Numerical Ability

EDUEgypt Program – Numerical Ability Participant's Guide

Ministry of Communications and Information Technology

Information Technology Institute

1 Numerical Ability | EDUEgypt Program

Aptitude Excellence: Your Guide to the Perfect Score

Numerical Ability: The Facilitator’s Manual




Table of Contents Introduction ................................................................................................................................................... 5

Module Objectives ........................................................................................................................................ 6

WIIFM ............................................................................................................................................................ 6

Relevance to BPO .......................................................................................................................................... 7

Introduction .................................................................................................................................................. 8

Numerical digits ........................................................................................................................................ 8

Place Values .............................................................................................................................................. 8

Binary Mathematical Operations ............................................................................................................ 10

Order of Operations ................................................................................................................................ 10

What is addition? ........................................................................................................................................ 12

Properties of addition ............................................................................................................................. 13

The Cumulative Property of addition .................................................................................................. 13

The Associative Property of addition .................................................................................................. 13

How to add two numbers ....................................................................................................................... 14

Quick Facts .............................................................................................................................................. 15

What is subtraction? ................................................................................................................................... 16

The Inversion Concept ............................................................................................................................ 17

How to subtract two numbers ................................................................................................................ 18

Multiplication & Division............................................................................................................................. 26

Multiplication .......................................................................................................................................... 26

Properties of Multiplication .................................................................................................................... 27

The Cumulative Property of Multiplication ........................................................................................ 27

The Associative Property of Multiplication ........................................................................................ 27

Identity element .................................................................................................................................. 27

The Zero Element ............................................................................................................................... 28

Quick facts ............................................................................................................................................... 28

How to multiply two numbers ................................................................................................................ 29

Division ........................................................................................................................................................ 35

How to divide two numbers ................................................................................................................... 35




Averages ...................................................................................................................................................... 47

Quick facts: .............................................................................................................................................. 52

Adding two fractions ............................................................................................................................... 52

Subtracting Two Fractions ...................................................................................................................... 53

Multiplying Fractions .............................................................................................................................. 53

Dividing Fractions .................................................................................................................................... 54

How to find missing numbers in fractions .............................................................................................. 55

Percentage .................................................................................................................................................. 59

How to calculate percentage .................................................................................................................. 61

Converting fractions to percentage ........................................................................................................ 62

Quick fact ................................................................................................................................................ 62

Data Interpretation ..................................................................................................................................... 67

Bar Charts ................................................................................................................................................ 68

Double bar chart ..................................................................................................................................... 68

Pie Charts ................................................................................................................................................ 70

Ratio & Proportion ...................................................................................................................................... 78

Ratio ........................................................................................................................................................ 78

Ratio of Greater Inequality ................................................................................................................. 79

Ratio of Less Inequality ....................................................................................................................... 79

Proportion ............................................................................................................................................... 80

Profit & Loss ................................................................................................................................................ 85

Profit and Loss ......................................................................................................................................... 85

Cost Price: ............................................................................................................................................... 85

Selling Price: ............................................................................................................................................ 85

Aptitude Tests ............................................................................................................................................. 93

Aptitude Test 1 ........................................................................................................................................ 94

Aptitude Test 1 Answers ......................................................................................................................... 98

Aptitude Test 2 ...................................................................................................................................... 101

Aptitude Test 2 Answers ....................................................................................................................... 104

Aptitude Test 3 ...................................................................................................................................... 108





Aptitude Test 4 ...................................................................................................................................... 114





Introduction

Welcome Aptitude Excellence: Your Guide to the Perfect Score !

This module has been developed specifically to equip you with the essential knowledge that can help your

trainees secure a job at a BPO company.

As a part of the hiring process, many companies require candidates to pass a test to make sure they are

qualified enough to carry out the basic responsibilities of the job.

There are three types of tests:

Achievement: what you have accomplished in the past.

Ability : what you are able to demonstrate in the present.

Aptitude: how quickly or easily you will be able to learn in the future.

We are concerned here with the aptitude tests, because these tests can measure how likely you are going

to respond to the tasks of your new job. Thus, every job profile has its own aptitude tests that are relevant

to the needed skills.

What skills does a BPO-specific aptitude test measure?

BPO-specific aptitude tests cover a range of skills:

- numerical ability: the ability to work with numbers accurately and in a timely fashion

- logical reasoning & analytical thinking: the ability to think clearly, and apply common sense to

reach an answer.

- attention to details: the ability to handle large ranges of data accurately

- data interpretation: the ability to comprehend, interpret, and apply mathematical operations to

information represented in graphs and diagrams.

- logical reasoning and analytical thinking are among the most important skills in the arsenal of any

job candidate. Mastery of these two skills will make you very employable.




Module Objectives

Upon the completion of this module, you will be able to:

list the benefits of develop you numerical skills

recognize the importance of numerical skills in BPO

relate numerical skills to BPO

carry out the basic numerical operations correctly, effectively, and in a timely fashion

solve numerical ability questions accurately

WIIFM This module will help you to:

understand numbers better

carry out the basic numerical operations more effectively

pass the numerical section on aptitude tests

think clearly and logically




Relevance to BPO

In a BPO company, you will be required to deal with large arrays of clients’ data

accurately and effectively. Mastering the basics of numerical ability will help you do just

that. In frontline processes like sales and customer, you will need to explain offers to

customers, and answers their queries effectively. Imagine for a moment that a customer

needs to know how much a 15% bonus is in money, so he/she can decide to accept your offer

or turn it down. You can either ask him to hold as you try to remember, grab a pen and paper,

scribble the formula, apply it to the figures, and return to him with an answer (which will

take a lot of time and can make him/her doubt your credibility) or you can present yourself as

very professional by giving him/her the answer confidently without asking him/her to wait

for a long time. If you go for the second choice, then welcome to the numerical ability

module.

This module has been specifically developed to equip you with the essential knowledge and

skills that will help you solve numerical problems effectively.




Introduction There are primarily four binary mathematical operations. An operation is an action or a procedure which produces a new value from one or more input values. Binary operations involve two values or numbers. Binary operations primarily include addition, subtraction, multiplication and division.

Numerical digits A digit is a symbol which is used to represent numbers or integers or real numbers. Each digit in

a number system represents an integer. An integer is any of the natural numbers Positive or

negative) or zero. There are ten digits in mathematics:

0 1 2 3 4 5 6 7 8 9

Example

The digits 5 & 2 are used to denote the number 52.

The digit 1 represents the number 1.

The digits 4 & 8 are used to denote the number 48.

Place Values Numbers can have multiple digits. Each digit in a number has a different place value.

Establish by giving an example:

The number 987 is a 3 digit number.

The first digit is called the hundreds' place. It shows how many sets of one hundred are in the

number. The number 987 had nine hundreds.

The middle digit is the tens' place. It tells you that there are 8 tens in addition to the nine

hundreds.

The last or right digit is the ones' place or the units' place, which is 7 in this case. Therefore,

there are 9 sets of 100, plus 8 sets of 10, plus 7 ones in the number 987.

9 8 7

| | |__ones' place

| |_________tens' place

|________________hundreds' place




Some more examples:

Number Hundreds Tens Units Solution




Binary Mathematical Operations There are primarily four binary mathematical operations.

An operation is an action or a procedure which produces a new value from one or more input

values. Binary operations involve two values or numbers. Binary operations primarily include

addition, subtraction, multiplication and division.

Order of Operations BODMAS:

B= Brackets first

O= Orders (ie Powers and Square Roots, etc.)

D= Division

M= Multiplication

A= Addition

S= Subtraction

Divide and multiply rank equally

Add and Subtract rank equally

In any calculation once you have completed "B" and "O" operations, just go from left to right

doing any "D" or "M" as you find them. Then go from left to right doing any "A" or "S" as you

find them.

Example 1

3 + 6 × 2 = ?

3 + (6 × 2) = ?

3+ (12) = ?

3+ (12) = 15

Example 2

(3 + 6) × 2 = ?

(3 + 6) = 9

9 × 2 = 18




Example 3

12 / 6 × 3 = ?

Since, Division and Multiplication rank equally, so just solve it from left to right:

First 12 / 6 = 2, then 2 × 3 = 6




What is addition? Addition represents combining collections of objects together into a larger collection. It can also

be defined as the "putting together" of two units and finding how many in all. It is demonstrated

by the plus sign (+). The numbers being added are called the addends.

Example:

There are 3 + 2 oranges—meaning three oranges and two other oranges —which is the same as

five oranges.

That means:

Addition as an operation has some properties. We’ll look at the Cumulative and Associative

property in detail. Explain both the properties with the help of the examples listed below.




Properties of addition The Cumulative Property of addition

Addition is cumulative. That means changing the order of addends does not change the end

result.

Example:

3 oranges + 2 oranges = 5 oranges

2 oranges + 3 oranges = 5 oranges

4 apples + 5 apples = 9 apples

5 apples + 4 apples = 9 apples

$ 5 + $ 2 = $ 7

$ 2 + $ 5 = 9

The Associative Property of addition

Addition is associative. That means when we add more than two numbers, order in which

addition is performed does not matter.

