# 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:
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:
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:
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:
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:
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:
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:
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:
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:
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: