MATHS OLYMPIAD PRACTICE BOO K
GRADE
6
Empowering Children to become Global Olympiad Champions
ISFO Practice Book
1
ACK A CK NOWL NOW L EDGEM ED GEMEN ENTS TS
Curriculum and Content Sanjay K Singh Su b j ec t M at t e r E x p er t s
Gr ap h i c Des i g n er
N ih arika Verma
Md . F arh an
Ab hishek Sing h Amit Kumar Singh Sapna Srivastava
The Math Olympiad series Olympiad series is an initiative of International Society for Olympiad (ISFO) International Society for Olympiad acknowledges the contribution of all its authors, content writers and designers in the creation of this book.
Copyright
International Society for Olympiad
All rights reserved with the publisher. No part of the work may be reproduced, reprodu ced, stored in retrieval retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without the prior written permission of the publisher. The publisher apologizes to its readers for any errors or omissions and would be grateful for notification of corrections that should be incorporated in the future reprints.
First published 2016 Revised edition 2017
Published by:
International International Society fo r Olympiad 193, Ganpati Enclave, Jharsa Road, Gurgaon (India) www.isfo.in, www.isfo.ae
2
Grade 6
PREFACE
Our education systemeffectively provides an introduction to the concepts of math and science and helps us understand the underlying concepts. Butin its overly generalized approach, which aims to enlighten and test all students of varying caliber and interests, it leaves the exploration of application of all these concepts completely on the students. This workbook is designed to enable students to explore math effectively. Designed in accordance with the requirements of the Math Olympiads , the workbook is an efficient tool to achieve comprehensive success at the ISFO - Math O lympiad and other talent examinations. The main aim of this workbook is to assist students in developing and improving their ability to solve problems of varying levels. This book consists of two sets of questions: Section-A (Groundwork) and Section-B (Thought Provoking) . Questions in section A is of basic level aiming to strengthen the basic concepts and section B has been designed to have questions of higher difficulty level, aiming to instill the application of the basic concepts. Answer keys have been provided to accelerate the learning process.
ISFO Practice Book
3
CONTENTS CONTENTS
4
Chapter 1 : Whole Numbers
...
5
Chapter 2 : Fractions
...
11
Chapter 3 : Ratio and Proportion
...
18
Chapter 4 : Percentage
...
23
Chapter 5 : Speed and Time
...
28
Chapter 6 : Algebra
...
35
Chapter 7 : Lines and Angles
...
40
Chapter 8 : Area and Perimeter
...
48
Chapter 9 : Graphs
...
57
A N S W E RS
...
64
S a m p le Pa p e r
...
67
Grade 6
1 WHOLE NUMBERS
CHAPTER
Some Facts: The numbers used for counting arecalled natural numbers. Thevalueofnothingis representedby thenumberzero. Natural numbers together with the number zero arecalled whole numbers. Thesumof twowholenumbersis alwayswholenumber.
Sec on - A: Groundwork
1.
There are 26,955 pupils in a school. The number in nearest thousand is (A) 26,000
2.
(D) 30,000
(B) 16
(C) 19
(D) 25
Which of the following can be divided by 3 with a remainder of 1? (A) 170
4.
(C) 27,000
The sum of 6 numbers is 96. The average of these 6 numbers is (A) 15
3.
(B) 26,900
(B) 187
(C) 189
(D) 215
Ekta and Chetna shared ` 91. For every ` 4 that Ekta received, Chetna received ` 9. How much money did Chetna receive? (A) ` 60
ISFO Practice Book
(B) ` 61
(C) ` 62
(D) ` 63
5
5.
Ankit bought 12 similar pencils. If each pencil cost 5 paise less, he would be able to buy 4 more pencils. How much did Ankit pay for the 12 pencils? (A) ` 2.40
(B) ` 3.40
(C) ` 2.60
(D) ` 3.60
Study the statement carefully and answer the questions 6 and 7. Lovely bought a cap and a pair of shorts for ` 28. Rakesh bought a similar cap and a T-shirt for ` 64. Karan bought 4 similar caps, 2 pairs of similar shorts and a T-shirt for ` 130.
6.
What was the cost of each cap? (A) ` 10
7.
(B) ` 11
(C) ` 15
(D) ` 20
What was the total cost of a pair of shorts and a T-shirt? (A) ` 64
8.
(B) ` 68
(C) ` 72
(D) ` 76
2 balls are rolling towards each other from the opposite ends of a straight tube that is 420 cm long. Ball A travels 50 cm while ball B travels 30 cm in the 1st second. Both balls travel 2 cm less than the previous distance in each subsequent second. How long does it take for the two balls to meet? (A) 4 second
9.
(B) 6 second
(C) 8 second
(D) 12 second
2 boxes, X and Y, contained some beads. If 30 beads were transferred from box X to box Y, both boxes would have the same number of beads. If 18 beads were transferred from box Y to box X, box X would have 4 times as many beads as box Y. How many beads were there in box X at first? (A) 90
10.
6
(C) 110
(D) 120
Lucky and Ajay are given some money each week. If Lucky and Ajay each spend ` 40 and ` 10 respectively in a day, Lucky will still have ` 700 when Ajay has spent all his money. If Lucky and Ajay each spend ` 10 and ` 40 a day, Lucky will still have ` 1075 when Ajay has spent all his money. How much money is given to Lucky each week? (A) ` 900
11.
(B) 100
(B) ` 1000
(C) ` 1100
(D) ` 1200
Ghazali has 7 stacks of chairs with 20 chairs in each stock. He places each chair equally spaced apart to form the perimeter of a rectangle. The number of chairs along its length is twice the number of chairs along its breadth. How many chairs are there on each side of the rectangle?
Grade 6
(A) 48 chairs along the length and 24 chairs along the breadth (B) 24 chairs along the length and 48 chairs along the breadth (C) 24 chairs along the length and 24 chairs along the breadth (D) 48 chairs along the length and 48 chairs along the breadth
12.
13.
Multiply the second largest factor and the third largest factor of 15,120 by 10 and 6 respectively. Then, add the two results. How many times larger is the answer compared to the original number? (A) 5
(B) 6
(C) 7
(D) 9
Happy Candy Shop is having a special promotion for the month of June. Happy Deal! For every 5 sweet wrappers you collect, you may exchange it for another sweet.
If you have 29 wrappers, how many sweets can you exchange for in total?
14.
15.
(A) 5
(B) 6
C) 7
(D) 9
Tina and Divya have a total of ` 260. If Divya buys a calculator. Tina will have 4 times as much money as Divya. If Tina buys the same calculator, both of them will have the same amount of money. How much does Tina have? (A) ` 160
(B) ` 170
(C) ` 180
(D) ` 190
Naman is 4 times as old as his sister now. In 20 years’ time, Naman’s age will be 14 years less than twice his sister’s age. How old is Naman now? (A) 10 years
(B) 11 years
(C) 12 years
D) 13 years
ISFO Practice Book
7
Sec on - B: Thought Provoking
Study the below table and answer the questions 16 and 17. The charges of three catering companies are shown below.
16.
Cost per person
A
` 95
` 15
B
Nil
` 22
C
` 50
` 18
(B) B
(C) C
(D) None of these
Companies A and C would charge the same amount for Lisa’s 3-day event. How many people did she want to cater for? (A) 25
18.
Cost per day
Which company will charge the lowest price if Zack wants to cater for 80 people for 2 days? (A) A
17.
Company
(B) 35
(C) 45
(D) 55
Three containers P, Q and R had 162 buttons altogether. Some buttons were transferred from container P to container Q and the number of buttons in container Q became thrice of its original number. Then, some buttons were transferred from container Q to container R and the number of buttons in container R became thrice its original number. As a result, the number of buttons in the 3 containers were equal. How many buttons were there in container P at first? (A) 111
19.
(C) 113
(D) 114
In a tennis match, each player plays with every other player once only. If there are 5 players, how many games will be played? (A) 6
8
(B) 112
(B) 8
(C) 10
(D) 12
Grade 6
20.
There were 10 questions in a mathematics quiz. Cindy answered all 10 questions and scored 29 points. If 5 points were awarded for each correct answer and 2 points were deducted for each incorrect answer, how many questions did Cindy answer correctly? (A) 3
21.
23.
(B) 202
(C) 203
(A) 50, 55, 110, 215
(B) 60, 65, 120, 225
(C) 55, 65, 90, 115
(D) 40, 55, 110, 215
(D) 204
The number of science club members in a school is between 34 and 60. If the teacher groups them into groups of 6, there will be a remainder of 2 pupils. If they are put into groups of 8, there will be a remainder of 4 pupils. How many members are t here in the club? (B) 44
(C) 48
(D) 52
12 stacks of 34 coins were used to form the perimeter of a square which had the same number of coins on each side. The coins were arranged side-by-side and were equally spaced. How many coins were there on each side of the square? (A) 101
25.
(D) 9
The sum of four numbers is 430. The first number is 5 less than the second number. The third number is twice the second number. The fourth number is equal to the sum of the first, second and third numbers. Find each of four numbers respectively.
(A) 40
24.
(C) 7
Mira and Bharat had a total of 1134 marbles. After each of them gave away some marbles, the number of marbles Mira had left was 4 times t he number of marbles she had given away. The number of marbles Bharat had left was three times the number of marbles he had given away. If they had a total of 897 marbles left, how many marbles did Bharat have at first? (A) 201
22.
(B) 5
(B) 102
(C) 103
(D) 104
Amanda, Bella and Carrie have some money each. If Amanda gives 4 to Bella, both of them will have an equal amount of money. If Bella gives ` 4 to Amanda, Amanda will have thrice the amount of money Bella has. The amount of money Carrie has is equal to the sum of money that Amanda and Bella have. How much money do the three girls have altogether? (A) ` 62
ISFO Practice Book
(B) `64
(C) ` 66
(D) ` 68
9
26.
Jake was born in the 20th century. Jake’s age in the year 2010 is the sum of all the digits of his year of birth. How old is Jake in the year 2010? (A) 20
27.
(C) 15
(D) 16
(B) ` 12970
(C) ` 13970
(D) ` 14970
(B) 4
(C) 3
(D) 2
Rakesh and Dheeraj are given some money each. Dheeraj spends all his money. If Rakesh spends twice as much as Dheeraj, he will have ` 240 left. If Rakesh spends half of what Dheeraj spends, he will have ` 720 left. How much money is given to Rakesh and Dheeraj respectively? (A) 880,320
10
(B) 14
A school bus can either seat 40 children or 30 adults. Given that there are already 24 children and 8 adults seated in the bus, how many more adults can be seated in the bus? (A) 5
30.
