##### UNITS OF TIME

1 minutes = 60 seconds

1hour = 60 minutes

1 hour = 3600 seconds

1 days = 24 hours

1 days = 1440 minutes

1 days = 86,000 seconds

1 second = \frac{1}{60} minutes

1 minutes = \frac{1}{60} hours

##### MEASUREMENT OF LENGTH

10 Millimetre = 1 Centimetre

100 Centimetre = 1 Metre

1000 Metre = 1 Kilometre

12 inches = 1 feet

660 feet = 1 furlong

8 furlong = 1 mile

##### MEASUREMENT OF WEIGHT

1000 milligram = 1 gram

1000 grams = 1 kilogram

1000 kilograms = 1 tonne

28 grams= 1 ounce

16 ounce = 1 pound

2000 pound = 1 tonne

##### MEASUREMENT OF VOLUME

1000 milli litre = 1 litre

1000 litre = 1kilo litre

10 metre = 1 decametre

100 metre = 1 hectametre

1000 metre = 1 kilometre

{1}{10} metre = 1 decimetre

{1}{100} metre = 1 centimetre

{1}{1000} metre = 1 millimetre

##### NUMBER SYSTEM

INDIAN NAME | INTERNATIONAL NAME | NUMBERS | NUMBER OF ZEROES |

ONES | ONES | 1 | 0 |

TENS | TENS | 10 | 1 |

HUNDRED | HUNDRED | 100 | 2 |

THOUSAND | THOUSAND | 1000 | 3 |

TEN THOUSAND | TEN THOUSAND | 10000 | 4 |

ONE LAKHS | HUNDRED THOUSAND | 100000 | 5 |

TEN LAKHS | ONE MILLION | 1000000 | 6 |

ONE CRORE | TEN MILLION | 10000000 | 7 |

HUNDRED CRORES | ONE BILLION | 1000000000 | 9 |

### Various Types of Numbers

##### Natural Numbers

Counting numbers are called natural numbers . Thus , 1 , 2 , 3 , 4 , etc. are all natural numbers.

##### Whole Numbers

All counting numbers , together with 0 , form the set of whole numbers . Thus , 0 , 1 , 2 , 3 , 4 , etc are all whole numbers .

##### Integers

All counting numbers , zero and negatives of counting numbers , form the set of integers . Thus , ….- 3 , -2 , -1 , 0 , 1 , 2 , 3 , …. are all integers .

##### Even Numbers

A counting number divisible by 2 is called an even number . Thus , 0 , 2 , 4 , 6 , etc. are all even numbers .

##### Odd Numbers

A counting number not divisible by 2 is called an odd number . Thus , 1 , 3 , 5 , 7 , etc. are all odd numbers .

##### Prime Numbers

A counting number is called a prime number if it has exactly two factors , namely itself and 1 .

All prime numbers less than 100 are : 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97

##### Rational Numbers

A number of the {p}{q} where p and q are both integers and q not equal zero .

Example

\frac{2}{1},\frac{4}{8},etc. \\##### Irrational Number

A number having a non-terminating and non-recurring decimal expansion is called an irrational number.

Example

\sqrt{2},\sqrt{3},\sqrt{7},etc \\##### FACTORIAL OF A NUMBER

Natural numbers is called factorial

##### Formula

n!=n(n-1)(n-2)(n-3)….3.2.1

##### Example

Find the factorial value of 6

n=6

6!=(6-1)(6-2)(6-3)…….(6-5)

6!=5\times4\times3\times2\times1

6!=120

##### QUESTION 01

Which number should come in the place of the question mark?

3 | 6 | 9 |

5 | 3 | 6 |

3 | 2 | ? |

18 | 20 | 60 |

##### ANSWER

Step – 1

3\times5 + 3 =18

15 + 3 = 18

18 = 18

Step – 2

6\times3 + 2 =20

18 + 2 =20

20 = 20

Step – 3

9\times6 + ? =60

54 + ? = 60

54 + 16 = 60

**Answer = 16**

##### QUESTION 02

Which number should come in the place of the question mark?

9 | 4 | 12 |

4 | 1 | 5 |

3 | ? | 4 |

15 | 12 | 28 |

##### ANSWER

Step – 1

9 – 4 \times 3 =15

5 \times 3 = 15

15 = 15

Step – 2

12 – 5 \times 4 = 28

7 \times 4 = 28

28 = 28

Step – 3

4 – 1 \times ?=12

3 \times ?=12

3 \times 4 = 12

12 = 12

**Answer = 4**

##### QUESTION 03

Complete the series

4 | 15 | 9 |

5 | ? | 18 |

6 | 7 | 12 |

3 | 13 | 15 |

##### ANSWER

Step – 1

5 + 4 – 6 = 3

9 – 6 = 3

3 = 3

Step – 2

9 + 18 – 12 = 15

27 – 12 = 15

15 = 15

Step – 3

15 + ? – 7 =13

15 + 5 – 7 = 13

20 – 7 = 13

13 = 13

**Answer = 5**

##### QUESTION 04

Given below are two series with specific pattern

2 | 4 | 16 | 96 | 768 |

3 | a | b | c | d |

What will come in place of (c) ?

##### ANSWER

First Row

2 \times 2 = 4

4 \times 4 = 16

16 \times 6 = 96

96 \times 8 = 768

Second Row

3 \times 2 = 6

6 \times 4 = 24

24 \times 6 = 144

144 \times 8 = 1152

a=6, b=24, c=144, d=1152

**Answer = 144**

##### QUESTION 05

Given below are two series with specific pattern

4 | 3 | 16 | 9 | 256 | 81 |

6 | a | b | c | d | e |

What will come in place of (C) ?

##### ANSWER

First Row

4^1 = 4

3^1 = 3

4^2 = 16

3^2 = 9

4^4 = 256

3^4 = 81

Second Row

6^1 = 6

5^1 = 5

6^2 = 36

5^2 = 25

6^4 = 1296

5^4 = 625

a=5, b=36, c=25, d=1296, e=625

**Answer = 25**

##### Instruction

Alphabet letters

a b c d e f g h i j k l m n o p q r s t u v w x y z

a + 1 meaning adding one alphabet letter = b

a +5 next five alphabet letters = f

f -4 back four alphabet letters= b

r -10 back ten alphabet letters= h

##### QUESTION 06

Find the next term in the series:

DF, GJ, KM, NQ, RT, ____?

##### ANSWER

**Answer = UX**

##### QUESTION 07

What comes next ?

c+y, d+x+1, e+w+2, f+v+3,….

##### ANSWER

**Answer = g+u+4**

##### QUESTION 08

Complete the series

k,15w, j, 18x, i, 21y, ?

##### ANSWER

**Answer = h24z**

##### QUESTION 09

Find out the missing term in the series :

126,217,344,____,730

##### ANSWER

5^3 + 1 = 125 + 1 = 126 \\ 6^3 + 1 = 216 + 1 = 217 \\ 7^3 + 1 = 343 +1 =344 \\ 8^3 + 1 = 512+ 1 = 513 \\ 9^3 + 1 = 729 + 1 = 730 \\**Answer = 513**

**QUANTITATIVE APTITUDE STUDY MATERIAL**

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