Example:

(5 Oranges + 2 Oranges) + 1 orange = 7 Oranges + 1 Orange= 8 Oranges

5 Oranges + (2 Oranges + 1 orange) = 5 Oranges + 3 Oranges=8 Oranges

(4 Apples + 3 Apples) + 2 Apples = 7 Apples + 2 Apples= 9 Apples

4 Apples + (3 Apples + 2 Apples) = 4 Apples + 5 Apples=9 Apples

($ 2 + $ 4) + $4 = $6 + $4 = $10

$2 + ($4 + $4) = $2 + $8 = $10




How to add two numbers We need to follow some simple steps to add numbers. We’ll look at one example. Solve the

following example on the board. Also tell them that it’s easy to count small numbers as most of

the calculations can be done verbally. We need to follow a process while dealing with bigger

values.

Example: Add 1893 + 343

Step 1: Write the numbers you wish to add one below the other, aligning the Nunits’ place (one

place) of one numbers right below the other

Step 2: Start by adding the two numbers in the far right column

Step 3: Add the two numbers in the next column. If the result is a two digit number then the units

place is written at the bottom and tens’ place is put on the digit as a carry number.

Step 4: Add the two numbers in the next column and the carry digit. (8+3+1). Put 2 in the

result’s place and carry 1.

Step 5: Add the numbers in the last column (1 + carry 1)




Answer: 2236

Quick Facts The sum of two negative integers is a negative integer.

(-2) + (-7) = (-9)

(-1) + (-2) = (-3)

(-3) + (-5) = (-8)

The sum of two positive integers is a positive integer.

(2) + (7) = (9)

(1) + (2) = (3)

(3) + (5) = (8)

To add a positive and a negative integer (or a negative and a positive integer), follow

these steps:

o Subtract the smaller number from the larger number

The result takes the sign of the integer which is greater than the other

(2) + (-7) = (-7)

(-1) + (2) = (1)

(3) + (-5) = (-2)




What is subtraction? Subtraction tells "how many are left" or "how many more or less." It is denoted by a minus sign

(-).

Example:

There are 5 oranges, if we take out 3 oranges; we are left with 2.

That means:

5 Oranges - 3 Oranges = 2 Oranges

Explain:

Subtraction also has many properties. The most important one is the Inversion concept. Explain

with the help of the examples given.




The Inversion Concept It’s said that addition and subtraction are inverse operations as one operation can undo the other

operation. This is why the two operations are taught together.

Example

Adding 2 and 5 to get 7 is the inverse of 7 minus 5, leaving 2





This is why the two operations are taught together.




How to subtract two numbers We need to follow some simple steps to subtract two numbers. We’ll look at one example. Solve

the following example on the board.

Example: 1893 - 343

Step 1: Write the numbers you wish to subtract one below the other, aligning the units’ place

(one place) of one numbers right below the other

Step 2: Start by subtracting the two numbers in the far right column

Step 3: Subtract the two numbers in the next column. If the number to be subtracted is bigger

than the number from which it’s being subtracted then carry 1 from the adjacent number.

Step 4: Subtract the two numbers in the next column

Step 5: Subtract the numbers in the last column

Answer: 1490

Give more examples to establish the process.




Exercise 1

1. 3 + 6 - 3 + 2 =

2. 20 - (3 + 2 - 5) =

3. 7 + (6 - 5 + 3) =

4. (15 - 3 + 4) - (18 - 7 + 2) =

5. 67 + 521 =

6. 875 + 235 =

7. 76 + 612 =

8. 986 + 145 =

9. 483 + 214 =

10. 675 + 318 =

11. 321 + 281 =

12. 423 + 326 =

13. 501 + 239 =

14. 792 + 100 =

15. 120 + 420 =




Exercise 2




Exercise 3

1. Ron loves to collect coins. He has 123 Indian coins, 167American coins and 234 African

coins. How many coins does he have in his collection?

2. A man buys 4 fishes for $ 560 the first time and 23 fishes for $986 the second time. How

many fishes does he have now and how much money did he spend?

3. A man spends $2000 on a pair of shoes, $230 on a pair of sunglasses and $1000 n a pair

of sunglasses. How much money did he spend shopping for all the items?

4. There are 22 horses and 18 donkeys on a farm. How many animals are there on the farm?

5. Martha has $143. She gives away $19 to her best friend. How many dolls does she have

now?

6. An aquarium contains 47 fish of which 9 are not moving. How many fish in the tank are

moving?

7. There are 82 birds in a sanctuary of which 79 are white. How many birds are there of

other colors?

8. The Royal Circus has 10 Lions. 2 of them are injured. How many lions can take part in

the circus?

9. A woman pays $ 2785 to the maid every month. This month she pays her $2875 by

mistake. How much extra money did she pay?

10. Mr. Smith drove 44 miles in his new car on Monday and 7 miles on Wednesday. How

many miles did he drive in these two days?

11. Harry has 3 jobs and earns $567 per day from each job. How much money does he earn

every day?

12. There are 9 buses and 75 cabs in a parking lot. After some time 4 buses and 6 cabs leave.

How many vehicles are there in the parking lot?

13. Martha is given money by her mother, her father and her sister. They give $999, $576

and $300 respectively. However, her brother takes $248 from her. How much money is

she left with?

14. A bus drove under a huge bridge which was 17 m high. There was a gap of 9 m between

the top of the bus and the bridge. How many meters was the Bus in height?

15. A milk van started with 13 bottles of milk. It delivered 9 bottles. Later 6 bottles were

returned to him by one of the customers. How many bottles are still to be delivered?




Exercise 4:




Exercise 1: Answer key






1. 524

2. 27 fishes & $ 1546

3. $3230

4. 40 animals

5. $124

6. 38 fishes

7. 3 birds

8. 8 Lions

9. $90




10. 51 miles

11. $1701 everyday

12. 74 vehicles

13. $1627

14. 8 m

15. 10 bottles





Multiplication & Division

Multiplication

Multiplication is one of the four basic operations in elementary mathematics. It is the

mathematical operation of scaling one number by another.

Example

5 multiplied by 2 (often said as "5 times 2") can be calculated by adding 5 copies of 2 or by

adding 2 copies of 5:

5 x 2 = 2 + 2 +2 +2 +2 = 10

5 x 2 = 5 + 5 = 10 (Here 5 and 2 are the "factors" and 10 is the "product")

Multiplication is written using the multiplication sign (X) or period (.) between the terms. The

result is expressed with an equality sign.

Example

5 x 2 = 10 or 5 . 2 = 10 (Verbally, "Five times two equals ten")

3 x 7 = 21 or 3 . 7 = 21

3 x 4 x 5 = 12 x 5 = 60 or 3 . 4 . 5 = 12 . 5 = 60

Establish:

Multiplication also has some properties like addition and subtraction. We’ll look at some

property in detail. Explain the properties with the help of the examples listed below.




Properties of Multiplication

The Cumulative Property of Multiplication

Multiplication is cumulative. That means changing the order of numbers does not change the end

result.

ab = ba

Examples

2 x 3 = 3 x 2 = 6

4 x 5 = 5 x 4 = 20

7 x 8 = 8 x 7 = 56

The Associative Property of Multiplication

Multiplication is associative. That means when we multiply more than two numbers, order in

which multiplication is performed does not matter.

A(bc) = (ab)c

Examples

3 x (2 x 5) = 3 (15) = 30

(3 x 2) x 5 = (6) x 5 = 30

5 x (7 x 2) = 5 (14) = 70

(5 x 7) x 2 = (35) x 2 = 70

4 x (5 x 6) = 4 (30) = 120

(4 x 5) x 6 = (20) x 6 = 120

Identity element

The multiplicative identity is 1; anything multiplied by one is itself. This is known as the identity

property.

5 x 1 = 5

4 x 1 = 4

8 x 1 = 8




The Zero Element

Anything multiplied by zero is zero. This is known as the zero property of multiplication. Zero is

sometimes not included amongst the natural numbers.

5 x 0 = 0

4 x 0 = 0

8 x 0 = 0

Quick facts:

When you multiply

Negative Number x Negative Number = Positive result

(-) 4 x (-4) = 16

(-) 5 x (-2) = 10

(-) 3 x (-4) = 12

Positive Number x Positive Number = Positive result

4 x 4 = 16

5 x 2 =10

3 x 4 = 12

Negative Number x Positive Number = Negative result

(-) 4 x 4 = -16

(-) 5 x 2 =-10

(-) 3 x 4 = -12

Positive Number x Negative Number = Negative result

4 x (-) 4 = -16

5 x (-) 2 =-10

3 x (-) 4 = -12

Let’s look at some more examples:




Establish:

We need to follow some simple steps to multiply numbers. We’ll look at some examples.

Solve the following example on the board. Also tell them that it’s easy to multiply small

numbers as most of the calculations can be done verbally. However, we need to follow a process

while dealing with bigger values.

How to multiply two numbers

Example 1

Step1: Multiply the 2 and 3 to get 6.




Step 2: Multiply the 1 and 3 to get 3.

Example 2

Step 1: Multiply 3 and 2 to get 6.

Step 2: Multiply 3 and 2 to get 6.

Step 3: Multiply 3 and 1 to get 3 and write it at the tens place below 66

Step 4: Multiply 3 and 1 to get 3




Step 5: Add the two numbers together to get the answer

Answer: 396

Example 3

Step 1: Multiply 6 and 7 to get 42. Since 42 is greater than 9, you'll have to carrythe 4.

Step 2:

n 9, you'll have to carry the 3.

Step 3:

Multiply the 1 and 7 to get 7.

And, add the carried 3 to get 10.




10 is greater than 9, but there are no more digits to carry over, so just write the 1 down in

front.










Step 10: Add the three numbers together to get the answer

Answer: 16692




Division In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that

is the inverse of multiplication.

Like all other mathematical operations we have to follow some simple steps to divide numbers.

We’ll look at some examples.

Solve the following example on the board.

How to divide two numbers

Example 1: 430/2

Solution:

Dividend = 430

Divisor = 2

Step 1: The first number of the dividend is divided by the divisor. (4 divided by 2)




Step 2: The quotient is placed at the top (2 placed at the top)

Step 3: The remainder is written below the result of the first operation (0 is the remainder)

Step 4: Bring down the next number of the dividend (3 is brought down)

Step 5: Divide this number by the divisor (3 divided by 2)

Step 6: The quotient is placed at the top (1 placed at the top)

Step 7: The remainder is written below the result of the second operation (1 is the remainder)

Step 8: Bring down the next number of the dividend (0 is brought down)

Step 9: Divide this number by the divisor (10 divided by 2)

Step 10: The remainder is written below the result of the third operation (0 is the remainder)

The answer is 215.

The steps are repeated till the time, the remainder is 0 or the remainder is no longer divisible by

the divisor.




Example 2:

Solution;

Dividend = 435

Divisor = 25

Step 1: 4 divided by 25

Step 2: 0 (quotient) placed at the top, as 4 is not divisible by 25)

Step 3: 3 (next number) is brought down


Step 5: 1 (quotient) placed at the top

Step 6: 18 (remainder) is written below 25(the result of the second operation)

Step 8: 5 (next number) is brought down


Step 10: 10 (remainder) is written below 175(the result of the third operation)

The answer is expressed as 17 remainder 10




Exercise 1




Exercise 2




Exercise 3

1. Ron invites 4 friends to his anniversary party. He distributes 36 pens equally among them.

How many pens did each friend get?

2. There are 9 flowers in each bouquet. How many flowers are there in 4 bouquets?

3. Martha bought 40 chocolates for the birthday party and put them equally in 4 gift pouches.

How many chocolates did she put in each pouch?

4. The principal has planned 18 total prizes for the batch. Each class would have 3 winners. How

many classes can win the prize?

5. A florist has 8 Roses. He has 3 times as many gladioli as roses. How many gladioli does the

florist have?

6. Mary places 54 paper plates on the table in 6 rows. How many paper plates are there in each

row?

7. In each of 27 vases at a flower shop, there are 6 roses and 6 daisies. How many total flowers

are there in the vases?

8. There are 50 muffins to be arranged equally in 10 trays in a wedding. How many sandwiches

will there be in each tray?

9. There are 10 butterflies with 30 green spots on their wings. If each butterfly has the same

number of spots, how many spots on each moth?

10. A magician has 10 bunnies. He wants to place 2 bunnies in each cage. How many cages will

he need?

11. An Arab merchant had 70 camels. He gave them equally to his 5 sons. How many camels did

each son get?

12. A tailor stitches 2 shirts every day. Each shirt uses 6 buttons and has two pockets. How many

buttons and pockets will be put in 8 days?

13. The bus ticket to Central Park costs 2 times more than that to the Lotus valley. If the ticket to

Central Park costs $ 240, how many dollars is the ticket to the Lotus valley?

14. There are 2 men in the bus. There are 3 times more women in the bus.

How many women are there in the bus?

15. A man brings home 10 flowers from a park. His wife loves the flowers and wants him to

bring 5 times as many this time. How many flowers will he bring?




Exercise 4

Multiply the following:




Exercise 5




Exercise 1: Answer Key






1. 9 pens

2. 36 flowers

3. 10 chocolates

4. 6 classes

5. 24 Gladioli

6. 9 rows

7. 324 flowers

8. 5 muffins




9. 300 spots

10. 5 cages

11. 12 camels

12. 128 buttons and pockets

13. $120

14. 6 women

15. 50





Averages Formula used to find average:

The straight average, or arithmetic mean, is the sum of all values divided by the number of

values. It is a single value that is meant to typify a list of values.

The methodology to find average of two or more numbers

Example 1:

Find the average of the first 5 prime numbers.

Solution:

The first five prime numbers are: 2, 3, 5, 7, 11

The total of the first five prime numbers is: 28

Solution:

The first five prime numbers are: 2, 3, 5, 7, 11

The total of the first five prime numbers is: 28

The average = 28/5 = 5.6

Example 2:

A man earns $3092 in the first 6 months during a year. He earns $4400 in the next 3 months and

$5000 in the last 3 months. What is his average salary?

Solution:

The total money earned= $3092 +$4400 +$5000 = $12492

Total number of months he worked for = 6+3+3 = 12 months

Therefore, the man earned $1041 on an average.




Exercise 1

Find the average of the following numbers:

Exercise 2

1. The average of 6 numbers is 20. If one number is removed, the average of the remaining

numbers is 15. What number was removed?

2. The average of four tests of a student is 75 and he wants to raise it to 80. What must he score

in the fifth test?

3. Ron has $78. Harry has twice as much as money as Ron. What is the average amount of

money each boy has?

4. Martha scored 85, Sam scored 89 and Rob scored 99. What is the average of all the scores?

5. Holly read six books in February, four in March and eight in April. How many books on an

average did she read?

6. A man has three orange trees. The first tree produced 90 oranges, the second one produced 82

oranges and the third one produced 95 oranges. Find the average number of Oranges.

7. The average of 3 numbers is 26. Two of the numbers are 11 and 21. What is the third number?

8. The average savings of 2 girls and 2 boys is $250. Each girl saves $50 more than each boy.

Find the savings of one boy.

9. The average mass of 6 boxes is 5.65 kg. Find the total mass of the 6 boxes.




10. Bag X weighs 4.8kg. Bag Y is 0.8kg heavier than Bag X. What is the average mass of the

two bags?

11. The average mass of Caili and her three sisters is 42kg. If Caili is 48kg, what is the average

mass of her three sisters in kg?

12. The average mass of 3 boys is 45 kg. Two of the boys are 56kg and 34kg. What is the mass

of the third boy?

13. The average height of 2 men is 1.65m. When the third man joins them, their average height

becomes 1.6m. What is the height of the third man?

14. After 4 games, Rita's average bowling score was 99. What score must she bowl on her next

game to increase her bowling average to 100.

15. Peter has 10 metres of rope. Sam has 3 times more rope than Peter. What is the average

length of rope each boy has?

16. Hela bought 7 pens, one for each of her seven friends, for $9.95 each. The shopkeeper

charged her an additional $13.07 as sales tax. She left the store with $7.28. How much money

did Hela start with?

17. The average monthly rainfall for 6 months was 28.5 mm in Cairo. If it had rained 1mm more

each month what would the average have been?






1. 45

2. 100

3. 117

4. 91

5. 6 books

6. 89

7. 45

8. 225

9. 33.9 kg

10. 5.2 kg

11. 39

12. 45

13. 1.5 m

14. 104

15. 20 m

16. $90

17. 29.5mm




Fractions

A fraction is a part of an entire object. Fractions consist of two numbers. The top number is

called the numerator. The bottom number is called the denominator.

Establish: WIFM

Fractions are an integral part of real life in many different ways. If you look around you,

fractions are everywhere. For example, fractions find their way into the kitchen quite a lot. There

are fractions in recipes, in cooking measurements and in planning the cutting up of a birthday

cake. Fractions also come up when you travel to find out how much of a trip we have done

already (one third of the route covered). Fractions can also be found in money transactions as

well (half a dollar).

Example:

This pizza has been cut into four equal parts.

Let’s think about one slice:

Total no of slices in the pizza = 4

We can say one slice is 1 or ¼ (verbally ―one fourth‖) of the whole pizza.




Quick facts: Factions should always be written in the simplest form.

Simplifying (or reducing) fractions means to make the fractions as simple as possible. Why say

four-eighths (4/8) when you really mean half (1/2)?

In order to simplify the fraction try dividing both the top and bottom of the fraction with the

same number until you can't go any further (try dividing by 2,3,5,7,... etc).

Example:

24 / 108

Adding two fractions To add two fractions with the same denominator:

Add the numerators and place that sum over the common denominator.

Examples:

1 / 5 + 3 / 5 = (1+3) / 5 = 4/5

1 /3 + 1 / 3 = (1+1) / 3 = 2 / 3

1 / 7 + 2 / 7 = (1+2) / 7 = 3 / 7

To add two fractions with the same denominator:

Example

1/ 3 + 1/ 5

Step 1: The denominators must be equal. Multiply the denominators (3 x 5 = 15)

Now in order to make the denominators same:




Step 2: The bottom numbers are now the same, so we can go ahead and add the top numbers:

3 / 15 + 5 / 15 = 8 / 15

Subtracting Two Fractions

To subtract two fractions with the same denominator:

Subtract the numerators and place the result over the common denominator.