(D) 26
XYZ Company paid ` 23600 in salaries to 17 male and some female employees. Each female employee received ` 500 more than each male employee. There were 14 more male employees than female employees. Find the difference between the total amount of money received by the female employees and that received by the male employees. (A) ` 11970
29.
(C) 24
There are 27 cars and motorcycles in a parking. If there are 84 wheels altogether, how many cars are there? (A) 13
28.
(B) 22
(B) 320,880
(C) 770,430
(D) 430,770
Grade 6
2 FRACTIONS
CHAPTER
Some Facts: A fractionis numberrepresenting apart of awhole. The wholecanbea group of objects or a single object. A fractioncan berepresented onthe numberline. Every fraction has a corresponding point on the number line. Fractionsinwhich thenumeratoris less thanthedenominatorarecalledproper fractions. Fractionsinwhichthenumeratoris equaltoorbiggerthanthedenominatorare called improper fractions. A combination of awhole number and aproper fractionis called a mixed fraction. It is the combination of a whole and a part.
Sec on - A: Groundwork
1.
Which of the following fraction is the smallest? (A)
2.
2 9
(B)
4 11
(C)
Which of the following fraction is greater than
(A)
7 15
ISFO Practice Book
(B)
6 10
(C)
6 13 3 5
(D)
8 15
?
12 20
(D)
16 20
11
3.
1 How many sixths are there in 3 ? 6
(A) 4
(B) 10
(C) 18
(D) 19
Study the given table carefully and answer the questions 4 and 5. The table shows the length of 3 rods. Rod A
Rod B
3 1 m 4
4.
1 3
1 (B) 2 m 3
m
2 12
m
(B) 3
1
(C) 2
12
m
What fraction when added to 1
(A) 2
7.
4
m
2 3
m
(D) 3
2
m
3
Find the total length of the 3 rods. (A) 3
6.
12
3
m
Find the total length of rod A and rod B. (A) 1
5.
7
Rod C
7
(B) 2
8
(C) 3
3 12
m
(D) 3
4 12
m
3
1 3 gives ? 8 2
5 8
(C) 2
3 8
(D) 2
1 8
The average age of Simon and his mother is 45 years. Given that Simon is
1 4
as old as
his mother, what is Simon’s age now? (A) 18
8.
The mass of a container is 39 kg when it is when it is (A) 1.6 kg
12
(B) 21
5 8
(C) 24 5 6
(D) 27
filled with water. Its mass is 29.85 kg
filled with water. What is the mass of the container when it is empty? (B) 2.0 kg
(C) 2.4 kg
(D) 2.8 kg
Grade 6
9.
Johny needs to sell ` 315 worth of tickets for a school concert. He sold 4 adult tickets 1 and 3 child tickets. Each adult ticket costs 1 times as much as a child ticket. If the 2
value of the tickets Johny had left is
3 7
of the original amount, what is the cost of a
child ticket? (A) ` 10
10.
(B) ` 15
(D) ` 25
the cost of a slow cooker. The slow cooker costs
7
that of an 5 8 oven. The oven costs ` 99 more than the slow cooker. How much does the blender cost? (A) ` 277.20
11.
2
The cost of a blender is
(C) ` 20
(B) ` 275.20
(C) ` 265.20
Amy, Ben and Diana bought a present for their father. Amy paid Ben and Diana paid. Ben paid
(D) ` 255.20 1 7
of the total amountt
1
of the total amount Amy and Diana paid. Diana paid 4 `132 more than the amount Amy paid. How much did the present cost? (A) ` 160
12.
(B) ` 200
(C) ` 240
Maria earned ` 600 less than Gloria. Gloria saved
1 6
(D) ` 280
of her salary while Maria saved
4
of hers. Both girls spent the rest of their money. If Gloria spent twice as much ass 9 Maria, how much did Gloria earn? (A) ` 2000
(B) ` 2400
(C) ` 2800
(D) ` 3200
Study the given statement carefully and answer the questions 13 and 14. In a garden, there were flowers was
ISFO Practice Book
2 5
2 7
as many red flowers as yellow flowers. The number of pink
of the number of red flowers.
13
13.
If there were 72 pink flowers, how many flowers were there in the garden altogether? (A) 242
14.
(C) 882
(D) 1082
What fraction of the flowers were yellow?
(A)
15.
(B) 442
1
(B)
6
Ajay jogged 1
1
1
(C)
4
(D)
7
1 9
3
km more on Saturday than on Friday. Onn 10 5 Sunday, he jogged 1 km more than on Saturday. What was the total distance Ajay jogged on the 3 days? (A) 1
1
km on Friday. He jogged
1
(B) 3
2
1 2
(C) 5
1
(D) 7
2
1 2
Sec on - B: Thought Provoking
16.
The graph below shows the height of ladders A, B and C. The total height of the 3 ladders is (A) 7
(B) 7
1
3
14
m
4
(C) 16
(D) 7
m
2
1 4
5 8
m
m
3 1 m 4 5 2 m 8 1 3 m 4 A
B
C
Grade 6
17.
18.
The capacity of an empty tank is 40 litres. Water from 3 pails shown below can be emptied into the tank to fill it exactly. Which of the 3 pails can be used?
l
3 13 l 5
1 13 l 3
2 13 l 5
Pail P
Pail Q
Pail R
Pail S
Pail T
10
(C) Pail R, S and T
(D) Pail P, S and T
3 1 1 What fraction when subtracted from gives ? 5 4 1 20
(B) 1
3
2
(B)
5
(C) 1
20
Find the difference between
7 8
5
(D) 1
20
7 20
and 0.075 in fraction.
4 5
(C)
1
(D)
3
2 3
A tray containing 3 dozen eggs is 1 kg in mass. Given that the empty tray is 100 g, find the average mass of an egg in kg. (A)
(C)
21.
1
(B) Pail P, Q and T
(A)
20.
13
(A) Pail R, Q and T
(A) 1
19.
1 13 l 2
1 80
kg
(B)
kg
(D)
3 100
1 40 3 40
kg
kg
The total number of pupils in class A and class B is 75. The total number of pupils in class B and class C is 51. The number of pupils in class C is
2 5
as many as that in class
A. How many pupils are there in class B? (A) 28
(B) 35
(C) 42
(D) 49
ISFO Practice Book
15
22.
A jug contained 4 l of pure orange juice.
1 4
of the juice was removed and replaced by
an equal amount of lemon juice. The content was thoroughly mixed and
1
of the 4 mixture was removed and replaced by an equal amount of lemon juice. What fraction of the final mixture was lemon juice? (A) 1
23.
3 4
l
(B) 2
3 4
l
(C) 3
3 4
(D) None of these
l
On monday, 800 more children than adults watched a movie. On tuesday, the number of children that watched the same movie decreased by that watched the same movie increased by
1 10
while the number of adults
1
. 1875 people watched the movie on 5 Tuesday. How many children watched the movie on monday? (A) 1300
24.
(B) 1350
(C) 1375
Raphael had ` 40 less than Sam. When he spent
1
(D) 1390
of his money and Sam spent
3
8 4 his money, Raphael had ` 80 more than Sam. How much money did Sam have left? (A) ` 42
(B) ` 44
(C) ` 46
of
(D) ` 48
Study the given statement carefully and answer the questions 25 and 26. Jaya and Pari had ` 1524 altogether. Pari had ` 244 more than Jaya. Pari spent
1 5
ass
much as Jaya and was left with twice as much money as Jaya.
25.
How much did Pari have at first? (A) ` 884
26.
(C) ` 880
(D) ` 878
(C) ` 330
(D) ` 440
How much did Jaya spend? (A) ` 110
16
(B) ` 882
(B) ` 220
Grade 6
Study the given statement carefully and answer the questions 27 and 28. There were 170 people in a hall.
3
of the males were boys and
5 girls. There were a total of 82 adults.
27.
9
of the females were
The number of girls are (A) 44
28.
4
(B) 40
(C) 36
(D) 32
(C) 40
(D) 44
The number of men are (A) 32
(B) 36
Study the given statement carefully and answer the questions 29 and 30. Sapna and Dipti have 596 altogether. money.
29.
5
of Dipti’s money is 10 more than
1 8
of Sapna’ss
How much money does Sapna have? (A) ` 328
30.
1
(B) ` 332
(C) ` 336
(D) ` 328
What fraction of Sapna’s money is Dipti’s money? (A) `
57 84
ISFO Practice Book
(B) `
59 84
(C) `
61 84
(D) `
65 84
17
3
RAT I O AN D PROPORTION
CHAPTER
Some Facts: Comparisonbetweenthequantitiescanbemadeby usingdivision. Tocalculateratio, thetwoquantities havetobemeasuredusingthesameunit. If not, theyshouldbeconvertedtothesameunit beforeratio is taken. Two ratios are said to be equivalent if the fractions corresponding to themare equivalent. If the ratios between quantity A and quantity B is equal to the ratio between quantity C and quantity D, then thefour quantities A, B, C and D, aresaid to be in proportion. Proportion is denotedby thesigns ' ’ or ‘ =’.
Sec on - A: Groundwork
Study the given statement and answer the questions 1 to 3. If A : B = 8 : 13, then
1.
Find the value of B, if A = 64. (A) 102
2.
(D) 117
(B) 16
(C) 20
(D) 24
Find the value of A, if the sum of A and B is 105. (A) 60
18
(C) 104
Find the value of A, if B = 26. (A) 12
3.
(B) 109
(B) 55
(C) 45
(D) 40
Grade 6
Study the given statement and answer the questions 4 to 6. If A : B : C = 9 : 4 : 6, then
4.
Find the value of A, if B = 16. (A) 36
5.
(C) 28
(D) 24
Find the value of B, if the sum of A, B and C is 171. (A) 24
6.
(B) 32
(B) 28
(C) 32
(D) 36
Find the value of C, if the difference of A and B is 55. (A) 77
(B) 66
(C) 55
(D) 44
Study the given statement and answer the questions 7 to 9. On a shelf, the ratio of the number of cookies to the number of puffs is 3 : 8.
7.
If there are 6 pieces of cookies, how many puffs are there? (A) 4
8.
(C) 12
(D) 16
If there are 32 puffs, how many cookies are there? (A) 12
9.
(B) 8
(B) 16
(C) 18
(D) 22
If there are 20 more puffs than cookies, how many cookies and puffs are there altogether? (A) 40
(B) 42
(C) 44
(D) 46
Study the given statement and answer the questions 10 to 12. The length of the sides of a triangle are in the ratio 4 : 7 : 9.
10.
If the length of the longest side is 45 cm, find the length of the shortest side. (A) 14 cm
11.
(C) 18 cm
(D) 20 cm
If the total length of all the sides is 200 cm, find the length of the longest side. (A) 100 cm
12.
(B) 16 cm
(B) 90 cm
(C) 80 cm
(D) 60 cm
If the difference between the length of the longest side and the length of the shortest side is 35 cm, find the length of the shortest side. (A) 24 cm
ISFO Practice Book
(B) 26 cm
(C) 28 cm
(D) 30 cm 19
Study the given statement and answer the questions 13 to 15. If A : B = 1 : 2 and B : C = 4 : 5, then
13.
The ratio of A : C is (A) 1 : 2
14.
(C) 2 : 5
(D) 1 : 5
(B) 1 : 2 : 3
(C) 1 : 4 : 3
(D) 5 : 4 : 2
(C) 12
(D) 15
The ratio of A : B : C is (A) 2 : 4 : 5
15.
(B) 4 : 5
If A is 6 less than B, then the value of C is (A) 6
(B) 9
Sec on - B: Thought Provoking
16.
There are 5 times as many blue pens as red pens in a bookshop. What is the ratio of the number of blue pens to the total number of pens? (A) 1 : 5
17.
(C) 5 : 6
(D) 13 : 15
(B) 20 cm
(C) 22 cm
(D) 24 cm
(B) ` 125
(C) ` 315
(D) ` 350
The pupils at a camp are divided equally into team A and team B. The ratio of the number of boys to the number of girls in team A is 2 : 1 and in team B is 4 : 11. What is the ratio of the total number of boys to the total number of girls? (A) 1 : 2
20
(B) 2 : 3
Alan, Bobby and Caleb shared a sum of money in the ratio 2 : 3 : 4. If the sum of Bobby’s money and Caleb’s money was ` 175 more than Alan’s, what was the sum of money shared by the three boys? (A) ` 75
20.
(D) 5 : 6
The perimeter of a rectangle is 56 cm. The ratio of its length to its breadth is 5 : 2. Find the length of the rectangle. (A) 18 cm
19.
(C) 5 : 1
Express 14 days as a ratio of 21 days in its simplest form. (A) 1 : 2
18.
(B) 1 : 6
(B) 7 : 8
(C) 8 : 11
(D) 8 : 13
Grade 6
21.
The ratio of the number of sweets Jason has to the number of sweets Mathew has is 3 : 5. If Jason and Mathew have 32 sweets altogether, how many sweets does Jason have? (A) 3 sweets
22.
(C) 9 sweets
(D) 12 sweets
The ratio of the perimeter of square A to the perimeter of square B is 1 : 4. If the perimeter of square B is 64 cm, find the difference betw een the area of the two squares. (A) 120 cm2
23.
(B) 6 sweets
(B) 160 cm2
(C) 200 cm2
The figure below is not drawn to scale. The area of X is
(D) 240 cm2 1
of the area of the whole 4 rectangle. The ratio of area of Y to the area of Z is 5 : 4. What is the ratio of the area of X to the area of Y to the area of Z? (A) 3 : 5 : 4
Z
(B) 5 : 4 : 3
Y
(C) 3 : 4 : 5
X
(D) None of these
24.
A square and a rectangle overlap each other as shown in the figure below. The ratio of the area of the shaded part to the area of the square is 1 : 3. Find the ratio of the area of the unshaded parts to the area of the shaded part. (A) 1 : 3 9cm
(B) 1 : 5
9cm
(C) 5 : 1 (D) 3 : 1
25.
Jeffrey’s age is half of Pamela’s age. In 5 years time, the ratio of Jeffrey’s age to Pamela’s age will be 2 : 3. How old is Pamela now? (A) 4
26.
12cm
(B) 6
(C) 8
(D) 10
The ratio of the number of apples to the number of peaches in a box was 7 : 4. When 20 apples were replaced by 20 peaches, the ratio of the number of apples to the number of peaches became 1 : 2. How many apples were there at first? (A) 44 apples
ISFO Practice Book
(B) 42 apples
(C) 40 apples
(D) 38 apples
21
27.
Seven years ago, the ratio of Samuel’s age to George’s age was 2 : 1. The ratio of their ages is 5 : 3 this year. What will be the ratio of their ages in seven years time? (A) 3 : 2
28.
(B) 2 : 3
(C) 1 : 2
(D) 2 : 1
The diagram below is not drawn to scale. The sum of the area of circle A and circle B is 3 5
of the area of circle C.
The fraction of each circle is shaded as follows: 1 3 1 2 1 4
C
of circle A is shaded.
of circle B is shaded.
B A
of circle C is shaded.
Find the ratio of the area of circle A to the area of circle B. (A) 2 : 1
29.
3 5
(D) 4 : 1
(B)
1 5
(C)
3 7
(D) 1
7 11
A, B and C represents three numbers respectively. The ratio of A to (B + C) is 1 : 3. The ratio of (A + B) to C is 4 : 1. Find the ratio of A : B : C. (A) 5 : 7 : 4
22
(C) 3 : 1
The sum of the numerator and denominator of a fraction is 10. When 3 is added to the numerator and 2 is added to the denominator. The ratio of the numerator to the denominator is 2 : 3. Find the fraction. (A)
30.
(B) 1 : 1
(B) 4 : 7 : 5
(C) 4 : 11 : 5
(D) 5 : 11 : 4
Grade 6
4 P ER CEN T A G E
CHAPTER
Some Facts: PercentisanabbreviationfortheLatinpercentum, whichmeansforeach100. Percentagesarehelpfulincomparison. Theincreaseordecreasein acertain quantitycanbeexpressedaspercentageincreaseordecrease. Percentageincrease/ decrease=
Change ×100 Original
Sec on - A: Groundwork
1.
Express 250 m as a percentage of 5 km. (A) 20%
2.
(C) 10%
(D) 5%
Express 15 minutes as a percentage of 3 hours. 1 (A) 6 % 3
3.
(B) 15%
1 (B) 7 % 3
1 (C) 8 % 3
1 (D) 9 % 3
Raju bought a dining set for ` 2400. He made a downpayment of 15 % and paid the balance in 12 monthly instalments. How much was the downpayment? (A) ` 340
ISFO Practice Book
(B) ` 345
(C) ` 355
(D) ` 360
23
Study the given information below and answer the questions 4 and 5. The table below shows the amount of money that Mrs. Charu spent on 3 items at the supermarket.
4.
Detergent
Poultry
` 21
` 12
` 17
How many more percent of the money was spent on seafood than on detergent? (A) 20%
5.
Seafood
(B) 18%
(C) 16%
(D) 14%
What percentage of Mrs. Charu’s money was spent on poultry? (A) 28%
(B) 30%
(C) 32%
(D) 34%
Study the given information below and answer the questions 6 and 7. Aminah, Belle and Sapna shared a box of chocolates in the ratio 18 : 20 : 12.
6.
What percentage of the chocolates in the box belonged to Sapna? (A) 22%
7.
(B) 24%
(C) 26%
(D) 28%
Express Aminah’s share as a percentage of Belle’s share. (A) 60%
(B) 70%
(C) 80%
(D) 90%
Study the given information below and answer the questions 8 and 9. Mark donated 20% of his money to charity. He gave 50% of the remainder to his wife and t he rest was shared equally among his 4 children. Each child r eceived ` 5000.
8.
9.
24
How much money did Mark have at first? (A) ` 45,000
(B) ` 50,000
(C) ` 55,000
(D) ` 60,000
How much money did he donate to charity? (A) ` 16 000
(B) ` 14,000
(C) ` 12 000
(D) ` 10,000 Grade 6
Study the given information below and answer the questions 10 and 11. The length of a rectangular pool is 60% longer than its breadth. The perimeter of the pool is 156 m.
10.
The length of the pool is (A) 52 m
11.
(B) 48 m
(C) 44 m
(D) 40 m
(C) 32 m
(D) 30 m
The breadth of the pool is (A) 36 m
(B) 34 m
Study the given information below and answer the questions 12 and 13. Rahman is paid 16% more for working on a saturday than on a weekday. He is paid 25% more on a sunday than on a saturday. His pay for working on a weekday is ` 50.
12.
How much will he earn for working 3 sundays? (A) ` 219.50
13.
(D) ` 213.50
(B) ` 365.50
(C) ` 375.50
(D) ` 380.50
Mathew had 10 out of 50 sums incorrect in a mathematics quiz. What percentage of the sums did he get correct? (A) 10%
15.
(C) ` 215.50
How much will he earn for working 1 whole week? (A) ` 360.50
14.
(B) ` 217.50
(B) 20%
(C) 80%
(D) 90%
The pie chart below shows the proportion of pupils participating in various sports. What percentage of the pupils participates in soccer? Badminton
Soccer Basketball
8% Swimming
(A) 17%
ISFO Practice Book
(B) 42%
(C) 82%
(D) 92%
25
Sec on - B: Thought Provoking
16.
The number of beads that Liza has is 75% of the number of beads that Jimmy has and 3
of the number of beads that Vimla has. If Jimmy has 180 beads, how many beads 5 does Vimla have? (A) 235
17.
(C) 245
(D) 255
There are 600 jellybeans in a container. 25% of them are red, 40% of them are yellow and the rest are green. How many yellow jellybeans less than green jellybeans are there? (A) 30
18.
(B) 225
(B) 60
(C) 90
(D) 210
ABCD is a rectangle. AE + FB = EF and AE = FB. What percentage of the rectangle is shaded? D C (A) 47.5 (B) 37.5 (C) 27.5 A
(D) 17.5
19.
E
F
B
A rectangle measures 50 cm by 30 cm. If both the length and the breadth of the rectangle are increased by 30% each, what is the total percentage increase in the area of the rectangle? (A) 61%
(B) 65%
(C) 69%
(D) 73%
Study the given information below and answer the questions 20 and 21. Jane has 40% more stamps than Emily. Gareth has 20% of the number of stamps Jane has.
20.
What is the ratio of the number of stamps Emily has to the number of stamps Gareth has? (A) 7 : 25
26
(B) 25 : 7
(C) 3 : 25
(D) 25 : 3
Grade 6
21.
If Jane has 84 more stamps than Gareth, find the total number of stamps Jane and Emily have. (A) 120
22.
(C) 160
(D) 180
Basket A contains 200 pens and 700 pencils. Basket B contains 1000 pens and 800 pencils. How many pens and pencils must be transferred in total from basket B to basket A such that 80% of the items in basket A are pencils and 75% of the items in basket B are pens? (A) 400
23.
(B) 140
(B) 500
(C) 600
(D) 700
The figure below consists of 2 overlapping rectangles P and Q. The ratio of the area of rectangle P to that of rectangle Q is 5 : 6. 20% of rectangle P is shaded. What percentage of the figure is not shaded? P (A) 70% Q (B) 80% (C) 90% (D) 100%
24.
The figure below consists of 2 overlapping trapeziums R and S. The ratio of the area of trapezium R to that of trapezium S is 2 : 5. 30% of trapezium R is shaded. What percentage of the figure is not shaded? S
(A) 56% (B) 88%
R
(C) 92% (D) 98%
25.
A music player cost the same at shop E and shop F. During a weekend sale, shop E offered a 4% discount on saturday and a further 5% discount on sunday. Shop F offered a 10% discount on both days. If the music player costs ` 6 more in shop E than in shop F after the final reductions, find the original price of the music player. (A) ` 200
(B) ` 300
(C) ` 400
(D) ` 500
ISFO Practice Book
27
Study the given information below and answer the questions 26 to 28. In a group of 120 pupils, 75% like soccer,
5 12
like badminton and 10 do not like either
sport.
26.
How many pupils like both sports? (A) 10
27.
(C) 30
(D) 40
(C) 50
(D) 60
(C) 20
(D) 25
How many only like soccer? (A) 30
28.
(B) 20
(B) 40
How many only like badminton? (A) 10
(B) 15
Study the given information below and answer the questions 29 and 30. Ismail received a 5% commission for the first 100 comic books he sold and 8% for every subsequent comic book sold. Each comic book cost ` 12.
29.
How much commission did Ismail receive for selling 150 comic books? (A) 150
30.
(C) 170
(D) 180
If Ismail received ` 194.40 in commission, how many comic books did he sell? (A) 120
28
(B) 160
(B) 180
(C) 240
(D) 260
Grade 6
5 SPEED A N D T I M E
CHAPTER
Some Facts: Distance Speed = Time
Distance Time = Speed
Distance = speed × time
1 km/ hr =
1 m/ s =
5 m/ s 18
18 km/ hr 5
Sec on - A: Groundwork
1.
A marathon runner ran a total distance of 35 km in 4 hours. What was the average speed of the runner? (A) 8.57 km/h
2.
5 (C) 8 km/h 7
(D) 8.75 km/h
Sonny drove from Jaipur to Delhi which is 260 km away. How long will he take if his average speed was 78 km/h? (A) 3 h 10 min
3.
2 (B) 8 km/h 3
(B) 3 h 20 min
(C) 3 h 30 min
(D) 3 h 33 min
A train travelled 120 km at an average speed of 90 km/h. Find the time taken for the journey in hours and minutes. (A) 1 h 5 min
ISFO Practice Book
(B) 1 h 10 min
(C) 1 h 15 min
(D) 1 h 20 min
29
4.
Tina ran 100 m in 20 minutes. Find her average speed in m/min. (A) 5 m/min
5.
(B) 4 m/min
If Wayne walked
(B) 1 h 13 min
(C) 1 h 17 min
(D) 1 h 18 min
1
of the distance from his home to the school and cycled the remain4 ing distance, he would take 11 minutes for the whole journey. If he cycled the entire distance, he would take 4 minutes. How long will Wayne take if he walked the entire distance to school? (A) 22 min
7.
(D) 2 m/min
Jenny jogged from her home to a park 3 km away at a speed of 6 km/h. She continued jogging to the swimming pool which was 4 km away from the park at a speed of 5 km/h. How long did she take to jog from her home to the swimming pool? (A) 1 h 11 min
6.
(C) 3 m/min
(B) 26 min
(C) 30 min
(D) 32 min
5 speed cameras were placed at a distance of 50 km apart from each other along a highway. The table shows the time at which a car travelling along the highway was photographed by each camera.
Speed Camera
Time
1
08 : 45
2
09 : 10
3
09 : 50
4
10 : 20
5
10 : 55
Between which two speed cameras did the car travel at an average speed of more than 100 km/h?
8.
30
(A) 1 and 2
(B) 2 and 3
(C) 3 and 4
(D) 4 and 5
James started jogging at 6.30 a.m. He jogged for 8 km. He took 15 min to jog the first 3 km and then finished the remaining distance at an average speed of 15 km/h. At what time did he complete the jog? (A) 6 : 55 a.m.
(B) 7 : 00 a.m.
(C) 7 : 05 a.m.
(D) 7 : 10 a.m.
Grade 6
Study the given statement carefully and answer the questions 9 and 10. At 9 : 30 p.m, train X left station A and travelled towards station B at a speed of 80 km/h. Half an hour later, train Y left station B and travelled towards station A at a speed of 90 km/h.
9.
How far has train X travelled when train Y left station B? (A) 30 km
10.
(C) 50 km
(D) 60 km
If the distance between station A and station B is 720 km, at what time would the two trains pass each other? (A) 1 a.m.
11.
(B) 40 km
(B) 2 a.m.
(C) 3 a.m.
(D) 4 a.m.
At 8 a.m., a bus left alpha town and travelled towards beta town at an average s peed of 70 km/h. At the same time, a van left Beta town and travelled towards Alpha town at an average speed of 55 km/h. At 10 a.m., the two vehicles were 35 km apart. If the two vehicles had already passed each other before 10 a.m., find the distance between the two towns. (A) 215 km
(B) 210 km
(C) 205 km
(D) 200 km
Study the given statement carefully and answer the questions 12 and 13. Tim drove from sky city to rainbow city. After travelling
1 3
of the journey at an average e
speed of 72 km/h for 45 min, he stopped at cloud city to have a snack for
1
hour. He 2 then carried on with his journey, increasing his speed by 18 km/h. He reached rainbow city at 1 : 15 p.m.
12.
What was the distance between cloud city and rainbow city? (A) 108 km
13.
(B) 81 km
(C) 57 km
(D) 55 km
(C) 11 : 00 a.m.
(D) 11 : 12 a.m.
What was the time when Tim left sky city? (A) 10 : 36 a.m.
(B) 10 : 48 a.m.
Study the given statement carefully and answer the questions 14 and 15. Towns X and Y are 60 km apart. At 10 a.m., Michael left town X and cycled towards town Y at 12 km/h. At the same time, Paul left town Y and cycled towards town X along the same path at 18 km/h. ISFO Practice Book
31
14.
At what time did they pass by each other? (A) 11 : 00
15.
(B) 12 : 00
(C) 13 : 00
(D) 14 : 00
How far was Michael from town Y when Paul reached town X? (A) 20 km
(B) 18 km
(C) 16 km
(D) 14 km
Sec on - B: Thought Provoking
16.
Terry and Joe left Point X and cycled in opposite directions in a straight line. After 5 h, they were 352 km apart. Terry’s average speed was 4.8 km/h faster than Joe’s average speed. What was Joe’s speed? (A) 28.8 km/h
17.
(B) 30.8 km/h
(C) 32.8 km/h
(D) 34.8 km/h
A 200 m track and a 400 m track are located side by side, touching at A. Paul and Bala started running from A at 10 a.m. with average speeds of 2 km/h and 20 km/h respectively. At what time would they pass each other at point A again? (A) 10 : 00 a.m.
Bala
Paul
(B) 08 : 06 a.m. A
(C) 10 : 06 a.m. (D) 11 : 06 a.m.
18.
19.
32
200 m track
400 m track
A bus left argon lake for boron lake at 8 : 45 a.m. while a car left half an hour later. The car overtook the bus at 11 : 15 a.m. and arrived at boron lake at 12 : 15 p.m. At what time did the bus reach boron lake? (A) 11 : 00 p.m.
(B) 11 : 30 p.m.
(C) 12 : 00 p.m.
(D) 12 : 30 p.m.
A 400 m long train travelling at 120 km/h enters a tunnel that is 2 km long. How long does it take for the train to pass through the tunnel, from the moment the front of the train enters the tunnel to the moment the rear of the train emerges from the tunnel? (A) 0.8 min
(B) 1 min
(C) 1.2 min
(D) 1.4 min
Grade 6
20.
Daniel took 45 minutes to jog 18 times around a park. If one round of the park was 450 m, his average speed is (A) 160 m/min
21.
(C ) 200 m/min
(D) 22 220 m/min
At 8 : 45 a.m., a car left sunny s unny town travelling travelling at a speed s peed of 60 km/h. 45 min later, later, a motorcycle left sunny town. After travelling 195 km, the motorcycle caught up with the car. The motorcycle continued to travel at this speed before stopping for a 30 minute lunch break at 1 : 45 p.m. How far apart will the two vehicles be at 3 : 30 p.m.? (A) 24 km
22.
(B) 18 180 m/min
( B ) 26 k m
( C ) 28 k m
( D ) 30 k m
Jill took 12 minutes to complete a 3 km race while Mary took 15 minutes. The difference in their speeds is (A) 50 50 m/min
23.
(B) 48 m/min
(C ) 46 46 m/min
(D) 44 m/min
The table shows the time taken by 3 boys to complete a lap of 1.2 1. 2 km at the t he pool.
Raju
Ken
Tom
5 min
?
4.8 min
If the average speed of the boys was 240 m/min, find the time taken by Ken to complete the lap. (A) 4.0 min
24.
(B) 4.4 min
(C ) 4.8 min
(D) 5.2 min
1 2 h to The ratio of a motorbike’s speed to a car’s speed was 2 : 3. The motorbike took o 2 travel from town A to town B. How long would it take for the car to cover the same distance?
(A) 55 min
(B) 50 min
(C ) 45 min
(D) 40 min
Study the given statement carefully and answer the questions 25 and 26. Rahman set off from city W at 11 : 30 a.m. for city X which was 180 km away. away. He arrived at city X at 2 : 30 p.m.
25.
What was Rahman’s Rahman’s average speed? (A) 55 km/h
ISFO Practice Book
(B) 60 km/h
(C ) 65 km/h
(D) 70 km/h
33
26.
On his return journey from city X to city W, he increased his speed by 50%. How long did he take for his return journey? (A) 2 h
1 (B) 1 h 2
(C ) 1
1 4
h
(D) 1 h
Study the given statement carefully and answer the questions 27 and 28. Jack and Ben both set off from Jaipur for Delhi at the same time. After driving for 5 h at 1 an average speed of 48 km/h, Jack completed the journey but Ben had only covered 3 of the journey.
27.
At what speed was Ben driving? (A) 12 km/h
28.
(B) 16 km/h
(C ) 20 km/h
(D) 24 km/h
How long did Ben take to cover the whole journey? (A) 15 h
( B ) 16 h
( C ) 14 h
( D ) 13 h
Study the given statement carefully and answer the questions 29 and 30. In a cross-country marathon, Jumad covered the first
4
of the journey at an average 5 speed of 40 km/h. He then decreased his speed by 20% for the last 240 km of the journey journey..
29.
What was the total distance covered by Jumad? (A) 800 km
30.
