# Number System Questions

## Definition of Number System

Number System is used in nearly every single subject matter in maths. It to a great extent describes the significance of this subject. Number System mostly involves additional sub-topics such as HCF & LCM, factors, factorials, cyclicity, Euler number, digital root, unit digit, and more. The conception of unit digit can be well-read by assuming out the unit digits of all the sole digits ranging from 0 – 9 when elevated to definite capacities. The numbers are widely categorized into three groups for this use.

### Rules

• One of the key things to note while solving questions related to number systems is that the difference between the square of two consecutive values is the total of the two consecutive numbers.
• The result is always an odd number if the squares of two consecutive numbers are subtracted.
• If there is an even number in the unit place of the value given, then afterwards the times it is multiplied, it will still have the similar number in the unit place, which is:
(…..1)n=(…1)
(…7)n=(….7)
(……4)n=(……..4)
• If there is an odd number at the unit place (excluding 5), multiply the value by the same until it reaches to 1 in the unit place:
(……….1)n= (……….1)
(…..3)4n = (……1)
(…….7)4n = (…….1)
Where n = 1, 2, 3

Question 1

Time: 00:00:00
If R713 is divisible by 11. What is the value of the smallest natural number R?

9

9

3

3

1

1

4

4

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Question 2

Time: 00:00:00
By dividing 14528 by a certain number, Rita gets 83 as quotient and 3 as remainder. What is the divisor?

155

155

147

147

125

125

175

175

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Question 3

Time: 00:00:00
How many 3 digit number, in all are divisible by 9?

52

52

85

85

99

99

100

100

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Question 4

Time: 00:00:00
The LCM of two numbers is 210. If their HCF is 35 and one of the numbers is 105, find the other number.

35

35

70

70

68

68

42

42

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Question 5

Time: 00:00:00
Find the remainder when 413Â divided by 3?

6

6

8

8

9

9

1

1

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Question 6

Time: 00:00:00
How many numbers less than 1000 are multiples of both 10 and 17?

6

6

8

8

5

5

4

4

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Question 7

Time: 00:00:00
Which of the following will have the maximum number of factors?

99

99

101

101

52

52

176

176

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Question 8

Time: 00:00:00
A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is

5

5

6

6

3

3

7

7

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Question 9

Time: 00:00:00
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:

65

65

98

98

85

85

32

32

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Question 10

Time: 00:00:00
What is the value of 2 consecutive natural numbers, sum of whose squares is 145?

8,9

8,9

5,7

5,7

14,12

14,12

3,1

3,1

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Question 11

Time: 00:00:00
What smallest number should be added to the sum of squares of 15 and 14, so that the resulting number is a perfect square?

25

25

20

20

11

11

9

9

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Question 12

Time: 00:00:00
At a telephone exchange, three phones ring at intervals of 20 sec, 24 sec and 30 seconds - If they ring together at 11:25 am, when will they next ring together?

11:32

11:32

11:27

11:27

11:40

11:40

11:34

11:34