Example

3 / 5 - 1 / 5 = (3-1) / 5 = 2/5

1 /3 - 2 / 3 = (1-2) / 3 = -1 / 3

5 / 7 - 2 / 7 = (5-2) / 7 = 3 / 7

To subtract two fractions with the same denominator:

Step 1: The denominators must be equal. Multiply the denominators (3 x 5 = 15)

Now in order to make the denominators same:

Step 2: The bottom numbers are now the same, so we can go ahead and subtract the top numbers:

5 / 15 - 3 / 15 = 2 / 15

Multiplying Fractions

There are 3 simple steps to multiply fractions

Example:




Step 1. Multiply the top numbers:

Step 2. Multiply the bottom numbers:

Step 3. Simplify the fraction:

Dividing Fractions

There are 3 simple steps to divide fractions:

Example:

Step 1. Turn the second fraction upside-down (the reciprocal):

Step 2. Multiply the first fraction by that reciprocal:

Step 3. Simplify the fraction:




How to find missing numbers in fractions

Type I (when we do not have addition and subtraction operations in any of the fractions)

Example 1:

Solution:

Step 1: cross multiply numbers in such a manner that X (number to be found) is on one side of

the

Step 3: Simplify the fraction and find the missing number

Example 2:

Solution:

X = 5 x 11

X = 55




Type II (when we addition and subtraction operations in any of the fractions)




Exercise 1

1. A class has 10 girls and 30 boys. What part of the class are boys?

2. If I earns $x in a week and spend $y, what part of my weekly salary did I save?

3. 14 is of what number?

4. Basim won 251/5 dollars and Paki won 152/5 dollars in a contest. What was the total amount

of price they won?

5. Doaa spent of her allowance on shopping. What fraction of her allowance is she left with?

6. In a group of children were girls. If there were 24 girls in the group, how many children were

there in the group?

7. Basma had 120 dolls in her toy store. She sold of them at $12 each. How much money did she

earn?

8. A class took a poll to find out their favorite ice cream. 1/4 chose chocolate, 1/4 chose vanilla

and 1/2 chose strawberry. 2 kids have throat infection and can't eat ice cream. If there are 22 kids

in the class, how many kids liked each flavor?

9. Nirvana had 12 baseball cards. She gave Ghaida 3 cards, Dina 3 cards, and islam 3 cards.

What is the fraction of cards that she gave away? 10. There are 30 Easter eggs hidden in the

basket. 6 are pink, 6 are green, 8 are yellow and the rest are purple. If Aya found all of the purple

eggs, what fraction of eggs did she find?


1. 3/4

4. 403/5

5. 5/9

6. 40

7. $960

8. 5 chocolate, 5 vanilla, 10 strawberry

9. 3/4

10. 1/ 3




Percentage ―Examine the table closely

Percentage square‖




Count the following:




How to calculate percentage

Given amount x 100 = ___ %

Total amount

Let’s look at this square. It has been divided into 100 equal parts. 50 parts are

shaded green.

Total number of squares= 100

Given amount: Green squares = 50 or 50 x 100 = 50 % squares are green

100

Given amount: Blue squares = 60 or 60 x 100 = 50 % squares are blue

100

Given amount: Yellow squares = 40 or 40 x 100 = 50 % squares are yellow

100

Triangles = 4

Fractions: 4 or 4/50 squares have triangles in them

50

Percentage: 4 x 100 = 8% squares have triangles in them

50

We use percentages every day in our life for calculating many things like discount, sales

commission, sales tax, simple interest, etc.




Converting fractions to percentage Any fraction can be converted into a percentage by simply multiplying the fraction by 100.

Example:

Converting percentage to fractions

Percentages can be converted into fractions by simply dividing the percentage by 100 and

simplifying it.

Example:

Quick fact:

Exercise 1

1. What is 70% of 30?

2. What is 20% of 60?

3. What is 50% of 54?

4. What is 50% of 30?

5. Find a number so that 50% of it is 17.


7. What is 50% of 58?

8. What is 50% of 26?




9. What is 50% of 62?


11. What is 10% of 70?



14. What is 25% of 56?

15. What is 25% of 24?

Exercise 2

1. What is 50% of 96?


3. What is 50% of 78?

4. What is 50% of 86?






10. What is 100% of 90?

11. What is 60% of 65?


13. What is 100% of 54?

14. What is 50% of 46?

15. What is 40% of 5?




Exercise 3

1. The $3.50 purse I purchased was on sale for 25% off, what did I pay for it?

2. John had $350 in his savings account. He spent 40% of his savings. How much money

does he have left?

3. The market price of my new cell phone was $99.50 but it was on sale with 30% off. What

did I pay for it?

4. There are 500 tickets for a concert. 90% of the tickets were sold. 60% of the tickets old

were adult tickets and the rest sold were children tickets. How many tickets for children

were sold?

5. A new pair of denims was being sold for $59.99 but I got 30% off. What did I pay?

6. $50.00 spring jackets were on sale for 30% off, how much are they now?

7. Susan bought 25kg of meat. 15% of the meat was chicken and 45% of the meat was fish.

The rest was beef. What percentage of meat bought was beef?

8. I didn’t have to pay $119.95 for my new wallet because it was on sale for 35% off so I

only paid?

9. Daisy bought 60 kg of flour. She used 35% of the flour to make cakes and 15% of the

flour to make biscuits. How much flour does she have left?

10. I purchased a pair of shoes regularly priced at $19.50. I got a 40% off on my purchase.

How much did I pay?


1. 70% of 30 is 21

2. 20% of 60 is 12

3. 50% of 54 is 27

4. 50% of 30 is 15

5. 50% of 34 is 17

6. 50% of 70 is 35

7. 50% of 58 is 29

8. 50% of 26 is 13

9. 50% of 62 is 31

10. 50% of 28 is 14




11. 10% of 70 is 7

12. 50% of 38 is 19

13. 50% of 56 is 28

14. 25% of 56 is 14

15. 25% of 24 is 6


1. 50% of 96 is 48

2. 20% of 95 is 19

3. 50% of 78 is 39

4. 50% of 86 is 43

5. 52% of 25 is 13

6. 25% of 72 is 18

7. 90% of 30 is 27

8. 50% of 62 is 31

9. 50% of 86 is 43

10. 100% of 90 is 90

11. 60% of 65 is 39

12. 75% of 44 is 33

13. 100% of 54 is 54

14. 50% of 46 is 23

15. 40% of 5 is 2


1. $2.63

2. $210

3. $69.95

4. 180

5. $41.99

6. $35

7. 10kg




8. $77.97

9. 30 Kilos

10. $11.90




Data Interpretation “Count the Oranges”

Examine the table closely.

How many oranges does each box have?

Establish:

Data collected can be recorded in forms of charts, tables or graphs. Common graphs use bars,

lines, or parts of a circle to display data. A graph is a chart or drawing that shows the relationship

between two or more things for e.g. numbers, percentages or amounts.

Also tell them the picture that we just covered is called a pictograph. A pictogram or

pictograph represents data in the form of pictures or symbols.

It was easy to count the number of oranges in the first activity even though the data was big.

Large data can be organized in the form of graphs, charts and tables to understand the

information.




Data

When facts, observations or statements are taken on a particular subject, they are collectively

known as data. Data can be numbers arising from counting or measurement, words recorded or

images taken, etc.

Tell the class that sometimes data is called raw data because It is merely collected or recorded

without any processing. Data collected needs to be organized and processed to give useful

information.

Bar Charts

A bar chart represents the data as horizontal or vertical bars. The length of each bar is

proportional to the amount which it represents. There are 3 main types of bar charts.

Double bar chart The double bar chart is used when we want to represent two sets of data on the same chart.




Line

Graphs

A line graph is formed by joining the points given by the data with straight lines.

If the data table is:

Then the line graph will look like:




Pie Charts If the data table is:

Then the pie chart will look like:

Example:

Given below is a graph that represents the salary of some employees of the same team:




Find out the following information:

1. What is the salary of the following people?

Mary -

Harry -

Sally -

2. Who earns the maximum money? __________

3. Who earns the least money? _________

4. Which two employees earn the same amount of money? _______ & ________

Solution

1. Mary - $ 6250

Harry - $ 7500

Sally -$ 8750

2. Sally

3. Jim

4. Harry and Fred




Information Application

Exercise 1

Given below is a graph that represents the salary of some employees of the same team:

1. Which Gift is liked the most by people?

2. Which gifts are equally like by people?

3. What’s the difference between the number of people who like Money and the ones who

like DVDs?

4. How many different items are mentioned in this graph?

5. After Ipods which gift is liked the most?

Answers:

1. Ipod

2. Game and Money

3. 9

4. 8

5. Video games




Exercise 2

The following graph shows the monthly expenditure of a family.

1. Most of the income is spent on __________ ?

2. Least money is spent on _________ ?

3. On which other component, is the maximum money spent apart from mortgage

4. If the family’s income is $ 50,000, then what is amount of money spent on the car?

5. If the family’s income is $ 50,000, then what is amount of money spent on bills?

6. If the family’s income is $ 50,000, then what is the difference between the amount of

money spent on Mortgage and amount of money spent on Food?

