divided by 682, the remainder is 420. What is the remainder when the same number is divided by 31 ?

1. 0
2. 12
3. 17
4. 30

Solution since 31 is a factor of 682 i.e. 682 is completely divided by 31.

So, the remainder comes when 420 is divided by 31

Remainder = 17, when 420 divided by 31

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5 A rational number lies between 2/7and 3/5 is

1. 9/26
2. 3/11
3. 6/23
4. 12/47

Solution 2 + 3/7 + 5 = 5/12 lies between 2/and 3/5

5 + 2/7 + 12 = 7/19 lies between 2/7 and 5/12

7 + 2/19 + 7 = 9/26 lies between  2/7 and 7/19

9/26 lies between  2/7 and 3/5

### Number System Question asked in IBPS exam

6 The numbers 2272 and 875 are divided by a 3_ digit number N, giving the same remainders. The sum of the digits of N is

1. 10
2. 11
3. 12
4. 13                                                            ssc cgl prelim exam, 04/02/2007

Solution Let the remainder be x

Then, 2272 – x and 875 – x are completely divide by the N

Then their difference i.e. (2272 – x) – (875 – x) = 1397 is completely divide by the N

1397 = 11×127

Where 11 is prime, which has no other factor than 1 and 11 itself

N= 127

1 + 2 + 7 = 10

7. The total number of integers between 100 and 200, which are divisible by both 9 and 6, is

1. 5
2. 6
3. 7
4. 8                                                                                 ssc cgl prelim exam, 08/02/2004

Solution If a number is divisible by 9 and 6, then it is divisible by the lcm of 9 and 6 i.e. by 18

108, 126, 144, 162, 180, and 198 are the six numbers between 100 and 200 which are divisible by 18

8 which of the following is not an irrational number ?

1. √214
2. π√4
3. e/√6
4. √8/√2

Solution √8/√2 = √2/√2

= √4×√2/√2

= √4

= 2

2 is a rational number, hence it is not an irrational number

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