(C ) 1100 km
(D) 1200 km
How long did Jumad take to complete the whole journey? 1 (A) 31 h 2
34
(B) 900 km
1 (B) 31 h 3
1 (C ) 31 h 4
1 (D) 31 h 5
Grade 6
6 ALGEBRA
CHAPTER
Some Facts: Facts: An Anunknown quantity whichtakes various numerical valueis calledvariable. An Anunknownquantity canberepresented by avariable. Usually, avariableis any letterfromtheE Engli nglish shalphabetthatrepresentsanunknownquantity. ntity. A quantity whosevaluedoes not vary is called aconstant. An Anexpressionconsisting of variables, constants and mathematical operators is called an algebraic expression. expression. Mathematical operations such as addition, ddition, subtraction, multipli ltiplication cation and divi divisio sion n canbeeasily performedonvariables.
Secc on - A: Se A: Gr Grou ound ndwo work rk
1.
James’ mass is x kg. Kathy is 3 times as heavy as James. What is Kathy’s mass? (A) (3 + x) kg
2.
(C ) 3x kg
Donna bought a mango for p rupees and 4 oranges for 90 paisa . She paid the cashier `10. How much change did she receive? (A) ` (9.10 – p)
3.
(B) (3 – x) kg
x (D) kg 3
(B) ` (9.20 – p)
(C ) ` (9.30 – p)
(D) ` (9.40 – p)
Which of the following is correct for the equation 3k – 8 + 2k – 1 = ? (A) 5k – 10
ISFO Practice Book
(B) 5k – 9
(C ) 5k + 9
(D) 5k + 10
35
4.
The values of the 18b – 7b – 26, when b = 8, is (A) 62
5.
(B) 64
(C) 66
(D) 68
Which of the following is correct for the equation 18h + 13 – 10h = ? (A) 8h - 13
(B) 8h - 11
(C) 8h + 11
(D) 8h + 13
Study the given statement carefully and answer the questions 6 and 7. Mrs. Baany bought n chickens at ` 9 each and 6 ducks for ` 3 n.
6.
Total cost of the chickens and the ducks in terms of (A) ` 12 n
7.
(B) ` 12
is
n
(C) `(12 + n)
(D) ` (12 – n)
How much cheaper were the ducks than the chickens in terms of n? (A) ` n
(B) ` 3n
(C) ` 6 n
(D) ` 4n
Study the given figure carefully and answer the questions 8 to 10. The figure below shows 2 rulers.
8.
3y cm
5y cm
(B) 2y cm
(C) 8y cm
(D) 16 cm
The difference in their lengths in terms of y is (A) 2y cm
10.
Ruler B
The total length of the rulers in terms of y is (A) 8 cm
9.
Ruler A
(B) y cm
(C) (2 - y) cm
(D) 8y cm
(C) 10 cm
(D) 8 cm
If ruler A is 6 cm, how long is ruler B? (A) 2 cm
(B) 4 cm
Study the given statement carefully and answer the questions 11 to 13. The average length of 4 ribbons is y cm.
11.
Express the total length of the ribbons in terms of y. (A) (4 + y) cm
12.
(C) 16 cm
(D) 8y cm
(C) 52 cm
(D) 28 cm
If y = 24, find the total length of the ribbons. (A) 96 cm
36
(B) 4y cm
(B) 48 cm
Grade 6
13.
14.
If the total length of 3 of the ribbons is 75 cm, find the length of the fourth ribbon in terms of y. (A) (4y + 75) cm
(B) (3y + 75) cm
(C) (3y – 75) cm
(D) (4y – 75) cm
The figure shown below is a square. x cm
Find the perimeter of the square in terms of x.
15.
(A) (4 + x) cm
(B) 4x cm
(C) 8x cm
(D) (8 + x) cm
Harry is x years old. Leonard is 5 years older than Harry. What will be their total age in 12 year’s time? (A) (2x + 29) years
(B) (2x + 39) years
(C) (3x + 29) years
(D) (4x + 29) years
Sec on - B: Thought Provoking
16.
Kelvin is k years old. In 7 year’s time, his father will be twice as old as he. How old will his father be, in terms of k, in 7 year’s time? (A)
k 7 2
years old
(B)
(C) (2k + 7) years old
17.
years old
(D) 2(k + 7) years old
(B) 2u
(C) 2u + 1
(D) 2u + 2
Wayne paid ` 6.60 for 6 erasers and some sharpeners. Each eraser cost y cents and each sharpener cost (y – 50) paise. If y = 90, how many sharpeners did Wayne buy? (A) 3
19.
2
The sum of 3 consecutive numbers is 6u. The smallest number is (A) 2u – 1
18.
2k 7
(B) 4
(C) 5
(D) 6
The average mass of 7 watermelons is w kg. If the total mass of 3 watermelons is 8 kg, what is the average mass of the remaining watermelons in terms of w? (A)
7w 8 4
ISFO Practice Book
kg
(B)
7w 8 4
kg
(C)
8w 7 4
kg
(D)
8w 7 4
kg
37
Observe the given figure carefully and answer the questions 20 and 21. The figure below shows the outline of a plot of land.
20.
The perimeter of the plot of land is (A) (10x + 36)m (4x – 8)m
(B) (10x + 24)m (C) (10 x+ 4)m (D) (10x + 8)m
21.
If the cost of fencing is `14 perimeter, then the total cost of fencing is (A) ` 756
22.
(x + 10)m
(B) ` 576
(C) ` 765
(D) ` 657
5 hotdogs and 8 hamburgers cost ` 49. If 1 hotdog and 1 hamburger cost `p, find the cost of 3 hamburgers. (A) ` (49 – p)
(B) ` (49 – 3p)
(C) ` (49 + 5p)
(D) ` (49 – 5p)
Study the given statement carefully and answer the questions 23 and 24. In January, Susan withdrew 1/3 of her savings from the bank. This amount was ` 640. In February, she deposited 1/4 of her salary into the bank and her savings become ` z.
23.
Susan’s salary for the month of February in terms of z is (A) ` (4z – 5120)
24.
(B) ` (4z – 5012)
(C) ` (4z + 5012)
(D) ` (4z + 5120)
If z = ` 1804, then the Susan’s salary for the month of February is (A) ` 2069
(B) ` 2096
(C) ` 2036
(D) ` 2063
Study the given statement carefully and answer the questions 25 and 26. The charges for using a mobile phone are as follows: Fixed charge: ` 21 per month Per minute usage: 2 paise Per text message sent: 2 paise
25.
38
Last month, Gary used the phone for q hours and sent 10 text messages. Find the amount he had to pay in paise, in terms of q. (A) (2130 + 120q) paise
(B) (2130 + 140q) paise
(C) (2120 + 120q) paise
(D) (2130 + 110q) paise Grade 6
26.
If q = 4.2, how much did he have to pay in dollars? (A) ` 22.34
27.
(B) ` 23.34
(C) ` 24.34
(D) ` 26.34
If |4w - 8| is a multiple of 12, find the next 3 multiples of 12 after (4w - 8) in terms of w. (A) 4w + 4, 4w + 16, 4w + 28
(B) 4w + 4, 4w + 16, 4w + 32
(C) 4w + 4, 4w + 8, 4w + 16
(D) 4w + 4, 4w + 28, 4w + 48
Study the given statement carefully and answer the questions 28 and 29. The table below shows the price list of the items available in a bookshop. Item
Ruler
w paise
Pen
(12w + 40) paise
Marker
(22w – 15) paise
Calculator
28.
29.
` w
Helmi bought 2 rulers, a pen, a marker and a calculator. Find the amount he spent in terms of w in cents. (A) (136w + 25) paise
(B) (136w + 45) paise
(C) (134w + 25) paise
(D) (136w + 35) paise
Ailing paid ` 86.45 for 2 calculators, 3 markers and some pens. If w = 25, how many pens did she buy? (A) 2
30.
Price per item
(B) 4
(C) 6
(D) 8
Raihan had ` (50 + 8s). Samad had ` 9 s more than Raihan. Raihan was given ` s and Samad was given twice as much. How much do they now have altogether? (A) ` (90 + 28s)
ISFO Practice Book
(B) ` (100 + 28s)
(C) ` (110 + 28s)
(D) ` (100 + 38s)
39
7
LINES AND
CHAPTER
A N G LES
Some Facts: The angle whose measure is equal to 180° is called a straight angle. Theanglewhosemeasureisgreaterthan180°andlessthan360°iscalledareflex angle. Two angles sumof whose measures is 90° are called complementary angles. Two angles sumof whose measures is 180° arecalled supplementary angles. Angles withacommonvertex anda commonarmarecalled adjacent angles. A pairof adjacent angles whosenon–commonarms areoppositerays is called a linearpair. Twoanglesthatarenotadjacentbuthaveacommonvertex arecalledvertically oppositeangles. Vertically oppositeanglesareoppositeto eachotherandareequal.
Sec on - A: Groundwork
1.
In the figure, XY and PR are straight lines. Find x in the figure shown. P X O 120°
x Y R
(A) 30°
40
(B) 40°
(C) 45°
(D) 50°
Grade 6
2.
In the figure, PQR is an equilateral triangle, the value of a is a 60° P
R
Q
(A) 195°
3.
(B) 200°
(C) 240°
(D) 280°
ABCD is a rectangle and EBC is a triangle. The value of BEC is E A
52°
120°
B
(A) 60o
4.
D
C
(C) 58o
(B) 68°
(D) 50o
ABCD is a rhombus, ADE is an isosceles triangle and BDE is a st raight line. The value of ADE is A B
E
D
144° C
(A) 142°
5.
(B) 152°
(C) 162°
(D) 172°
EFGH is a square. EJL and FKL are straight lines. The value of EJG is H J
E
25° 80° F
(A) 105° ISFO Practice Book
(B) 104o
L
K G
(C) 110o
(D) 114o 41
6.
PQRV is a square, VSTU is a rectangle and PRT is a straight line. The value of PTV is V P U (A) 19° 64° (B) 21o (C) 23o (D) 25
Q
R
o
T
S
7.
JKLM is a parallelogram and NM = NL. The value of JNL is M
(A) 112°
N
(B) 116°
28°
J
(C) 120°
L
(D) 124° K
8.
PQRS is a parallelogram. QP = QT and PUT is a straight line. The value of SPQ is P
(A) 128°
S
(B) 132° (C) 136°
Q
U
(D) 140°
R 38°
T
9.
FGHJ is a trapezium and GF = GK. The value of JKL is K
F
50° G (A) 20°
42
(B) 25°
J 84°
L
H (C) 30°
(D)35°
Grade 6
10.
PQRS is a trapezium and PQ = PT. The value of PS R is
T
(A) 120° (B) 125°
P
65°
(C) 130° (D) 135° S 60°
Q
11.
R
GMH, GNJ and HJKL are straight lines. MN || HL. The value of MNJ is G
(A) 59° 25°
(B) 61° M
(C) 63° (D) 65°
36°
H
12.
