# Number System Questions and Answers

## Number System Questions and Answers for Competitive placement exams

On this page we are going to discuss Number System Questions with Solutions, with basic definition and practice examples. ## Number system Questions with solution

### Important definitions for solving Number System Questions:

• Natural Numbers: All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers. N = {1, 2, 3, 4, 5, 6……..∞}
• Whole Numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers. They are also called as Non-negative integers. W = { 0,1,2,3,4,5,6,7,8,………∞}
• Integers: All numbers that do not have the decimal places in them are called integers. Z = {∞…….-3, -2, -1, 0, 1, 2, 3………∞}
• Real Numbers: All numbers that can be represented on the number line are called real numbers.
• Rational Numbers: A rational number is defined as a number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0. The rational numbers that are not integers will have decimal values. These values can be of two types
• Irrational Numbers:  It is a number that cannot be written as a ratio.An Irrational numbers are non-terminating and non-periodic fractions.

### Formulas to solve Questions

Expression Formula
$a^{m} * a^{n}$$a^{m+n}$
$(a^{m}n)$$a^{mn}$
$a^{m}/a^{n}$$a^{m-n}$
$a^{m} * b^{m}$$(ab)^{m}$

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## Number System questions with solution

1. Find the L.C.M of 15, 30, 45 90

90

86.62%

95

95

4.99%

92

92

1.66%

None of the above

None of the above

6.73%

2 | 15, 30, 45
3 | 15, 15, 45
3 | 5, 5, 15
5 | 5, 5, 5
| 1, 1, 1

L.C.M = 2*3*3*5 = 90 2. The given ratio of two numbers is 3:2. If the L.C.M of them is 30, then calculate their sum. 34

34

8.35%

25

25

78.01%

55

55

6.55%

None of the above

None of the above

7.08%

Given:

Ratio of the two numbers = 3: 2

LCM of two numbers = 30

To find: Sum of the two numbers

The formula used: Product of two numbers = LCM × HCF

Solution:

Let the numbers be 3x and 2x

Product of two numbers = LCM × HCF

The HCF of two numbers will be x as the numbers are in ratio due to which it c an be conclude that their will be a HCF factor of x also.

The two numbers are 3x,2x

Product of two numbers = LCM × HCF

(3x )(2x) = 30 (x)

6x2 = 30x

6x = 30

x = 30/6

x = 5

The first number is 3x

3x = 3(5)

= 15

The first number is 15

The second number is 2x

2x = 2(5)

=10

The second number is 10

Therefore the two numbers are 15,10

The sum of two numbers = 15 + 10 = 25

The ratio of two numbers is 3 ratio 2 and the lcm of them is 30 then  the sum​ of the numbers is 25 3. Find the L.C.M of 25, 35, and 55 1900

1900

6.9%

1990

1990

6.1%

1925

1925

81.82%

None of the above

None of the above

5.18%

5 | 25, 35, 55
5 | 5, 7, 11
7 | 1, 7, 11
11 | 1, 1, 11
| 1, 1, 1

L.C.M = 5*5*7*11 = 1925 4. Calculate the HCF of 22 and 33 11

11

93.07%

12

12

3.08%

15

15

1.76%

None of the above

None of the above

2.09%

22 = 2*11

33 = 3*11

So the HCF will be 11 5. If 20 is the HCF of two particular numbers and the other two factors of their LCM are 10 and 12, find the larger number? 220

220

12.04%

210

210

8.26%

240

240

76.19%

None of the above

None of the above

3.5%

20* 10 = 200

20*12 = 240

So the larger number will be 240

HCF of two numbers is the number that is a common factor for both numbers given

Here 20 is the common factor.

Other than this common factor, we also will have the product of uncommon factors for the two numbers (10 and 12 here).

The first number = 20*10 = 200

and second number = 20 × 12 = 240

The greatest of two numbers is definitely 20 × 12 = 240 6. The HCF  of three specific numbers 6, 12, and 18 is 24 , find the LCM? 55

55

5.95%

54

54

73.29%

67

67

3.92%

None of the above

None of the above

16.84%

(6*12*18)/24

The next number will be = 54 7. The two specific numbers are in the ratio 6:7, if the HCF of the given numbers is 30, what will be the numbers? 160, 180

160, 180

7.83%

180, 210

180, 210

86.18%

200,160

200,160

3.07%

None of the above

None of the above

2.92%

Let the numbers be 6y and 7y

HCF = 30

The numbers will be 6*30 = 180

And 7*30 = 210 8. Determine the largest length of the tape, which can measure tape of 5 cm, 7cm, and 13 cm? 1

1

53.76%

7

7

6.04%

13

13

35.2%

None of the above

None of the above

5.01%

As all these numbers have no factors and are considered as prime numbers so their HCF will be 1. 9. The HCF of two numbers is 45, and their LCM is 90, if one specific number is 9, find the other number. 450

450

88.69%

435

435

5.57%

426

426

2.79%

None of the above

None of the above

2.95%

HCF * LCM = Products of Numbers

45 * 90 = 9 * x

Another number will be = (45*90)/9 = 450 10. Street lamps start at the interval of 5, 10, 15, 20, and 25 seconds, calculate the number in which the street lamps began together in 40 minutes. 9 times

9 times

19.42%

10 times

10 times

15.43%

16 times

16 times

54.99%

None of the above

None of the above

10.16%

we need to calculate the number of occurrences when the time intervals (5 seconds, 10 seconds, 15 seconds, 20 seconds, and 25 seconds) align perfectly with each other within the 40-minute interval.

First, let's convert 40 minutes to seconds:

40 minutes * 60 seconds/minute = 2400 seconds

Now, let's find the least common multiple (LCM) of the given time intervals (5, 10, 15, 20, 25 seconds) to determine when the street lamps will start together. The LCM of these intervals is 150 seconds.

Next, we'll divide the total interval time (2400 seconds) by the LCM (150 seconds):

2400 seconds / 150 seconds = 16

So, the street lamps will start together 16 times within a 40-minute interval.

Therefore, the number of times the street lamps began together in 40 minutes is 16.  ×