Answers:

1. Mortgage

2. Misc

3. Food

4. $4500

5. $7000

6. 6500

Exercise 3

The FIFA cup final scores for the last couple of years are as follows:




1. How many times did the Newcastle win?

2. Which club is in the 6th position in this period?

3. How many clubs share the fifth position?

4. Who has had the maximum number of wins?

Answers:

1. 6

2. Everton

3. 3 clubs

4. Manchester United

Exercise 4

In a class all the children like candy. They all like a particular colour of candy.

Their preferences are represented in the graph:




1. How many children like brown candy?

2. Which candy colour is liked by the children the most?

3. How many children are there in the class?

Answers:

1. 3

2. Blue

3. 29

Exercise 5

The following graph shows time spent in reading everyday:

1. What do people like to read the most?

2. Which type of reading is the least popular?

3. Which two types of reading get almost the same attention?

Answers:

1. Newspapers

2. Reference Books

3. Magazines and internet




Exercise 6

Study the following pie-chart which shows the percentage division of the expenditure incurred in

publishing a book and answer the questions based on it.

Q1. If for a certain quantity of books, the publisher has to pay $ 30,600 as printing cost, then

what will be amount of royalty to be paid for these books?

a. $19,450 b. $21,200 c. $22,950 d. $26,150

Q2. The price of the book is marked 20% above the C.P. If the marked price of the book is $180,

then what is the cost of the paper used in a single copy of the book?

a. $36 b. $37.50 c. $42 d. $44.25

Q3. Royalty on the book is less than the printing cost by:

a. 5% b. 33.2% c. 20% d. 25%

Answers:

Q1. $22,950

Q2. $37.50

Q3. 25%

Exercise 7

The following table mentions IBM’s expenditures (in million dollars) per Annum over the years




Q1. What is the average amount of investments the company made during this period?

a. $ 36.66 million b. $ 37.82 million c. $ 24.18 million d. $ 36.01 million

Q2. The total expenditure of the company over these items during the year 2005 is?

a. $ 444.44 million b. $ 544.44 million c. $ 646.46 million d. $ 674.44 million

Q3. The ratio between the total expenditure on sales for all the years and the total expenditure on

Infrastructure for all the years respectively is approximately?

a. 5:7 b. 4:5 c. 10:13 0d. 7:4

Answers:

Q1. $ 36.66 million

Q2. $544.44 million

Q3: 10/13




Ratio & Proportion

Ratio

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with

a colon (:).

Suppose we want to write the ratio of 8 and 12. We can write this as 8:12 or as a fraction 8/12,

and we say the ratio is eight to twelve.

Example:

George's schoolbag has 3 pens, 5 books, 4 erasers and 1 sharpener.

What is the ratio of books to pens?

Numerator = the first quantity= 5

Denominator = the second quantity= 3

Hence the ratio is 5 or 5:3 or 5/3

3

What is the ratio of erasers to the total number of items in the bag?

Numerator= The first quantity= Number of erasers = 4

Denominator = The second quantity = Total number of items = 13

Hence the ratio is 4 or 4:13 or 4/13

13

Note: The ratios should always be expressed in their simplest form.

Example

The ratio 4:8 can be simplified by dividing both the numerator and the denominator by 2. Both 4

and 8 are divisible by 2.




Ratio of Greater Inequality

In a ratio if the numerator is greater than the denominator then the ratio is called a ratio of greater

inequality. If we look at the ratio9:4, the numerator is 9 and the denominator is 4. Since the

numerator is greater than the denominator, it's called the ratio of greater inequality.

Examples

7:2, 5:1, 3:2, 8:3

Ratio of Less Inequality

In a ratio if the denominator is greater than the numerator then the ratio is called a ratio of greater

inequality. If we look at the ratio4:9, the numerator is 4 and the denominator is 9. Since the

denominator is greater than the numerator, it's called the ratio of greater inequality.

Examples

2:7, 1:5, 2:3, 3:8




Proportion The equality of two ratios is called proportion. If a:b is equal to c:d, we say that a,b,c,d are

proportional and, we write a:b : : c:d

It can be written in two ways:

two equal fractions, a = c

b d

or,

using a colon, a:b = c:d

It can also be referred to as an equation with a ratio on each side. It is a statement that shows the

two ratios are equal.

3/4 = 6/8 is an example of a proportion.

When two ratios are equal, then the cross product of the ratios are equal.

That is, for the proportion, a:b = c:d or a = c = a x d = b x c

b d

Examples

20/25 = 4/5

10/100 = 1/10

6/16 = 3/8




Exercise 1

Exercise 2

1. In 2010, 57 women and 162 men were enrolled in the communication skills workshop in

the university. What was the ratio of women to men?

2. The ratio of Alex’s age to Sam’s age is 6:5 at present. Fifteen years from now, the ratio of

their ages will be 9:8. Find Alex's age.

3. If we divide $58 among 150 children in such a manner that each girl and each boy gets 25

cents and 50 cents respectively, then how many girls do we have?

4. What number must be added to 8, 21, 13 and 31 to make the ratio of first two numbers

equal to the ratio of last two numbers?

5. What is the fourth proportional to the numbers 60, 48, 30?

6. The incomes of Alex and Bob are in the ratio of 3:2 and their expenditure is in the ratio

of 5:3. Find the income of Alex if each saves dollars 1000.

7. A mixture contains alcohol and water in 12:5 ratio. If we add 14 litres of water to the

mixture, the ratio of alcohol to water becomes 1:1. Find the quantity of alcohol in the

mixture.

8. Sam and Kate have DVD’s in the ratio 8:1. Sam gave half of his DVD’s to Kate. Find the

new ratio of DVD’s that Sam and Kate own.




9. You have a £10 in your pocket. If you use £6 to buy a basket, what is the ratio between

what you have spent and what you are left with in your pocket?

10. In a study done on college students it was found that on an average, students spend 9

hours a week in watching TV and 3 hours e-mailing. What is the ratio between the two?

11. If 10 oranges cost £2, how much will 7 cost?

12. You buy 160 apples and sell 40 of them. What is the simplest ratio between the total

number of apples and the apples sold?

13. What is the simplest ratio of a pool's width to its length if it is 20m wide and 50m long?

14. The ratio of the ages of Rodger and Kip is 3:5 and that of Kip and Samuel is 3:5. If the

sum of their ages is 147, then how old is B?

15. A sum of money is distributed among George, Kip, Sally and John in the proportion of 5

: 2 : 4 : 3. If Sally gets Rs. 1000 more than John, what is B's share?

Exercise 3

1. The ratio between two numbers is 3:5 and there is 40.Find the larger of two numbers.

2. Two numbers are respectively 20% and 50% more than a third number. The ratio of the

two numbers is?

3. If 2A=3B=4C then A:B:C?

4. If a/3=b/4=c/7 then (a+b+c)/c=?

5. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If

C gets $1000 more than D, what is B's share?

6. $3650 is divided among 4 team leader, 3 managers and 5 trainers in such a manner that 3

trainers get as much as 2 managers and 3 team leaders as much as 2 trainers .Find the

share of a manager.

7. If 15% of x=20% of y then x:y is?

8. A sum of $1162 is divided among Ahmed, Basma and Charlie in such a manner that 4

times Ahmed’s share is equal to 5 times Basma’s share and 7 times Charlie’s share. What

is Charlie’s share?

9. I have one pound coins, fifty piaster coins and twenty five piaster coins. The number of

coins are in the ratio 2.5 : 3 : 4. If the total amount with me is 210 pounds, find the

number of one pound coins.




10. A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If

the passing marks are 50% of the maximum marks and each subject has the same

maximum marks, in how many subjects did he pass the examination?



1. 19/ 54

2. 30 years

3. 68

4. 5

5. 24

6. 6000

7. 24 litres

8. 4:5

9. 3:2

10. 3:1

11. £ 1.4

12. 4:1

13. 2:5

14. 45 years




15. Rs 2000


1. 25

2. 4:5

3. 6:4:3

4. 2

5. $2000

6. $450

7. 4:3

8. $280

9. 105

10. 4 subjects




Profit & Loss Profit is when a business makes money after expenses. It is the revenue that remains after all

expenses and costs have been paid. A loss is the opposite. It is when a business does not make

money or a profit after deducting all expenses and costs. The goal of a business is to increase

profits and reduce losses. Profit & loss helps us understand this aspect of an organization.

Profit and Loss In order to make profit we need to sell the goods at a price which was more than the cost

involved.

Cost Price: The price at which an item is bought is called its cost price, abbreviated as C.P.

Selling Price: The price at which an article is sold is called its selling price, abbreviated as S.P.

Profit or Gain = (S.P.) - (C.P.)

Profit % on Cost Price = (Profit x 100)

C.P.

Profit % on Selling Price = (Profit x 100)

S.P.

Loss = (C.P.) - (S.P.)

Loss % on Cost Price = (Loss x 100)

C.P.

Loss % on Selling Price = (Loss x 100)

S.P.

Sample problems

Example:

A shopkeeper buys scientific calculators in bulk for $25 each. He sells them for $40 each.

Calculate the profit on each calculator as a percentage of the cost price.

Solution:

Given: cost price = $25, selling price = $40




profit = selling price - cost price

= $40 - $25

= $15

Expressing the profit as a percentage of the cost price:

$profit

profit% = ---------------- × 100%

$cost price

$15

= -------- × 100% = 60%

$25




Example:

A belt that cost 80 cents is sold at a profit of 20 cents. Find the percent or rate of profit.

