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
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## Numbers

 Question 1
Which is not the prime number?
 A 43 B 57 C 73 D 101
Arithmetic Aptitude    Numbers
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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?
 A 25 B 12 C 13 D 14
Arithmetic Aptitude 4    Numbers
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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 n

Then 3 x 3n-1 = 531441

∴ 3n = 312

∴ n = 12```
 Question 3
If the average of four consecutive odd numbers is 12, find the smallest of these numbers?
 A 5 B 7 C 9 D 11
Arithmetic Aptitude 4    Numbers
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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?
 A 6 & 7 B 5 & 8 C 4 & 9 D 3 & 10
Arithmetic Aptitude 4    Numbers
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Question 4 Explanation:
Let the numbers be x and 13-x Then x2 + (13 – x)2 = 85 ∴ x2 + 169 + x2 – 26x = 85 ∴ 2 x2 – 26x + 84 = 0 ∴ x2 – 13x + 42 = 0 ∴ (x-6)(x-7)=0 Hence numbers are 6 & 7
 Question 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?
 A 5 B 7 C 6 D None of these
Arithmetic Aptitude 5    Numbers
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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:
 A 34 B 62 C 43 D 26
Arithmetic Aptitude 5    Numbers
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Question 6 Explanation:
```Let the ten’s and unit’s digit be x and y.

Then 10x + - 9 = 10 x + x

10x2 + 12 -9x = 120 + x2
9x2 – 9x – 108 = 0
x2 –x – 12 = 0
x2 –4x + 3x – 12 = 0
(x – 4) (x + 3) = 0
Therefore x = 4
Hence the required no. is 43```
 Question 7
Find a positive number which when increased by 16 is equal to 80 times the reciprocal of the number
 A 20 B -4 C -10 D 4
Arithmetic Aptitude 5    Numbers
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Question 7 Explanation:
```Let the number be x.

Then x + 16 = 80 * (1/x)

x2 + 16x – 80 = 0
x2 + 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?
 A 30 B 28 C 34 D 32
Arithmetic Aptitude 5    Numbers
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Question 8 Explanation:
```Let the no. be x and (x +2).
Then (x +2)2 – x2 = 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:
 A 5 B 4 C 3 D None of these
Arithmetic Aptitude 5    Numbers
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Question 9 Explanation:
```Let the numbers be x and y.
Then xy = 108 and x2 + y2 = 225
(x –y)2 = x2 + y2 – 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 1st 10 of them is 24 that of last 10 is 14. the result of 11'th is :
 A 42 B 44 C 46 D 40
Arithmetic Aptitude 6    Numbers
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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 27 questions to complete.
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