# Numbers

**TYPES OF NUMBERS**

- Integers : All numbers whose fractional part is 0 (zero) like -3, -2, 1, 0, 10, 100 are integers.
- Natural Numbers : Counting numbers like 1, 2, 3, 4, 5, 6 … Basically, all integers greater than 0 are natural numbers … More on Numbers

Question 1 |

Which is not the prime number?

43 | |

57 | |

73 | |

101 |

**Arithmetic Aptitude**

**Numbers**

**Discuss it**

Question 1 Explanation:

A positive natural number is called prime number if nothing divides it except the number itself and 1. 57 is not a prime number as it is divisible by 3 and 19.

Question 2 |

How many terms are there in 3,9,27,81........531441?

25 | |

12 | |

13 | |

14 |

**Arithmetic Aptitude 4**

**Numbers**

**Discuss it**

Question 2 Explanation:

3, 9, 27, 81..............531441 form a G.P. with a = 3 and r = 9/3 = 3 Let the number of terms be nAccording to the formula, N

^{th}term of the G.P is represented as T

_{n}= a x r

^{n-1}

Then 3 x 3^{n-1}= 531441 ∴ 3^{n}= 3^{12}∴ n = 12

Question 3 |

If the average of four consecutive odd numbers is 12, find the smallest of these numbers?

5 | |

7 | |

9 | |

11 |

**Arithmetic Aptitude 4**

**Numbers**

**Discuss it**

Question 3 Explanation:

Let the numbers be x, x+2, x+4 and x+6 Then (x + x + 2 + x + 4 + x + 6)/4 = 12 ∴ 4x + 12 = 48 ∴ x = 9

Question 4 |

If the sum of two numbers is 13 and the sum of their square is 85. Find the numbers?

6 & 7 | |

5 & 8 | |

4 & 9 | |

3 & 10 |

**Arithmetic Aptitude 4**

**Numbers**

**Discuss it**

Question 4 Explanation:

Let the numbers be x and 13-x
Then x

^{2}+ (13 – x)^{2}= 85 ∴ x^{2}+ 169 + x^{2}– 26x = 85 ∴ 2 x^{2}– 26x + 84 = 0 ∴ x^{2}– 13x + 42 = 0 ∴ (x-6)(x-7)=0 Hence numbers are 6 & 7Question 5 |

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 45. What is the difference between the two digits of that number?

5 | |

7 | |

6 | |

None of these |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 5 Explanation:

Let the ten’s digit be x and unit’s digit be y Then (10x + y) – (10y + x) = 45 9(x – y) = 45 x – y = 5

Question 6 |

A two-digit number is such that the product of the digits is 12. When 9 is subtracted from the number, the digits are reversed. The number is:

34 | |

62 | |

43 | |

26 |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 6 Explanation:

Let the tens digit of the number be

**a**and ones digit be**b**.Given: ab = 12 ................(i) and, (10a + b) - (10b + a) = 9 10a + b - 10b - a = 9 9a - 9b = 9 9(a-b) = 9 (a-b) = 1 .................(ii)Factors of 12 = 1, 2, 3, 4, 6, 12. and from equation (ii), (a - b) = 1 So, a = 4 & b = 3. Required number = ab = 43.

Question 7 |

Find a positive number which when increased by 16 is equal to 80 times the reciprocal of the number

20 | |

-4 | |

-10 | |

4 |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 7 Explanation:

Let the number be x. Then x + 16 = 80 * (1/x) x^{2}+ 16x – 80 = 0 x^{2}+ 20x – 4x – 80 =0 (x + 20) (x -4) Therefore x = 4

Question 8 |

What is the sum of two consecutive odd numbers, the difference of whose squares is 56?

30 | |

28 | |

34 | |

32 |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 8 Explanation:

Let the no. be x and (x +2). Then (x + 2)^{2}– x^{2}= 56 4x + 4 = 56 x + 1 = 14 x = 13 Sum of numbers = x + (x +2) = 28

Question 9 |

The product of two numbers is 108 and the sum of their squares is 225. The difference of the number is:

5 | |

4 | |

3 | |

None of these |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 9 Explanation:

Let the numbers be x and y. Then xy = 108 and x^{2}+ y^{2}= 225 (x –y)^{2}= x^{2}+ y^{2}– 2xy (x –y)^{2}= 225 – 216 (x –y)^{2}= 9 Therefore (x –y) = 3

Question 10 |

The average of 21 results is 20. Average of 1

^{st}10 of them is 24 that of last 10 is 14. the result of 11'th is :42 | |

44 | |

46 | |

40 |

**Arithmetic Aptitude 6**

**Numbers**

**Discuss it**

Question 10 Explanation:

11'th result = sum of 21 results – sum of 20 results = 21 x 20 – (24 x 10 + 14 x 10) = 420 – (240 + 140) = 420- 380 = 40

There are 28 questions to complete.