Solution:

Given: C.P. = 80 cents, Profit = 20 cents

Profit % = (Profit x 100)

C.P.

= (20 x 100) = 25%

80

Example:

A toy that cost $1.00 is sold for 80 cents. Find the percent loss.

Solution:

Given: C.P. = $1.0 or 100 cents, Loss = 20 cents

Loss % = (Loss x 100)

C.P.

Loss % = (20 x 100)

100

= 20 %

Example:

A damaged table that cost $110 was sold at a loss of 10%. Find the loss and the selling price.

Solution:

Given: C.P. = $110, Loss% = 10 %


C.P.

If we put the values we have in the formula we get:

10 % = (Loss x 100)

110

Or we can say Loss = (10 x 110)

100

Loss = $ 11

We know, Loss = (C.P.) - (S.P.)




$11 = $110 – S.P.

Or S.P. = $110 - $11

= $99

Example:

A chain was sold at a profit of $9,000. The rate of profit was 30%. What was the cost of the

chain?

Solution:

Given: Profit % = 30%, Profit = $ 9,000

We know that Profit % = (Profit x 100)

C.P.

30% = (9000 x 100)

C.P.

That means C.P. = (9000 x 100)

30

= $30,000

Example:

A shop sells dolls for $1.30 at a profit of 65 cents. What is the profit % on each doll?

Solution:

Given: S.P.= $1.30 or 130 cents, Profit = $65 cents

We know that Profit = S.P.- C.P.

That means 65= 130 – C.P.

Or C.P. = 65

Profit % = (Profit x 100)

C.P.

= (65x 100)

130

= 50%




Example:

A merchant is selling used watches for $40 at a loss of $8. What his loss % on selling price?

Solution:

Given: S.P. = $40, Loss = $8

Loss = C.P. - S.P.

$8 = C.P. - $40

That means C.P. = $32


S.P.

= (8 x 100)

40

=20% loss

Example:

A watch is sold for $8.00 at a profit of 25% of the selling price. Find out the cost price and profit.

Solution:

Given: S.P. = $8, Profit% on S.P. = 25%

We know, Profit % on Selling Price = (Profit x 100)

S.P.

Or 25% = (Profit x 100)

8

Profit = (25 x 8)

100

Profit = $2

We know Profit = S.P. – C.P.

$2 = $8 – C.P.

C.P. = $6




Exercise 1

1. A recorder is bought at $ 782 and sold at $967. Find the profit.

2. A bracelet is bought at $ 436 and sold at $399. Find the loss.

3. A cot is bought at $ 800 and sold at $1200. Find the profit% on C.P.

4. A man buys a toy for $25 and sells it for $30. Find his gain %.

5. An air conditioner is bought at $ 900 and sold at $1800. Find the profit% on S.P.

6. A man sells a pair of shoes for $477 which he had bought for $450. Find the profit % on

S.P.

7. A book is bought for 15 cents and was sold at 18 cents. What is the gain or loss%?

8. A vase is bought at $ 234 and sold at $222. Find the loss% on C.P.

9. A pair of earrings is sold for $600. The profit % is 27% on the sale price. Find the profit.

10. A man buys a pen for $25 and sells it for $20. Find his loss %.

Exercise 2

1. A man bought a new carry bag for Rs. 1400 and sold it at a loss of 15%. What is the

selling price of the new carry bag?

2. A vendor bought 6 eggs for a dollar. How many for a dollar must he sell to gain 20%?

3. A gold chain is sold for $635 making a profit of 27% on the selling price. Find the profit.

4. Sam buys an old car for $4700 and spends $ 800 on repairs. He sells the car for Rs. 5800.

Find out his profit%.

5. A merchant says that the cost price of 20 dogs is equal to the selling price of x dogs. If

the profit % is 25%, what is the value of x?

6. It is seen that if a merchant doubles the selling price of an article then his profit triples.

Find the profit%.

7. A shopkeeper realizes that the profit% earned by selling a pair of sunglasses for Rs. 1920

is same as the loss% incurred by selling them for Rs. 1280. At what price should the

article be sold to make 25% profit?

8. When a merchant sells 17 purses for $720, he incurs a loss equal to the cost price of 5

balls. What is the cost price of one purse?

9. A house owner sells his house for $18,700 and incurs a loss of 15%. At what price should

he sell his house, if he wants to make a profit of 15%?




10. If 20 dozen roses were purchased at the rate of Rs. 375 per dozen and sold at the rate of

Rs. 33. What is the percentage profit?





1. $185

2. $37

3. 50%

4. 20%

5. 50%

6. 6%

7. 20% gain

8. 5.13% (round off

9. $162

10. 20%


1. $1190

2. Rs 5

3. $171.5

4. 5.4%

5. 16

6. 100%

7. Rs 2000

8. Rs 60

9. 25,300

10. 5.6%




Aptitude Tests Aptitude tests are conducted for the trainees during the training program. Primarily four aptitude

tests are used during the training. All four aptitude tests are attached with their answer keys.

Once the content download for all concepts is over, these tests can be used for practice.




Aptitude Test 1

2. Arrange the dates in a chronological order, from the earliest to the most recent:

1) January 31, 2010 2) January 31, 2001 3) January 31, 2100 4) January 31, 2011

a) 3,2,4,1

b) 4,2,3,1

c) 2,1,4,3

d) 1,3,4,2

3. If 27 dates cost 12 GBP (Great Britain Pounds), what is the cost of 36 dates in Egyptian

Pounds if 1 GBP = 8EGP?

a) EGP 16

b) EGP 108

c) EGP 128

d) EGP 124

Read the following piece of information and answer the questions that follow.

An emergency meeting has been convened. Six people have come for it and are sitting around a

table. There are two people sitting between Mr. Weatherby and Archie. Reggie is sitting to the

left of Archie. Betty is not sitting next to Mr. Weatherby. Jughead and Veronica are also present

for the meeting.

Answer the following questions based on the information given above. Each question should be

answered independently of the others.

4. Who is sitting between Mr. Weatherby and Reggie?

a) Jughead




b) Veronica

c) Either Jughead or Veronica

d) Betty

5. Who is sitting to the right of Archie?

a) Betty

b) Jughead

c) Veronica

d) Either Jughead or Veronica

6. Arrange the following names in a logical sequence (alphabetical order):

1) Samuel Thomas Jefferson 2)Samual Thomas Jefferson 3)Samuel Thomes Jefferson

4)Samuel Thomas Jeffersan

a) 1,4,3,2

b) 4,2,3,1

c) 3,1,2,4

d) 2,4,1,3

7. The average age of 7 students is 21. If the age of the teacher is also included, the average

increases to 24. What is the age of the teacher?

a) 54

b) 45

c) 49

d) 55

8. The ratio of fat boys to tall girls in a class is 5:8. If there are 169 students in the class, how

many of them are boys who are fat?

a) 65

b) 13

c) 104

d) 56




9. Denzel Washington’s performance in the new movie is fantastic. It is amazing how he has

been able to portray the angst of the character in such a dignified manner. The supporting cast

has also done a commendable job. It would be very surprising

Complete the last sentence:

a) If the movie does well in the domestic and international markets.

b) If the movie is remembered as one of the finest of this decade.

c) If the movie boosts Denzel Washington’s career.

d) If the movie does not garner at least five nominations at the Oscars.

10. Identify the number of similar pairs

1)!Abraacaaadabraaa – Abraacaaadabraaa!

2) Jajuntaramananaan – Jajuntaramananaan

3) Mar0iepoppinono$ - Mar0iiepoppinono$

4) R@st$p0pular1siiy - R@st$p0pular1siiy

a) One pair

b) Two Pairs

c) Three Pairs

d) Four Pairs

11. Seventy percent of motorcycle accidents result in death while only one percent of jeep

accidents result in death. Hence, jeeps are safer than motorcycles.

Which of the following, if true, would seriously weaken the argument?

a) The number of jeep accidents is several times higher than the number of motorcycle accidents.

b) Motorcycles are of a higher quality than jeeps.

c) Jeep accidents are usually the fault of the drivers.

d) Jeeps carry more passengers than motorcycles.




12. Address: House # 43/A (Near the Warriors’ Cemetery), Arlington Avenue, San Diego

Identify the correct address from the options mentioned below:

a) House # 43/A (Near the Warriors Cemetery), Arlington Avenue, San

Diego

b) House # 43/A (Near the Warriors’ Cemetry), Arlington Avenue, San

Diego

c) House # 43/A (Near the Warriors’ Cemetery), Arlington Avenue, San

Diego

d) House # 43/A (Near the Warriors’ Cemetary), Arlington Avenue, San

Diego




Aptitude Test 1 Answers 1. If a: b = 3: 5, solve a2 + b2 + 2ab.

e) 30

f) 25

g) 64

h) 56


1) January 31, 2010 2) January 31, 2001 3) January 31, 2100 4) January 31, 2011

e) 3,2,4,1

f) 4,2,3,1

g) 2,1,4,3

h) 1,3,4,2

3. If 27 dates cost 12 GBP (Great Britain Pounds), what is the cost of 36 dates in Egyptian

Pounds if 1 GBP = 8EGP?

e) EGP 16

f) EGP 108

g) EGP 128

h) EGP 124

An emergency meeting has been convened. Six people have come for it and are sitting around a

table. There are two people sitting between Mr. Weatherby and Archie. Reggie is sitting to the

left of Archie. Betty is not sitting next to Mr. Weatherby. Jughead and Veronica are also present

for the meeting.

