Numbers System Aptitude Questions and Answer – Quantitative Aptitude

Numbers System Aptitude Questions and Answer – Formulas & Tricks

Number Theory – Tips

  • Sum of natural numbers form 1 to n = (n * (n + 1) / 2)
  • Sum of squares of first n natural number is = (n * (n + 1) * (2n + 1)) / 6
  • Sum of the squares of first n even natural numbers is = ((2 / 3) * n * (n + 1) (2n + 1))
  • Sum of Cubes of first n natural numbers is = [(n * (n + 1) / 2)]2
  • Any Number N can be represented in the decimal system of number as N = nk10k + nk-110k-1 + n … + ni10 + n0

Types of Numbers

  1. Natural Numbers : The counting numbers which are used for counting are known as natural numbers
    • 1, 2, 3, 4, 5, 6, 7, …
  2. Whole Numbers: All counting numbers along with zero from a set of whole numbers.
    • 0, 1, 2, 3, 4, 5, 6 ….
  3. Integers: The whole numbers including the negative numbers and excluding fractions are known as integer.
    • …. -3, -2, -1, 0, 1, 2, 3, 4, 5….
  4. Prime Numbers: A whole number which is greater than 1 and is divisible by 1 and itself is a prime number
    • 2, 3, 5, 7, 11,….
  5. Co-Prime Numbers: Two natural numbers p and q are said to be co-prime if their HCF is 1
    • (2, 3)(4, 5)(7, 9)(11, 9)
  6. Composite Numbers: It refers to a whole number which is greater than 1 and is not a prime number. It can be divided by numbers other than 1 and itself
    • 4, 6, 8, 9, 10, 12
  7. Even Number: An integer which is divisible by 2 is known as Even Number
    • 2, 4, 5, 8, 10
  8. Odd Number: An integer which is not divisible by 2 is known as Odd Number
    • 1, 3, 5, 7, 9
  9. Consecutive Numbers: It is a serious of numbers in which the numbers follow each other in an order, that is there is a difference of 1 between two successive numbers or each number is greater than the preceding number 1.
  10. Rational Number: The number in the form of P/Q where P and Q are integer and Q can? be zero are known as Rational Numbers.
  11. Irrational Numbers: The numbers which when written in decimal form do not terminate and repeat are known as irrational numbers. These Numbers cannot be expressed as a ratio of integer or a fraction.
  12. Real Numbers: The number which can e found on the number line and include both rational and irrational numbers are known as Real Numbers.
  13. Face Value: It is the actual value of a digit. It remains definite and does not change with the digit’s place.
  14. Place Value: The place value of a digit depends on its place or position in the number. It is the product of its place and face value. Each place in a number has a value of 10 times the place to its right.
  15. Unit Digit: The unit digit is the ones place digit of a number

Numbers System Aptitude Questions and Answer With Detailed ExplanationQuantitative Aptitude

Numbers

Question 1
If a and b are odd Numbers, then which of the following is even?
A
a + b
B
a + b + 1
C
ab
D
ab + 2
Question 1 Explanation: 
Answer: Option A
Explanation:
The Sum of two odd numbers is even. So, a + b is even
Question 2
If the Number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be:
A
0
B
1
C
2
D
None of these
Question 2 Explanation: 
Answer: Option C
Explanation:
Sum of Digits : (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x)
Which must be divisible by 3.
Therefore, x =2
Question 3
The sum of the three consecutive is 87. The greatest among these three numbers is
A
26
B
28
C
29
D
30
Question 3 Explanation: 
Answer: Option D
Explanation:
Let the three consecutive numbers be x, x+1, x+2
According to the question,
x+x+1+x+2 = 87
3x = 84
x = 28
Greatest Number, (x + 2) => (28 + 2)
Ans = 30
Question 4
8796 * 223 + 8796 * 77 = ?
A
2736900
B
2638800
C
2658560
D
2716740
Question 4 Explanation: 
Answer: Option B
Explanation:
8796 * 223 + 8796 * 77 = 8796 * (223 + 77) {According Distributive Law}
= 8796 * 300
Ans = 2638800
Question 5
The difference of two numbers is 1365. On dividing the large Number by the smeller, We get 6 as quotient and the 15 as Remainder. What is the Smaller Number?
A
240
B
270
C
295
D
360
Question 5 Explanation: 
Answer: Option B
Explanation:
Let the Smaller number be X. Then Larger number = (X+1365)
Therefore, X+1365 = 6x +15
=> 5x = 1350
=> X = 270
Therefore, Smaller Number = 270
Question 6
Which one of the following can't be the square of natural number?
A
30976
B
75625
C
28561
D
14362
Question 6 Explanation: 
Answer: Option D
Explanation:
The square of a natural number never ends in 2.
Therefore, 14362 is not the square of natural Number
Question 7
The Sum of First Five Prime Numbers is
A
11
B
18
C
21
D
28
Question 7 Explanation: 
Answer: Option D
Explanation:
Note: 1 is not a Prime Number
Required Sum = (2 + 3 + 5 + 7 + 11) = 28
Question 8
If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking 4 from the product, the number is
A
2
B
3
C
4
D
5
Question 8 Explanation: 
Answer: Option C
Explanation:
From the given question, We have
2a + 20..... (1)
8a - 4 ........ (2)
Since, both results same, we have
2a + 20 = 8a - 4
20 + 4 = 8a -2a
24 = 6a
Therefore a = 4
Question 9
-84 x 29 + 365 = ?
A
2436
B
2801
C
-2801
D
-2071
Question 9 Explanation: 
Answer: Option D
Explanation:
=> -84 x 29 + 365
=> -84 x (30 - 1) + 365
=> -(84 * 30) + (84 * 1) + 365
=> -2520 + 449
Therefore, -2071
Question 10
11 times a number gives 132. The Number is:
A
11
B
11.3
C
12
D
12.2
Question 10 Explanation: 
Answer: Option C
Explanation:
Number be a
11a = 132
a = 132 / 11
a = 12
There are 10 questions to complete.