Number System  Formulas, Examples, Shortcuts and Video
Number System Important Questions from Previous Year Exam
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Question 1 of 39
1. Question
1 pointsThe missing dig,it which makes 345 02 is divisible by 11,
Correct
If the number 345 02 is divisible by 11,
3 + 5 + 0  4 + +2 is multiple of 0 or 11.
8  6  0 is multiple of 0 or 11
2   is multiple of 0 or 11
Hence the possible value of is only 2.
Incorrect
If the number 345 02 is divisible by 11,
3 + 5 + 0  4 + +2 is multiple of 0 or 11.
8  6  0 is multiple of 0 or 11
2   is multiple of 0 or 11
Hence the possible value of is only 2.

Question 2 of 39
2. Question
1 pointsThe divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, the dividend is
Correct
Incorrect
Divisor= 25 x Quotient
=25 x 16= 400
and Divisor = 5 x Remainder
Remainder = = 80
We Know,
Dividend = Divisor Quotient + Remainder
= 400 16 + 80
= 6400 + 80 = 6480

Question 3 of 39
3. Question
1 pointsIf the following ration are arranged in in descending order, then which will be the last in the series?
Correct
=
Incorrect
=

Question 4 of 39
4. Question
1 pointsIf the fraction are arranged in ascending order of their values, then which one will be the third?
Correct
Incorrect

Question 5 of 39
5. Question
1 pointsWhich of the following is in descending order?
Correct
Incorrect

Question 6 of 39
6. Question
1 points3011.008+409.093=2025.250+?
Correct
3011.008 + 409.093 = 2025.250 + ?
= 3420.101=2025.250+?
= ? =3420.1012025.250=1394.851
Incorrect
3011.008 + 409.093 = 2025.250 + ?
= 3420.101=2025.250+?
= ? =3420.1012025.250=1394.851

Question 7 of 39
7. Question
1 pointsThe sur,n of all natural numbers between 100 and 200 which are multiples of 3, is
Correct
First number = 102
Last number = 198
Total number of the numbers = 33
The sum = [102 + 198]
[300] = 4950
Incorrect
First number = 102
Last number = 198
Total number of the numbers = 33
The sum = [102 + 198]
[300] = 4950

Question 8 of 39
8. Question
1 pointsThe difference between the place value or face value of 6 in the numeral 356719 is :
Correct
Since , Place value of 6 in the number = 6000 and face value of 6 = 6
Therefore, difference between 6000 and 6 ⇒ 6000 – 6 = 5994.
Incorrect
Since , Place value of 6 in the number = 6000 and face value of 6 = 6
Therefore, difference between 6000 and 6 ⇒ 6000 – 6 = 5994.

Question 9 of 39
9. Question
1 pointsThe difference between place value of 7 and face value of 8 in the numeral 67081 is :
Correct
Since , Place value of 7 in the numeral = 7000
The face value of 8 = 8
Therefore , the difference between 7000 and 8
⇒ 7000  8 = 6992.
Incorrect
Since , Place value of 7 in the numeral = 7000
The face value of 8 = 8
Therefore , the difference between 7000 and 8
⇒ 7000  8 = 6992.

Question 10 of 39
10. Question
1 pointsWhich of the following is a true statement ?
1. {0, +1, +2, +3,……….} is a set of all non negative integers.
2. { 1, 2, 3,………….. } is a set of nonpositive integers.
3. {0, 1, 2, 3,………...} is a set of all non positive integers.Correct
Statement 1 is a true statement as when we remove the set of all positive nonnegative integers in which 0 will also be there as an element .
Keeping the above statement in view, we can have the third statement as true statement .
But the second statement is false.
Incorrect
Statement 1 is a true statement as when we remove the set of all positive nonnegative integers in which 0 will also be there as an element .
Keeping the above statement in view, we can have the third statement as true statement .
But the second statement is false.