Answer the following questions based on the information given above. Each question should be

answered independently of the others.

4. Who is sitting between Mr. Weatherby and Reggie?

e) Jughead

f) Veronica

g) Either Jughead or Veronica

h) Betty




5. Who is sitting to the right of Archie?

e) Betty

f) Jughead

g) Veronica

h) Either Jughead or Veronica

6. Arrange the following names in a logical sequence (alphabetical order):

1) Samuel Thomas Jefferson 2)Samual Thomas Jefferson 3)Samuel Thomes Jefferson

4)Samuel Thomas Jeffersan

e) 1,4,3,2

f) 4,2,3,1

g) 3,1,2,4

h) 2,4,1,3

7. The average age of 7 students is 21. If the age of the teacher is also included, the average

increases to 24. What is the age of the teacher?

e) 54

f) 45

g) 49

h) 55

8. The ratio of fat boys to tall girls in a class is 5:8. If there are 169 students in the class, how

many of them are boys who are fat?

e) 65

f) 13

g) 104

h) 56

9. Denzel Washington’s performance in the new movie is fantastic. It is amazing how he has

been able to portray the angst of the character in such a dignified manner. The supporting cast

has also done a commendable job. It would be very surprising

Complete the last sentence:

e) If the movie does well in the domestic and international markets.

f) If the movie is remembered as one of the finest of this decade.




g) If the movie boosts Denzel Washington’s career.

h) If the movie does not garner at least five nominations at the Oscars.

10. Identify the number of similar pairs

1)!Abraacaaadabraaa – Abraacaaadabraaa!

2) Jajuntaramananaan – Jajuntaramananaan

3) Mar0iepoppinono$ - Mar0iiepoppinono$

4) R@st$p0pular1siiy - R@st$p0pular1siiy

e) One pair

f) Two Pairs

g) Three Pairs

h) Four Pairs

11. Seventy percent of motorcycle accidents result in death while only one percent of jeep

accidents result in death. Hence, jeeps are safer than motorcycles.

Which of the following, if true, would seriously weaken the argument?

e) The number of jeep accidents is several times higher than the number of

motorcycle accidents

f) Motorcycles are of a higher quality than jeeps.

g) Jeep accidents are usually the fault of the drivers.

h) Jeeps carry more passengers than motorcycles.

12. Address: House # 43/A (Near the Warriors’ Cemetery), Arlington Avenue, San Diego


e) House # 43/A (Near the Warriors Cemetery), Arlington Avenue, San Diego

f) House # 43/A (Near the Warriors’ Cemetry), Arlington Avenue, San Diego

g) House # 43/A (Near the Warriors’ Cemetery), Arlington Avenue, San Diego

h) House # 43/A (Near the Warriors’ Cemetary), Arlington Avenue, San Diego




Aptitude Test 2 1. Spot the odd one out.

2. A discount of 12% was given on a hand bag whose original price was EGP 150. What was the

final selling price?

a) EGP 18

b) EGP 120

c) EGP 132

d) EGP 138

3. If the ages of Mohammad and Ehab are in the ratio of 4:6 and Mohammad is younger than

Ehab by 4 years, then how old is Mohammad?

a) 12

b) 24

c) 8

d) 10

4. It has been noticed that though the students hardly attend classes anymore, there has been a

steady increase in their marks. This observation has stumped the university authorities and they

are planning to get to the bottom of this.

Which of the following statements would most logically help the college authorities understand

the situation better?

a) All the students are naturally intelligent

b) They are receiving regular lessons from a professor outside of college

c) The students have been eating food that increases brain power

d) The amount of time spent inside the classroom does not influence the marks that one

gets




5. Arrange the numbers in descending order, from the highest to the lowest:

1) 7738201876 2)7738021876 3)7738021879 4)7738201879

a) 1,3,2,4

b) 4,1,3,2

c) 2,4,1,3

d) 4,2,1,3

6. Solve 7*(30/6) – 9/(51/17)

a) 32

b) 35

c) 28

d) 42

7. Arrange the following names in a logical sequence (alphabetical order)

1) Adam Jose Mario Perez 2) Adam Jose Mario Parez 3) Adam Jose Mario

Periz 4) Adam Jose Mario Pirez

a) 3,4,1,2

b) 1,4,2,3

c) 3,1,4,2

d) 2,1,3,4

8. Whenever Ali starts the car, Hend hurts herself and Yomna shouts. If Yomna is not shouting,

which of the following statements must be true?

a) Hend has hurt herself but Ali is not necessarily starting the car.

b) Ali is starting the car but Hend has not necessarily hurt herself.

c) Ali is not starting the car.

d) Ali has been starting the car for a while and Hend has just hurt herself.




9. Mahmoud suffered a loss of 15% when he sold his house for EGP 15300. At what price should

he sell it to earn a profit of 15%?

a) 18000

b) 20300

c) 22000

d) 20700

10. Find the odd one out:

a) aU4h(kre87z0 - aU4h(kre87.z0

b) T8fgt%.275gt - T8fgt%.275gt

c) Zz06*KL32!y - Zz06*KL321y

d) Bt#yt874$?txI - Bt#yt874S?txI

11. It is a widely held assumption that nuclear scientists do not take any interest in soccer. This

assumption was recently proved false when an interview with the players of one of the amateur

soccer teams revealed that most of them were scientists. Which of the following statements, if

proved to be true, would most damage the above argument?

a) The interview shows the high level of skill of the amateur players.

b) The interview was conducted by a bunch of nuclear scientists.

c) The players who were interviewed had just won a tournament.

d) The payers who were interviewed were agricultural scientists.

12. Arrange the numbers in ascending order, from the lowest to the highest:

1) 3336999187 2)3336699187 3)3336969187 4)3336666987

a) 4,2,3,1

b) 2,4,3,1

c) 3,2,4,1

d) 4,3,2,1




Aptitude Test 2 Answers 1. Spot the odd one out.

2. A discount of 12% was given on a hand bag whose original price was EGP 150. What was the

final selling price?

e) EGP 18

f) EGP 120

g) EGP 132

h) EGP 138

3. If the ages of Mohammad and Ehab are in the ratio of 4:6 and Mohammad is younger than

Ehab by 4 years, then how old is Mohammad?

e) 12

f) 24

g) 8

h) 10

4. It has been noticed that though the students hardly attend classes anymore, there has been a

steady increase in their marks. This observation has stumped the university authorities and they

are planning to get to the bottom of this. Which of the following statements would most logically

help the college authorities understand the situation better?

e) All the students are naturally intelligent

f) They are receiving regular lessons from a professor outside of college

g) The students have been eating food that increases brain power

h) The amount of time spent inside the classroom does not influence the marks that one

gets

5. Arrange the numbers in descending order, from the highest to the lowest:




1) 7738201876 2)7738021876 3)7738021879 4)7738201879

e) 1,3,2,4

f) 4,1,3,2

g) 2,4,1,3

h) 4,2,1,3

6. Solve 7*(30/6) – 9/(51/17)

e) 32

f) 35

g) 28

h) 42

7. Arrange the following names in a logical sequence (alphabetical order)

1) Adam Jose Mario Perez 2) Adam Jose Mario Parez 3) Adam Jose Mario Periz 4)

Adam Jose Mario Pirez

e) 3,4,1,2

f) 1,4,2,3

g) 3,1,4,2

h) 2,1,3,4

8. Whenever Ali starts the car, Hend hurts herself and Yomna shouts. If Yomna is not shouting,

which of the following statements must be true?

e) Hend has hurt herself but Ali is not necessarily starting the car.

f) Ali is starting the car but Hend has not necessarily hurt herself.

g) Ali is not starting the car.

h) Ali has been starting the car for a while and Hend has just hurt herself.

9. Mahmoud suffered a loss of 15% when he sold his house for EGP 15300. At what price should

he sell it to earn a profit of 15%?

e) 18000

f) 20300




g) 22000

h) 20700

10. Find the odd one out:

e) aU4h(kre87z0 - aU4h(kre87.z0

f) T8fgt%.275gt - T8fgt%.275gt

g) Zz06*KL32!y - Zz06*KL321y

h) Bt#yt874$?txI - Bt#yt874S?txI

11. It is a widely held assumption that nuclear scientists do not take any interest in soccer. This

assumption was recently proved false when an interview with the players of one of the amateur

soccer teams revealed that most of them were scientists. Which of the following statements, if

proved to be true, would most damage the above argument?

d) The interview shows the high level of skill of the amateur players.

e) The interview was conducted by a bunch of nuclear scientists.

f) The players who were interviewed had just won a tournament.

g) The payers who were interviewed were agricultural scientists.

12. Arrange the numbers in ascending order, from the lowest to the highest:

1) 3336999187 2)3336699187 3)3336969187 4)3336666987

e) 4,2,3,1

f) 2,4,3,1

g) 3,2,4,1

h) 4,3,2,1




Aptitude Test 3 Seven friends have been allotted different slots to make a presentation. David has the first a lot.

