**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 = n
_{k}10_{k}+ n_{k-1}10^{k-1}+ n … + n_{i}10 + n_{0}

**Types of Numbers**

**Natural Numbers :**The counting numbers which are used for counting are known as natural numbers- 1, 2, 3, 4, 5, 6, 7, …

**Whole Numbers:**All counting numbers along with zero from a set of whole numbers.- 0, 1, 2, 3, 4, 5, 6 ….

**Integers:**The whole numbers including the negative numbers and excluding fractions are known as integer.- …. -3, -2, -1, 0, 1, 2, 3, 4, 5….

**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,….

**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)

**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

**Even Number:**An integer which is divisible by 2 is known as Even Number- 2, 4, 5, 8, 10

**Odd Number:**An integer which is not divisible by 2 is known as Odd Number- 1, 3, 5, 7, 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.**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.**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.**Real Numbers:**The number which can e found on the number line and include both rational and irrational numbers are known as Real Numbers.**Face Value:**It is the actual value of a digit. It remains definite and does not change with the digit’s place.**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.**Unit Digit:**The unit digit is the ones place digit of a number

Numbers System Aptitude Questions and Answer **With Detailed Explanation** – Quantitative Aptitude

## Numbers

Question 1 |

If a and b are odd Numbers, then which of the following is even?

a + b | |

a + b + 1 | |

ab | |

ab + 2 |

Question 1 Explanation:

**Answer: Option A**

__Explanation:__

The Sum of two odd numbers is even. So, a + b is even

Question 2 |

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?

240 | |

270 | |

295 | |

360 |

Question 2 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 3 |

Which one of the following can't be the square of natural number?

30976 | |

75625 | |

28561 | |

14362 |

Question 3 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 4 |

The Sum of First Five Prime Numbers is

11 | |

18 | |

21 | |

28 |

Question 4 Explanation:

**Answer: Option D**

__Explanation:__

Note: 1 is not a Prime Number

Required Sum = (2 + 3 + 5 + 7 + 11) = 28

Question 5 |

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

2 | |

3 | |

4 | |

5 |

Question 5 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 6 |

If the Number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be:

0 | |

1 | |

2 | |

None of these |

Question 6 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 7 |

8796 * 223 + 8796 * 77 = ?

2736900 | |

2638800 | |

2658560 | |

2716740 |

Question 7 Explanation:

**Answer: Option B**

__Explanation:__

8796 * 223 + 8796 * 77 = 8796 * (223 + 77) {According Distributive Law}

= 8796 * 300

**Ans = 2638800**

Question 8 |

11 times a number gives 132. The Number is:

11 | |

11.3 | |

12 | |

12.2 |

Question 8 Explanation:

**Answer: Option C**

__Explanation:__

Number be a

11a = 132

a = 132 / 11

**a = 12**

Question 9 |

-84 x 29 + 365 = ?

2436 | |

2801 | |

-2801 | |

-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 |

The sum of the three consecutive is 87. The greatest among these three numbers is

26 | |

28 | |

29 | |

30 |

Question 10 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**

There are 10 questions to complete.