Question 11 of 39
11. Question
1 pointsWhich of the following statement is true ?
1. ∏ is an irrational number.
2. 22/7 is a rational number.
3. 3.14 is a rational number.
Correct
Statement 1 is true as the actual value of ∏ is 3.141519265…. which shows that the decimal expansion is neither terminating nor repeating and hence ∏ is an irrational number.
Statement 2 is true as 22/7 = p/q where q ≠ 0 and hence, 22/7 is rational number .
Statement 3 is also true as decimal expansion in 3.14 is terminating and the number can be written in the form of p/q where q ≠ 0 . So , 3.14 is a rational number .
Incorrect
Statement 1 is true as the actual value of ∏ is 3.141519265…. which shows that the decimal expansion is neither terminating nor repeating and hence ∏ is an irrational number.
Statement 2 is true as 22/7 = p/q where q ≠ 0 and hence, 22/7 is rational number .
Statement 3 is also true as decimal expansion in 3.14 is terminating and the number can be written in the form of p/q where q ≠ 0 . So , 3.14 is a rational number .

Question 12 of 39
12. Question
1 pointsWhich of the following is an irrational number ?
Correct
As in 1.356365356……. the decimal is repeating, it is a rational number.
As per rational numbers property , when we add two rational number , we get a rational number . therefore (1/2 + 3/5) is also a rational number . and √196 = 14 which can be written as 14 / 1 = p/q and is rational number.
But is 0.101001000…… The decimal expansion is neither terminating nor repeating , so the number is an irrational one.
Incorrect
As in 1.356365356……. the decimal is repeating, it is a rational number.
As per rational numbers property , when we add two rational number , we get a rational number . therefore (1/2 + 3/5) is also a rational number . and √196 = 14 which can be written as 14 / 1 = p/q and is rational number.
But is 0.101001000…… The decimal expansion is neither terminating nor repeating , so the number is an irrational one.

Question 13 of 39
13. Question
1 pointsWhat is the unit digit In the product (784 x 618 x 917 x 463) ?(SBI 2008)
Correct
Let’s take the unit digit of every number in the product and multiply them.
Therefore, Unit digit in the given product = (4 x 8 x 7 x3) = 2.
Incorrect
Let’s take the unit digit of every number in the product and multiply them.
Therefore, Unit digit in the given product = (4 x 8 x 7 x3) = 2.

Question 14 of 39
14. Question
1 pointsWhat is the unit digit in the product ?
Correct
For base 3 & 7 , let’s divide the powers by 4 and get the remainder powers.
Unit digit in = Unit digit in =7
Unit digit in = unit digit in= =3
Now, Unit digit of 6 remains 6 for every power so, unit digit in =6
so = (7 × 6 × 3) = 6 .
Incorrect
For base 3 & 7 , let’s divide the powers by 4 and get the remainder powers.
Unit digit in = Unit digit in =7
Unit digit in = unit digit in= =3
Now, Unit digit of 6 remains 6 for every power so, unit digit in =6
so = (7 × 6 × 3) = 6 .

Question 15 of 39
15. Question
1 pointsThe difference between the local value and the face value of 6 in the numeral 82769415 is
Correct
Local Value (Place Value) of 6 in the numeral = 60000
Face Value of 6 in the numeral = 656 Difference between them = 60000 − 06 = 59994
Incorrect
Local Value (Place Value) of 6 in the numeral = 60000
Face Value of 6 in the numeral = 656 Difference between them = 60000 − 06 = 59994

Question 16 of 39
16. Question
1 pointsGiven that is equal to
Correct
Incorrect

Question 17 of 39
17. Question
1 pointsThe sum of first 20 odd natural numbers is equal to
Correct
The sum of last 20 odd natural number = = 400
Incorrect
The sum of last 20 odd natural number = = 400

Question 18 of 39
18. Question
1 pointsIf 3 4 a 6 8 is to be divisible by g, then the value of missing digit, a should be
Correct
Incorrect
If 34a68 is to be divisible by 9, then the sum of a1l digits must be divisible by 9.
3 + 4 + a + 6 + 8 is multiply by 9.
21 + a is multiple of 9
Hence, the possible value of a is 6.