N
L
J K
PQS, RSTU and PVU are straight lines. QV || RU, QS = QT = QV and VT = VU. The value of PVQ is
P
(A) 65° (B) 67°
Q
V
(C) 69° (D) 71°
13.
142° R
S
T
U
ABCG is a rhombus. ACDE is a rectangle and CGE is a diagonal of the rectangle. The A E value of AB C is (A) 80° (B) 100°
° 0 3
B
G
(C) 120° (D) 140° C ISFO Practice Book
D 43
14.
EFG is a right-angled triangle. JFGH is a parallelogram and EJG is a straight line. The value of EG H is E (A) 12° (B) 24° (C) 36°
108° J
(D) 48°
60°
G
F
15.
H
PQRS is a parallelogram and PSV is a straight line. The value of TU R is (A) 118°
S
P
V
148°
(B) 120°
T
(C) 122° Q
(D) 124°
R
U
Sec on - B: Thought Provoking
16.
In the figure, ABC is a straight line and BC is parallel to DE. The value of FDE is C
(A) 15°
B
(B) 55° A
(C) 70°
40°
85°
F E
(D) 85° D
17.
44
In the figure, KLMN is a rhombus, JLM is an isosceles triangle and NMJ is a straight line. The value of JLM is L K (A) 20°
(B) 25°
(C) 40°
(D) 80°
M
N
J
Grade 6
18.
In the figure, O is the centre of the circle. ABCD is a rectangle and EOF is a straight line. The lines EO and AO touch the circle. The value of AEO is E
(A) 50° (B) 65°
A
O 50°
(C) 90° D
(D) 130°
19.
F
B C
The figure, not drawn to scale, shows a circle with centre O and a trapezium ABCD. The value of p is A p
(A) 107o (B) 117o
O 74°
(C) 127° D
o
(D) 137
20.
B
C
E
WXYZ is a square, not drawn to scale. The ratio of a to b is 1 : 2. The value of c is W X (A) 30° a b (B) 60° (C) 90° (D) 120°
21.
c
Z
Y
In the figure, not drawn to scale, AB is parallel to CD and AC is parallel to EF. The sum of x and y is B E A
65° 100° x
y
D
F C
(A) 105°
ISFO Practice Book
(B) 115°
(C) 135°
(D) 155°
45
Study the given figure carefully and answer the questions 22 and 23. In the figure, ABCD is a rectangle and EFGD is a parallelogram. CGH is a straight line.
DEF 42, DCG 47 and CBG 77. A F
E
22.
77°
G
42°
47°
C
D
The value of C G D is (A) 61°
23.
B
(B) 91°
(C) 101°
(D) 111°
(C) 105°
(D) 95°
The value of B G H is (A) 120°
(B) 110°
Study the given figure carefully and answer the questions 24 to 26. In the figure, ABCD is a parallelogram and EFGH is a trapezium. AJ is a straight line.
ADC 49, AJG 129 and FEH 70. A
B
E 70° D
K J
49° L H
24.
(C) 70°
(D) 80°
(B) 129°
(C) 127°
(D) 125°
(C) 80°
(D) 90°
The value of D L E is (A) 60°
46
(B) 60°
The value of B K E is (A) 131°
26.
C 129° G I
The value of D A J is (A) 50°
25.
F
(B) 70°
Grade 6
Study the given figure carefully and answer the questions 27 and 28. ABC is an isosceles, right-angled triangle. AC is parallel to DE. HOG and EOF are straight lines BHO 20, FOG 28 and EDG 88. A
27.
28.
D
The value of D E F is
88°
(A) 35°
(B) 37°
(C) 39°
(D) 41°
H
C
The value of D G H is
B 20°
F 28°
(A) 57°
(B) 47°
(C) 37°
(D) 27°
E
G
Study the given figure carefully and answer the questions 29 and 30. The figure, not drawn to scale, is made up of a square ABCD and two rhombuses ATCP and DRBV. Given that BVD 135 and AT = BR, find D
29.
30.
A
P
The value of A D B is (A) 35°
(B) 45°
(C) 55°
(D) 65°
The value of A Q D is
R S
W 135° V
T
U
C
(A) 105°
(B) 115°
(C) 125°
(D) 135°
ISFO Practice Book
Q
B
47
8
AREA AN D P ER I M ET ER
CHAPTER
Some Facts: Perimeter of a closed figureis the distance around it, whereas area is the region enclosed by closed figure. Perimeter of a regular polygon = numberof sides × length of one side. Perimeter of a rectangle of length 'l ' units andbreadth 'b' units = 2(l + b). Areaof arectangle of length 'l ' units andbreadth'b' units = l ×b. Perimeterof a square with side s units = 4× s Areaof asquarewith side s units =s ×s
Sec on - A: Groundwork
1.
The perimeter of the given figure is 13 cm
21 cm
17 cm
7 cm (A) 68 cm
48
(B) 70 cm
(C) 72 cm
(D) 66 cm
Grade 6
2.
The perimeter of the given figure is (A) 72 cm (B) 70 cm (C) 68 cm (D) 66 cm
3.
The perimeter of the given figure is
(A) 90 cm
4.
(B) 92 cm
(C) 96 cm
(D) 98 cm
The area of the given figure is (A) 1260 cm.sq (B) 1262 cm.sq (C) 1264 cm.sq (D) 1266 cm.sq
5.
The area of the given figure is (A) 142 cm.sq (B) 146 cm.sq (C) 148 cm.sq (D) 150 cm.sq
ISFO Practice Book
49
6.
The shaded area of the given figure is (A) 70 cm.sq (B) 72 cm.sq (C) 74 cm.sq (D) 76 cm.sq
7.
The area of rectangle A is 96 cm 2. The perimeter of the whole figure is (A) 48 cm (B) 50 cm (C) 52 cm (D) 54 cm
8.
The area of the shaded triangle is (A) 65.5 cm2 (B) 67.5 cm2 (C) 69.5 cm2 (D) 71.5 cm2
9.
The perimeter of the unshaded part of the figure below is _______.
(A) 104 cm
50
(B) 106 cm
(C) 108 cm
(D) 110 cm
Grade 6
10.
11.
A rectangular floor measuring 21 m by 8.5 m, is laid with ceramic tiles at a cost of ` 54 per m 2. The cost of laying the floor with ceramic tiles is (A) ` 5510
(B) ` 5508
(C) ` 5506
(D) ` 5505
The area of following figure is (A) 151.5 cm2 (B) 153.5 cm2 (C) 155.5 cm2 (D) 157.5 cm2
12.
The figure below is made up of a square and two rectangles. The length of rectangle A is twice that of square B. The area of rectangle C is
(A) 18 cm2
13.
(B) 24 cm2
(C) 30 cm2
(D) 36 cm2
The figure consists of a right-angled triangle and a rectangle. If the area of the whole figure is 94 cm 2, the perimeter of the figure is (A) 47.5 cm (B) 43.5 cm (C) 41.5 cm (D) 39.5 cm
ISFO Practice Book
51
14.
The figure consists of rectangles A and B. The perimeter of rectangle A is 6 cm less than that of the whole figure. If the perimeter of the whole figure is 32 cm, the length x is (A) 1 cm (B) 2 cm (C) 3 cm (D) 4 cm
15.
In the figure below, the length of the three squares is in whole numbers and they are of different sizes. What is the greatest possible area of the figure? (A) 38 cm2 (B) 36 cm2 (C) 34 cm2 (D) 32 cm2
Sec on - B: Thought Provoking
16.
In the figure below, rectangles ABCD and PQRS are equal in size. Find the area of the shaded part. (A) 45 cm2 (B) 36 cm2 (C) 27 cm2 (D) 18 cm2
52
Grade 6
17.
The perimeter of rectangle EFGH is 36 cm. If EX is 4, the shaded area of rectangle EFGH is (A) 27 cm2 (B) 39 cm2 (C) 51 cm2 (D) 61 cm2
18.
Area of triangle ABC is (A) 64 cm2 (B) 32 cm2 (C) 48 cm2 (D) 40 cm2
19.
A square and a rectangle have a total area of 126 cm 2. The area of the square is 40 % of the area of the rectangle. The length of one side of square is (A) 6 cm
20.
(B) 3 cm
(C) 4 cm
(D) 5 cm
The rectangle is divided into 7 equal parts. Its breadth is 2/3 of its length. The area of the shaded part is (A) 168 cm2 (B) 164 cm2 (C) 160 cm2 (D) 156 cm2
21.
ABCD is a rectangular piece of wood. Two pieces, one in the shape of a square and the other in the shape of a triangle, are cut off. The area of the remaining part is (A) 98 cm2 (B) 96 cm2 (C) 94 cm2 (D) 92 cm2
ISFO Practice Book
53
22.
In triangle ABC, AB = BC. The area of the shaded part is (A) 125 cm2 (B) 130 cm2 (C) 135 cm2 (D) 140 cm2
23.
The area of the shaded part of rectangle ABCD is 1/7 of the area of the unshaded part. The length of ED is (A) 21 cm (B) 24 cm (C) 27 cm (D) 30 cm
24.
ABCD is a rectangle and its length is twice as long as its breadth. The area of the shaded triangle is (A) 21 cm2 (B) 24 cm2 (C) 27 cm2 (D) 30 cm2
25.
In the figure below, the perimeter of the shaded rectangle is 32 cm. The area of the unshaded portion is (A) 216 cm2 (B) 246 cm2 (C) 276 cm2 (D) 306 cm2
54
Grade 6
26.
A rectangular swimming pool is 50 m long and 30 m wide. It is filled with water by 2 pipes. 1 pipe supplies 64 m 3 of water per hour while the other pipe supplies 56 m 3 of water per hour. How many hours will it take to fill the pool to a depth of 2 m? (A) 20 hours
27.
(B) 25 hours
(C) 26 hours
(D) 27 hours
In the figure shown, The ratio of the area of the shaded part to that of the whole figure is
(A) 7 : 16
28.
(C) 15 : 7
(D) 7 : 15
(C) 65 cm2
(D) 67 cm2
The area of the shaded part is
(A) 61 cm2
29.
(B) 16 : 7
(B) 63 cm2
What is the area of the shaded portion shown? (A) 546 cm2 (B) 548 cm2 (C) 550 cm2 (D) 556 cm2
ISFO Practice Book
55
30.
1 In the given figure, the shaded area is 1 times the unshaded area. The area of the 2 whole figure is
(A) 700 cm2 (B) 780 cm2 (C) 800 cm2 (D) 880 cm2
56
Grade 6
9 GRAPHS
CHAPTER
Some Facts: A pie chartis acircularchartdividedinto sectors, eachsectorshows therelative size of each value. A graphdrawnusing rectangularbars to show how largeeach valueis. The bars can behorizontal or vertical. A linechart orlinegraphis atypeof chart whichdisplays informationas aseries of data points called 'markers' connected by straight line segments.