Matt does not have the second slot. Lisa’s slot is immediately after Jennifer’s slot. Mathew

cannot present before Courtney but has got a slot two slots after Jennifer. Courtney is the second

last to present.

Answer the following questions based on the information given above. Each question is

independent of the others.

1. Who is the last one to present?

a) Matt

b) Mathew

c) Bruce

d) Lisa

2. Which slot does Lisa get?

a) Fourth

b) Third

c) Seventh

d) Fifth

3. After whom does Bruce present?

a) David

b) Matt

c) Courtney

d) Lisa

4. Who presents after Matt?

a) Bruce

b) Courtney

c) Jennifer




d) Mathew

5. Which slot does Matt get?

a) Third

b) Fourth

c) Fifth

d) Second

6. Address: 576, New Line Studios Street, New York City, USA


a) 576, New Lines Studios Street, New York City, USA

b) 576, New Line Studio Street, New York City, USA

c) 576, New Line Studios Street, New York City, USA

d) 576, New Line Studios Street, New York City, U.S.A

7. If the average scores of three batches of 25, 30 and 15 students are 30, 35 and 40 respectively,

then what would be the average score of all the students?

a) 30

b) 34.28

c) 28

d) 32.46


1) July 21, 1933 2) July 21, 1988 3) June 28, 1939 4) June 21, 1933

a) 4,1,3,2

b) 2,3,1,4

c) 3,2,1,4

d) 4,1,2,3

9. Solve: 590 – 123 + 49 / 4

a) 129.5




b) 129

c) 130

d) 130.5

10. Ahmed buys soccer shoes for EGP 1400 and sells them at a loss of 15%. What is the selling

price of the soccer shoes?

a) 1190

b) 1200

c) 990

d) 1020

11. If 63/7 = 36/b, then what is the value of b?

a) 28

b) 9

c) 7

d) 4

12. Spot the odd one out.




Aptitude Test 3 Answers Seven friends have been allotted different slots to make a presentation. David has the first slot.

Matt does not have the second slot. Lisa’s slot is immediately after Jennifer’s slot. Mathew

cannot present before Courtney but has got a slot two slots after Jennifer. Courtney is the second

last to present.

Answer the following questions based on the information given above. Each question is

independent of the others.

1. Who is the last one to present?

e) Matt

f) Mathew

g) Bruce

h) Lisa

2. Which slot does Lisa get?

e) Fourth

f) Third

g) Seventh

h) Fifth

3. After whom does Bruce present?

e) David

f) Matt

g) Courtney

h) Lisa

4. Who presents after Matt?

e) Bruce

f) Courtney

g) Jennifer

h) Mathew




5. Which slot does Matt get?

e) Third

f) Fourth

g) Fifth

h) Second

6. Address: 576, New Line Studios Street, New York City, USA


e) 576, New Lines Studios Street, New York City, USA

f) 576, New Line Studio Street, New York City, USA

g) 576, New Line Studios Street, New York City, USA

h) 576, New Line Studios Street, New York City, U.S.A

7. If the average scores of three batches of 25, 30 and 15 students are 30, 35 and 40 respectively,

then what would be the average score of all the students?

e) 30

f) 34.28

g) 28

h) 32.46


1) July 21, 1933 2) July 21, 1988 3) June 28, 1939 4) June 21, 1933

e) 4,1,3,2

f) 2,3,1,4

g) 3,2,1,4

h) 4,1,2,3

9. Solve: 590 – 123 + 49 / 4

e) 129.5

f) 129

g) 130




h) 130.5

10. Ahmed buys soccer shoes for EGP 1400 and sells them at a loss of 15%. What is the selling

price of the soccer shoes?

e) 1190

f) 1200

g) 990

h) 1020

11. If 63/7 = 36/b, then what is the value of b?

e) 28

f) 9

g) 7

h) 4

12. Spot the odd one out.




Aptitude Test 4 1. George is putting his old books in the boxes. Every box can contain 49 books and he has

already put books in 2 boxes. How many more boxes does he need if he has 294 books?

a) 6 boxes

b) 4 boxes

c) 2 boxes

d) 7 boxes

2. 5(15-4)+6= ?

a) 61

b) 77

c) 85

d) 45

3. The average temperature on Monday, Tuesday and Wednesday was 30. The average

temperature on Tuesday, Wednesday and Thursday was 25. If the temperature on Thursday was

20, what was the temperature on Monday?

a) 40

b) 50

c) 35

d) 55

4. The price of a dress is $900. During the winter sale the same dress is available at the price of

$765. What is the discount given on the dress?

a) 15%

b) 20%

c) 12%

d) 21%

5. If John’s age is 3 times his brother’s age and the average of theirs ages is 16, what is John’s

age?




a) 8

b) 24

c) 20

d) 28

6. Which of the following options is correct?

a) 7+8*3=21+24=45

b) 7+8*3=21+8=29

c) 7+8*3=15+21=36

d) 7+8*3=7+24=31

7. Graham buys 10 books for $1. At what price should he sell a dozen apples if he wishes to

make a profit of 25%?

a) $2.25

b) $1.

c) $1.25

d) $1.5

8. Meg went shopping and bought 3 skirts, 7 shirts, 4 belts and 7 bottles of perfume.

What is the ratio of skirts to the rest of the items?

a) 3:21

b) 1:3

c) 1:4

d) 1:6

9. Pick the odd one out

a) 289, 306, 323

b) 324, 342, 260

c) 342, 361, 380

d) 351, 360, 365




10. Akshat wants to buy a a car worth $50,000 and has been saving at the rate of $2000 per

month for the last 15 months. After how many months will Akshat be able to buy the car if he

continues to save at the same rate?

a) 10 months

b) 12 months

c) 15 months

d) 25 months

11. What’s the next number in the series?

5, 12, 26, 54, 110, ?

a) 220

b) 224

c) 222

d) 228

12. There are 7 members in a family. The youngest member of the family is 1 year old. If the

average age of the family right now is 19. What was the average age of the family one year ago?

a) 3

b) 19

c) 22

d) 12

13. Rodger has $450 in his savings account. After a year the bank pays him interest and his

balance increases by $18. What percentage rate was applied to the account?

a) 7%

b) 5%

c) 4%

d) 13%

14. If 7/9=63/x then what is x?

a) 90

b) 71




c) 81

d) 9

15. A shopkeeper buys 360 oranges at $10 per dozen. If he sells them at the rate of $1.10 each,

what is his profit as a percentage of selling price?

a) 24.2%

b) 27.2%

c) 30%

d) 22%




Aptitude Test 4 Answers

1. George is putting his old books in the boxes. Every box can contain 49 books and he has

already put books in 2 boxes. How many more boxes does he need if he has 294 books?

e) 6 boxes

f) 4 boxes

g) 2 boxes

h) 7 boxes

2. 5(15-4)+6= ?

e) 61

f) 77

g) 85

h) 45

3. The average temperature on Monday, Tuesday and Wednesday was 30. The average

temperature on Tuesday, Wednesday and Thursday was 25. If the temperature on Thursday was

20, what was the temperature on Monday?

e) 40

f) 50

g) 35

h) 55

4. The price of a dress is $900. During the winter sale the same dress is available at the price of

$765. What is the discount given on the dress?

e) 15%

f) 20%

g) 12%

h) 21%




5. If John’s age is 3 times his brother’s age and the average of theirs ages is 16, what is John’s

age?

e) 8

f) 24

g) 20

h) 28

6. Which of the following options is correct?

e) 7+8*3=21+24=45

f) 7+8*3=21+8=29

g) 7+8*3=15+21=36

h) 7+8*3=7+24=31

7. Graham buys 10 books for $1. At what price should he sell a dozen apples if he wishes to

make a profit of 25%?

e) $2.25

f) $1.

g) $1.25

h) $1.5

8. Meg went shopping and bought 3 skirts, 7 shirts, 4 belts and 7 bottles of perfume. What is the

ratio of skirts to the rest of the items?

e) 3:21

f) 1:3

g) 1:4

h) 1:6

9. Pick the odd one out

e) 289, 306, 323

f) 324, 342, 260

g) 342, 361, 380




h) 351, 360, 365

10. Akshat wants to buy a a car worth $50,000 and has been saving at the rate of $2000 per

month for the last 15 months. After how many months will Akshat be able to buy the car if he

continues to save at the same rate?

e) 10 months

f) 12 months

g) 15 months

h) 25 months

11. What’s the next number in the series?

5, 12, 26, 54, 110, ?

e) 220

f) 224

g) 222

h) 228

12. There are 7 members in a family. The youngest member of the family is 1 year

old. If the average age of the family right now is 19. What was the average age of the family one

year ago?

e) 3

f) 19

g) 22

h) 12

13. Rodger has $450 in his savings account. After a year the bank pays him interest and his

balance increases by $18. What percentage rate was applied to the account?

e) 7%

f) 5%

g) 4%

h) 13%




14. If 7/9=63/x then what is x?

e) 90

f) 71

g) 81

h) 9

15. A shopkeeper buys 360 oranges at $10 per dozen. If he sells them at the rate of $1.10 each,

what is his profit as a percentage of selling price?

e) 24.2%

f) 27.2%

g) 30%

h) 22%

Numerical Ability

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