Question 19 of 39
19. Question
1 pointsis equal to
Correct
[By using ]
= 9
Incorrect
[By using ]
= 9

Question 20 of 39
20. Question
1 points1632 ÷ 4 ÷ 2 = ?
Correct
The given expression is 1632 ÷ 4 ÷ 2 = ?
⇒ = 204.
Incorrect
The given expression is 1632 ÷ 4 ÷ 2 = ?
⇒ = 204.

Question 21 of 39
21. Question
1 points4891 × 999 = ?
Correct
From the given equation :
4891 × 999
⇒ 4891 × (1000 – 1)
⇒ 4891 × 1000 – 4891
⇒ 4891000 – 4891 = 4886109.
Incorrect
From the given equation :
4891 × 999
⇒ 4891 × (1000 – 1)
⇒ 4891 × 1000 – 4891
⇒ 4891000 – 4891 = 4886109.

Question 22 of 39
22. Question
1 pointsIf the number 96327*5 is completely divisible by 11 , then smallest whole number in place of * will be :
Correct
Given number = 96327*5
So, Let's take * = x. then,
Now, Sum of its digits at even places = (6 + 3 + x) = (8 + x)
Now the difference = 24 – (8 + x)
= (24 – 8 – x ) = (16 – x)
As per rule of divisibility by 11 the difference must be either ‘0’ or a multiple of 11.
So, 16 – x = 11, therefore x = 5.
Incorrect
Given number = 96327*5
So, Let's take * = x. then,
Now, Sum of its digits at even places = (6 + 3 + x) = (8 + x)
Now the difference = 24 – (8 + x)
= (24 – 8 – x ) = (16 – x)
As per rule of divisibility by 11 the difference must be either ‘0’ or a multiple of 11.
So, 16 – x = 11, therefore x = 5.

Question 23 of 39
23. Question
1 pointsIf the number is 91876*2 is divisible by 8, then the smallest whole number in place of * will be :
Correct
As per the rule of divisibility by 8, we check last 3 digits of a numeral , that must be divisible by 8.
Now here 6*2 is must be divisible by 8, by hit & trial , by putting * = 1, 2, 3……,
we get * = 3 as the least number if 6*2 is to be divisible by 8.
Therefore * = 3.
Incorrect
As per the rule of divisibility by 8, we check last 3 digits of a numeral , that must be divisible by 8.
Now here 6*2 is must be divisible by 8, by hit & trial , by putting * = 1, 2, 3……,
we get * = 3 as the least number if 6*2 is to be divisible by 8.
Therefore * = 3.

Question 24 of 39
24. Question
1 pointsWhich one of the following numbers is completely divisible by 45 ?
Correct
Coprime factors of 45 = (9, 5)
Now all four options are divisible by 5, so we have to find out which number is divisible by 9.
In option C is 202860, total of digits = 2 + 0 + 2 + 8 + 6 + 0 = 18 that is divisible by 9
So, the answer is 202860.
Incorrect
Coprime factors of 45 = (9, 5)
Now all four options are divisible by 5, so we have to find out which number is divisible by 9.
In option C is 202860, total of digits = 2 + 0 + 2 + 8 + 6 + 0 = 18 that is divisible by 9
So, the answer is 202860.

Question 25 of 39
25. Question
1 pointsIf 7283xy is divisible by 80, then x + y = ?
Correct
rime factors of 80 = 2, 5, 8
Since, 7283xy is divisible by 5 & 2 , the last digit must be 0.
Now, for the divisibility by 8, we check last three digit of a numeral.
Therefore, 3x0 must be divisible by 8.
Therefore , the least value of x is, for which 3x0 is divisible by 8, will be = 2
Therefore x + y = 2 + 0 = 2.
Incorrect
rime factors of 80 = 2, 5, 8
Since, 7283xy is divisible by 5 & 2 , the last digit must be 0.
Now, for the divisibility by 8, we check last three digit of a numeral.
Therefore, 3x0 must be divisible by 8.
Therefore , the least value of x is, for which 3x0 is divisible by 8, will be = 2
Therefore x + y = 2 + 0 = 2.