Sec on - A: Groundwork
1.
The pie chart below shows the number of different types of DVDs on a shelf. There are 660 DVDs altogether. If a = 66, how many classical DVDs are there?
Rock 88 Pop 3a
Classical Jazz a Others
(A) 66
(B) 143
(C) 264
(D) 517
ISFO Practice Book
57
Study the pie chart carefully and answer the questions 2 and 3. The pie chart shows how Simon divides a sum of money among his family members.
Parents
Eldest son 10% Second son 30%
Wife
10%
Daughters
2.
If Simon gave his wife ` 10 000, how much did his sons receive? (A) ` 12 000
3.
(B) ` 13 000
(C) ` 14 000
(D) ` 16 000
Simon’s 4 daughters shared the money in the ratio 3 : 6 : 5 : 2. Find the difference between the largest share and the smallest share. (A) ` 1200
(B) ` 1100
(C) ` 1000
(D) ` 900
Study the pie chart carefully and answer the questions 4 to 7. The pie chart below shows the different types of fruits that Mrs. Tay keeps in her refrigerator.
Apples 2/5
Oranges 30
4.
Kiwi
What percentage of the fruits are apples? (A) 20%
58
Pears 20%
(B) 30%
(C) 40%
(D) 50%
Grade 6
5.
How many fruits are there altogether? (A) 120
6.
(C) 75
(D) 60
(C) 20
(D) 18
How many pears are there? (A) 24
7.
(B) 90
(B) 22
What fraction of the fruits are oranges? (A)
1 7
(B)
1
(C)
6
1 5
(D)
1 4
Observe the pie chart carefully and answer the questions 8 to 11. Madam Yong received a sum of money from her 5 children monthly as shown in the pie chart below. Rick 13% Jane Rs.240 Matt Rs.260
8.
9.
10.
Amelia 1/5 Sarah 17%
How much money did they give altogether? (A) ` 1200
(B) ` 1000
(C) ` 800
(D) ` 600
How much more money was given by Sarah than Rick? (A) ` 70
(B) ` 60
(C) ` 50
(D) ` 40
What percentage of the sum of money was given by Matt? (A) 32%
(B) 30%
(C) 28%
(D) 26%
ISFO Practice Book
59
11.
Find the ratio of Amelia’s contribution to Jane’s contribution. (A) 5 : 7
(B) 5 : 6
(C) 5 : 8
(D) 5 : 9
Study the pie chart carefully and answer the questions 12 to 15. The bar graph below shows the time that 5 boys spent reading for a week. David Mark Suhairi Muthu Ahmand 0
12.
12
15
18
21
(B) 620 min
(C) 610 min
(D) 600 min
(B) 15.6 h
(C) 15.3 h
(D) 15.1 h
Express as a ratio the time that Mark spent on reading to the time that Ahmad spent on reading. (A) 1 : 5
15.
9
What was the average time in hours that each boy spent on reading? (A) 15.4 h
14.
6
Express in minutes the time that Muthu spent on reading. (A) 630 min
13.
3
(B) 1 : 2
(C) 3 : 2
(D) 2 : 3
1 If each boy needed 3 hours to read a book, how many books did Suhairi read? 2
(A) 6
(B) 5
(C) 4
(D) 3
Sec on - B: Thought Provoking
Study the pie chart carefully and answer the questions 16 to 19. The line graph below shows the number of shoppers at a furniture mall from monday to saturday.
60
Grade 6
1250
s r e p p o h S f o r e b
1000 750 500
u
250
Mon
16.
Fri
Sat
(B) 175 %
(C) 150 %
(D) 125 %
(B) 7 : 10
(C) 10 : 7
(D) 10 : 3
What was the average daily number of shoppers from monday to friday? (A) 650
19.
Thu
The ratio of the number of shoppers on wednesday to that on thursday is (A) 3 : 10
18.
Wed
The percentage increase in the number of shoppers from monday to tuesday is (A) 200%
17.
Tue
(B) 700
(C) 725
(D) 750
If 40% of the shoppers on Monday spent ` 12 each and the rest spent ` 9 each, how much was collected on that day? (A) ` 2150
(B) ` 2350
(C) ` 2550
(D) ` 2550
Study the pie chart carefully and answer the questions 20 to 23. The pie chart below shows the monthly expenses of Mrs. Lee.
Food 2/5
1/10
Rent Rs.150 Medical bill Saving 3/20
Transport
ISFO Practice Book
61
20.
What percentage of the expenses was for rent? (A) 18%
21.
(B) ` 600
(C) ` 700
(D) ` 800
How much did she spend on her medical bill? (A) ` 50
23.
(D) 25%
What was the total monthly expenses of Mrs. Lee? (A) ` 500
22.
(C) 23%
(B) 20%
(B) ` 60
(C) ` 70
(D) ` 80
(C) ` 220
(D) ` 210
How much did she spend on food? (A) ` 240
(B) ` 230
Study the pie chart carefully and answer the questions 24 to 27. The pie chart below shows the tourists of various nationalities who visited India in December.
Australians Japanese 20% Swedish
Dutch 10%
Americans 38%
24.
How many percent of the tourists were Swedish? (A) 950
25.
(B) 10%
(C) 15%
(D) 20%
(B) ` 17750
(C) ` 15750
(D) ` 13750
What fraction of the tourists were Australians? (A)
62
(D) 1250
If the Dutch tourists paid a total of 400 for admission fees, how much did the Americans pay altogether? (A) ` 18750
27.
(C) 1150
If there were 100 Japanese, how many Australians were there? (A) 5%
26.
(B) 1050
1 10
(B)
1 5
(C)
3 5
(D)
3 10
Grade 6
28.
The pie chart shows the amount of hours Albert spends on various activities in a day while he is awake. What activity does Albert spend as much time on as reading? (A) Watching TV (B) Sports (C) Homework (D) School
School
Homework
Sports 1/6 Watching TV 12.5% Reading
Study the pie chart carefully and answer the questions 29 and 30. The pie chart shows the number of coins and notes Andrea has in her coin bank. 20-paise coins 10 50-paise coins 9
` 2
notes 15
10-paise 5-paise coins notes
29.
Complete the table using the information given in the pie chart. Types of coins
(A) 6, 10
Number of coins
10-paise coins
(B) 8, 12 (C) 4, 12 (D) 2, 6
20-paise coins
10
50-paise coins
9
` 2- coins
15
` 5- coins
30.
What is the total amount of money in Andrea’s piggy bank? (A) ` 80.10
ISFO Practice Book
(B) ` 82.10
(C) ` 84.10
(D) ` 87.10
63
ANSWERS Chapter 1 : Whole Numbers 1 2
(C) (B)
7 8
(C) (B)
13 14
(C) (A)
19 20
(C) (C)
25 26
(B) (C)
3 4 5
(B) (D) (A)
9 10 11
(C) (C) (A)
15 16 17
(C) (A) (C)
21 22 23
(D) (A) (B)
27 28 29
(C) (C) (B)
6
(A)
12
(C)
18
(D)
24
(C)
30
(A)
Chapter 2 : Fractions 1 2
(A) (D)
7 8
(A) (C)
13 14
(C) (C)
19 20
(B) (B)
25 26
(A) (B)
3 4 5
(D) (B) (B)
9 10 11
(C) (A) (C)
15 16 17
(C) (D) (B)
21 22 23
(B) (A) (B)
27 28 29
(B) (A) (C)
6
(D)
12
(B)
18
(D)
24
(C)
30
(D)
Chapter 3 : Ratio and Proportion 1 2
(C) (B)
7 8
(D) (A)
13 14
(C) (A)
19 20
(C) (B)
25 26
(D) (B)
3 4 5
(D) (A) (D)
9 10 11
(C) (D) (B)
15 16 17
(D) (D) (B)
21 22 23
(D) (D) (A)
27 28 29
(A) (B) (D)
6
(B)
12
(C)
18
(B)
24
(C)
30
(D)
Chapter 4 : Percentage
64
1 2
(D) (C)
7 8
(D) (B)
13 14
(D) (C)
19 20
(C) (B)
25 26
(D) (C)
3 4 5
(D) (B) (D)
9 10 11
(D) (B) (D)
15 16 17
(A) (B) (A)
21 22 23
(D) (C) (C)
27 28 29
(D) (C) (A)
6
(B)
12
(B)
18
(B)
24
(B)
30
(C)
Grade 6
Chapter 5 : Speed and Time 1 2
(D) (B)
7 8
(A) (C)
13 14
(B) (B)
19 20
(C) (B)
25 26
(B) (A)
3 4 5
(D) (A) (D)
9 10 11
(B) (B) (A)
15 16 17
(A) (C) (C)
21 22 23
(A) (A) (D)
27 28 29
(B) (A) (D)
6
(D)
12
(A)
18
(D)
24
(B)
30
(A)
Chapter 6 : Algebra 1 2
(C) (A)
7 8
(C) (C)
13 14
(D) (B)
19 20
(B) (C)
25 26
(A) (D)
3 4 5
(B) (A) (D)
9 10 11
(A) (C) (B)
15 16 17
(A) (D) (A)
21 22 23
(A) (D) (A)
27 28 29
(A) (A) (C)
6
(A)
12
(A)
18
(A)
24
(B)
30
(B)
Chapter 7 : Lines and Angles 1 2
(A) (C)
7 8
(D) (A)
13 14
(C) (D)
19 20
(C) (B)
25 26
(A) (B)
3 4 5
(B) (C) (A)
9 10 11
(B) (B) (B)
15 16 17
(C) (A) (C)
21 22 23
(A) (B) (A)
27 28 29
(B) (D) (B)
6
(A)
12
(D)
18
(B)
24
(D)
30
(D)
Chapter 8 : Area and Perimeter 1 2
(A) (C)
7 8
(A) (B)
13 14
(C) (C)
19 20
(A) (A)
25 26
(A) (B)
3 4 5
(D) (A) (A)
9 10 11
(A) (B) (A)
15 16 17
(A) (A) (D)
21 22 23
(B) (D) (B)
27 28 29
(A) (C) (A)
6
(D)
12
(B)
18
(A)
24
(A)
30
(B)
ISFO Practice Book
65
Chapter 9 : Graphs 1 2
(B) (D)
7 8
(D) (B)
13 14
(B) (D)
19 20
(C) (D)
25 26
(B) (A)
3 4 5
(C) (C) (A)
9 10 11
(D) (D) (B)
15 16 17
(A) (A) (B)
21 22 23
(B) (B) (A)
27 28 29
(D) (C) (A)
6
(A)
12
(A)
18
(D)
24
(D)
30
(D)
.