Question 26 of 39
26. Question
1 pointsHow many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Correct
132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11 , 3 , 4
396 11 , 3 , 4
462 11 , 3
792 11 , 3 , 4
968 11 , 4
2178 11 , 3
5184 3 , 4
6336 11 , 3 , 4
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
Incorrect
132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11 , 3 , 4
396 11 , 3 , 4
462 11 , 3
792 11 , 3 , 4
968 11 , 4
2178 11 , 3
5184 3 , 4
6336 11 , 3 , 4
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.

Question 27 of 39
27. Question
1 pointsWhich of the following is a prime number ?
Correct
All prime numbers less than 16 are 2, 3, 5, 7, 11 & 13.
If the number given in an option is divisible by any of these , the number can’t be a prime one and if it’s not then it will be a prime number.
Now , by the rules of divisibility , we find 161 is divisible by 7, 221 is divisible by 13 & 247 is also divisible by 13.
So , the answer is none of these.is a prime number ?
Incorrect
All prime numbers less than 16 are 2, 3, 5, 7, 11 & 13.
If the number given in an option is divisible by any of these , the number can’t be a prime one and if it’s not then it will be a prime number.
Now , by the rules of divisibility , we find 161 is divisible by 7, 221 is divisible by 13 & 247 is also divisible by 13.
So , the answer is none of these.is a prime number ?

Question 28 of 39
28. Question
1 pointsIf the fraction are arranged in ascending order of their values, then which one will be the fourth?
Correct
= 0.75 , = 0.571 , = 0.833 , = 0.545 , = 0.692
ascending order is Hence the fourth fraction is
Incorrect
= 0.75 , = 0.571 , = 0.833 , = 0.545 , = 0.692
ascending order is Hence the fourth fraction is

Question 29 of 39
29. Question
1 pointsWhich one of the following is the least fraction?
, , , ,
Correct
Incorrect

Question 30 of 39
30. Question
1 pointsCorrect
Incorrect

Question 31 of 39
31. Question
1 pointsCorrect
Incorrect
=216

Question 32 of 39
32. Question
1 pointsCorrect
Incorrect

Question 33 of 39
33. Question
1 pointsCorrect
Incorrect

Question 34 of 39
34. Question
1 pointsCorrect
Incorrect

Question 35 of 39
35. Question
1 pointsCorrect
Incorrect

Question 36 of 39
36. Question
1 pointsThe unit digit in the product (786 × 617 × 919 × 463) is
Correct
Unit digit in the given product = Unit digit of each number in the product
= (6 × 7 × 9 × 3) = 4Incorrect
Unit digit in the given product = Unit digit of each number in the product
= (6 × 7 × 9 × 3) = 4 
Question 37 of 39
37. Question
1 points8961 – ? = 6530
Correct
Let the finding number is x. then,
Given expression: 8961 – x = 6530. Then,
x = 8961 – 6530 = 2431.
Incorrect
Let the finding number is x. then,
Given expression: 8961 – x = 6530. Then,
x = 8961 – 6530 = 2431.

Question 38 of 39
38. Question
1 pointsThe difference between the place value of two nines in the numeral 68099472 is :
Correct
Since , Place value of two nines in the numeral 68099472 are 9000 and 90000.
Therefore, Difference between 9000 and 90000 ⇒ 90000 – 9000 = 81000.
Incorrect
Since , Place value of two nines in the numeral 68099472 are 9000 and 90000.
Therefore, Difference between 9000 and 90000 ⇒ 90000 – 9000 = 81000.

Question 39 of 39
39. Question
1 pointsIf the number 517*567 is completely divisible by 3, then the smallest whole number in place of * will be :
Correct
Since, Sum of the digits = ( 5 + 1 + 7 + x + 5 + 6 + 7 ) = 31 + x.
Now (31 + x ) will be divisible by 3 if x = 2.Incorrect
Since, Sum of the digits = ( 5 + 1 + 7 + x + 5 + 6 + 7 ) = 31 + x.
Now (31 + x ) will be divisible by 3 if x = 2.
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