66
Grade 6
GRADE - 6 Level - 1
Sample Paper
ISFO MATH OLYMPIAD - 2016 DO NOT OPEN THIS BOOKLET UNTIL ASKED TO DO SO Roll No.: Student’s Name:
Maximum Time: 60 Minutes
Maximum Marks: 80
INSTRUCTIONS
1.
Please DO NOT OPEN the contest booklet until the proctor has given permission to start.
2.
The question paper comprises of 3 sections: Mathematical Reasoning (20-Questions), Everyday Mathematics (10-Questions) and Logical Reasoning (10-Questions)
3.
All questions are compulsory. There is no negative marking. For each correct answer 2 marks will be rewarded.
4.
No electronic devices capable of storing and displaying visual information are allowed during the course of the exam.
5.
Use of calculator is strictly prohibited in the exam.
6.
Fill your Name , Roll No. and Grade and School in the answer sheet.
7.
There is only ONE correct answer of each question.
8.
To mark your choice of answers by darkening the circles in the Answer Sheet, use a HB Pencil or a Blue/Black Ball Point Pen only.
9.
Shade your answer clearly as per the example shown below:
ISFO Practice Book
67
SECTION A : MATHEMATICAL REASONING 1.
13 years ago, Sachin was 6n years old. How old was Sachin 3n years ago? (A) 3n years
2.
(B) (3n + 11) years
(C) (3n + 13) years
(D) (3n + 15) years
In a sequence 2001, 2002, 2003, …… each term after the third is found by subtracting the previous term from the sum of the two terms that proceeds. What is the 2004 th term in the sequence? (A) –2004
3.
(D) 4003
(B) 5
(C) 7
(D) 8
72% of the number of male members is equal to 90% of the number of female members in a club. If there are 70 more male members than female members, how many members is t here altogether in the club? (A) 620
5.
(C) 0
How many ordered triplets (a, b, c) of non-zero real numbers have the property that each number is the product of the other two? (A) 4
4.
(B) –2
(B) 630
(C) 640
(D) 650
If AB BC, AB = 6 cm and BC = 6 cm, then ABC is (A) A right triangle but not isosceles (B) An isosceles right triangle (C) Isosceles but not a right angle (D) Neither isosceles not right angle
6.
7.
The following figures are formed by joining six unit squares, which of the following has smallest surface area?
(A)
(B)
(C)
(D)
In the figure, XYZ is an equilateral triangle and XZQ is an isosceles triangle. The sum of YZQ and
YXP is
(A) 95O (B) 105 O (C) 85O (D) 115 O
68
Grade 6
8.
Bags A, B and C contained some sand.
1 3
of the sand in bag A was transferred to bag B. Then,
sand in bag B was transferred to bag C. Lastly
1 3
of the
1
of the sand in bag C was transferred to bag A. In the 3 end, there was 12 kg of sand in each bag. What was the mass of sand in bag B at first? (A) 15 kg
9.
(B) 18 kg
(C) 20 kg
(D) 22 kg
In the figure, ABC is an isosceles triangle. AB = AC. DG BC, DEFG and BHG are straight lines. Find the value of
x+
y.
(A) 100 O (B) 110 O (C) 120 O (D) 130 O
10.
11.
Two regular hexagons of perimeter 36 cm each joined as shown in figure. The perimeter of the figure is (A) 72 cm
(B) 66 cm
(C) 60 cm
(D) 54 cm
Jyoti and Bunti had a certain number of stamps each. If Jyoti gave 90 stamps to Bunti, they would have the same number of stamps. If Bunti gave 10 stamps to Jyoti, she would have 5 times as many stamps as Bunti. How many stamps did Jyoti have at first? (A) 220
12.
(C) 240
(D) 250
Arun spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Arun have when he entered the first store? (A) 248
13.
(B) 230
(B) 120
(C) 252
(D) 250
The figure is made up of 2 circles. The radius of the bigger circle is double that of the smaller circle. Find the area of the shaded portion of the figure. (A) 378 cm2 (B) 375 cm2 (C) 380 cm2 (D) 382 cm2
14.
When 265 is divided by a number A, the remainder is 7. When 660 is divided by A, the remainder is 58. When 970 is divided by A, the remainder is 24. What is the possible value of A? (A) 258
15.
(C) 87
(D) None of these
Find the number of zeroes in the expression 15 × 32 × 25 × 22 × 40 × 75 × 98 × 112 × 125. (A) 12
16.
(B) 130
(B) 9
(C) 14
(D) 7
4 men can check exam papers in 8 days working 5 hours regularly. What are the total hours when 2 men will check the double of the papers in 20 days? (A) 2hrs
ISFO Practice Book
(B) 4hrs
(C) 8hrs
(D) 10hrs 69
17.
On a 26 question test, 5 points were deducted for each wrong answer and 8 points were added for right answers. If all the questions were answered how many were correct if the score was zero. (A) 10
18.
(B) 11
(D) 12
(C) 2768
(D) 3168
How many 4-digit numbers contain number two? (A) 1168
19.
(C) 13
(B) 2368
In the figure, not drawn to scale, ABCD is a rhombus and QAD is a straight line. Find
p+
q+
r.
(A) 126° (B) 132° (C) 138° (D) None of these
20.
The length of rectangle ABCD is 2
1
times its breadth. AP : PB = 1 : 2, BQ : QC = 2 : 1, DR : RC = 3 : 2 2 and AS = SD. The ratio of the area of the shaded portion to that of the unshaded portion is _______.
(A) 29 : 34 (B) 43 : 47 (C ) 2 : 3 (D) 1 : 4
SECTION B : EVERYDAY MATHEMATICS 21.
Lalit travelled at an average speed of 60 km/h for the first 3 hrs of the journey. He then reduced his average speed by 2 km/h and drove for another 3 hrs before he reached his destination. Find his average speed for the whole journey. (A) 55 km/h
22.
(B) 57 km/h
(C) 59 km/h
(D) 61 km/h
Chairs in a hall are to be arranged in rows. If you put 8 chairs in a row, there will be 4 chairs left. If you put 9 chairs in a row, there will be 5 chairs short. The number of chairs in the hall is (A) 72
23.
(C) 80
(D) 84
Virat had 252 red balls and some white balls. The ratio of red balls to white balls was 7 : 13. He gave away some of his white balls. As a result, the ratio of red balls top remaining white balls becomes 7 : 8. Number of balls gave away by Virat was (A) 180
24.
(B) 76
(B) 210
(C) 240
(D) 270
A child likes to exchange stickers with his friend for every sticker he gives same one he gets 5 stickers back. If he starts the exchange with one sticker. How many stickers will have after 30 exchanges? (A) 105
70
(B) 109
(C) 113
(D) 117
Grade 6
25.
2
of the students in a class are girls and others are boys. In a test
5 8 students in the class failed the fraction of class failed is (A)
26.
1 5
(C)
10
1
(D)
18
1 6
of boys failed.
1 20
(B) 200 seconds
(C) 300 seconds
(D) 400 seconds
A man travelled 1/3 of his journey in the first hour and 1/5 of the journey in the second hour. He completed the remaining 63 Km in the third hour. The average speed of the jo urney (A) 45 Km/h
28.
1
4
of the girls and
Five traffic lights blink after every 5, 10, 15, 20 and 25 seconds. If they blink simultaneously at some point of time. All lights will blink simultaneously again after (A) 100 seconds
27.
(B)
1
(B) 55 Km/h
(C) 135 Km/h
(D) 155 Km/h
A train 150 m long in running with speed of 68 km/h. In what time will it pass a man who is running at 8 km/h in the same direction in which tr ain is going? (A) 3 sec
29.
(B) 6 sec
Mrs. Lim made 4k cookies. She gave
(C) 9 sec 2 5
of it to her children and
(D) 15 sec 1 4
of the remainder to her friend. How
many cookies did she have left? (A)
30.
9k 5
9 k 20
(B)
(C)
7k 5
13 20
(D) 4k
Towns A and B were 663 km apart. Jim left town A at 9:50 p.m. and travelled towards town B at a steady speed of 49 km/h. At the same time, William left town B and travelled towards town A at a steady speed. At 1:50 a.m. the following day the two men were still 255 km apart. Jim and William met on the way at ________ . (A) 2.30 a.m.
(B) 3.20 a.m.
(C) 4.10 a.m.
(D) 4.20 a.m.
SECTION C : LOGICAL REASONING 31.
Solid A has __________ face(s) than solid B. (A) 1 more (B) 1 l ess (C) 2 l ess (D) 2 more
32.
In a class, three-fourth of the boys play football, one half play cricket, one fourth of those who play cricket do not play football, which of the following statements is definitely true? (A) One-third of the boys play neither cricket nor football. (B) Two-third of the boys play only football. (C) One-eighth of the boys play neither cricket nor football. (D) One-fourth of the boys play neither cricket nor football.
ISFO Practice Book
71
33.
34.
How many triangles are in the given figure? (A) 16
(B) 22
(C) 28
(D) 23
In a certain code “ABOVE” is written as CAQUG. How is BELOW written in the code? (A) DCNMY
35.
(B) DDMNY
37.
(B) Brother
(D) None of these
(A) 5 Kilometres West
(B) 5 Kilometres North-east
(C) 7 Kilometres East
(D) 7 Kilometres West
The addition below is incorrect. It can be corrected by changing one digit a, whichever it occurs, to another digit b. The sum of digits a and b is 7
4
2
5
8
6
8
2
9
4
3
0
12
1
2
0
1
6
(A) 8
(B) 6
(C) 4
(D) 9
If the second half of the letters of the word ‘TRANSPORTATIONAL’ are reversed and placed before first half of the letters, which letter will be the third to the right of the thirteenth letter from right? (A) N
39.
(C) Father
Kapil walks 10 kilometres towards North. From there, he walks 6 kilometers towards South. Then, he walks 3 kilometres towards East. How far and in which direction is he with reference to his start ing point?
38.
(D) None of these
Introducing a girl, Ramprasad said, “Her mother is the only daughter of my mother-in-law” How is Ramprasad related to the girl? (A) Husband
36.
(C) DDNNY
(B) R
(C) A
(D) L
M, N, O and P are all different individuals; M is the daughter of N; N is the son of O; O is the father of P; Among the following statements, which one is true? (A) M is the daughter of P (B) If B is the daughter of N, then M and B are sisters (C) If C is the granddaughter of O, then C and M are sisters (D) P and N are bothers.
40.
A number is 101. 102. 103. 104. ... 150. What is reminder when divided by 3? (A) 0
(B) 1
(C) 2
For answer key visit our website: 72
(D) None of these
www.isfo.in Grade 6
