Class 7 Imo 5 Years e Book14

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INTERNATIONAL MATHEMATICS OLYMPIAD

5

7

INSTANT

(2009-2013)

Including Set A and Set B of Year 2012 and 2013

Copyright © 2014 MTG Learning Media (P) Ltd. No part of this publication may be reproduced, transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Publisher. Ownership of an ebook does not give the possessor the ebook copyright. All disputes subject to Delhi jurisdiction only.

Disclaimer : The information in this book is to give you the path to success but it does not guarantee 100% success as the strategy is completely dependent on its execution. And it is based on last years papers of IMO exam.

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2

CLASS 7

Contents ªª 3rd IMO 2009 ªª 4th IMO 2010 ªª 5th IMO 2011 ªª 6th IMO 2012 - SET A ªª 6th IMO 2012 - SET B ªª 7th IMO 2013 - SET A ªª 7th IMO 2013 - SET B

MTG Work-Books / olyMpiad Books CLASS 1

International Mathematics Olympiad

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CLASS 2

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National Science Olympiad

National Cyber Olympiad

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CLASS 3

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MTG CSS Series

CLASS 5

International Mathematics Olympiad

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CLASS 6

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MTG Work-Books / olyMpiad Books CLASS 7

National Science Olympiad

International Mathematics Olympiad

National Cyber Olympiad

Science IQ Challenge

Math IQ Challenge

International English Olympiad

MTG CSS Series

Master Mental Ability in 30 Days

CLASS 8

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

MTG CSS Series

Math IQ Challenge

Science IQ Challenge

Psychology of Success

The Secrets of SUCCESS

Master Mental Ability in 30 Days

MTG Work-Books / olyMpiad Books CLASS 9

International Mathematics Olympiad

Math IQ Challenge

National Science Olympiad

Science IQ Challenge

National Cyber Olympiad

Psychology of Success

The Secrets of SUCCESS

International English Olympiad

Master Mental Ability in 30 Days

CLASS 10

International Mathematics Olympiad

Math IQ Challenge

National Science Olympiad

Science IQ Challenge

National Cyber Olympiad

Psychology of Success

The Secrets of SUCCESS

International English Olympiad

Master Mental Ability in 30 Days

MTG Work-Books / olyMpiad Books CLASS 11

International Mathematics Olympiad

Math IQ Challenge

Science IQ Challenge

National Science Olympiad

Psychology of Success

National Cyber Olympiad

The Secrets of SUCCESS

Master Mental Ability in 30 Days

CLASS 12

International Mathematics Olympiad

Math IQ Challenge

Science IQ Challenge

National Science Olympiad

Psychology of Success

National Cyber Olympiad

The Secrets of SUCCESS

Master Mental Ability in 30 Days

Class

1 to 10

JEE Main & Advamced | AIPMT | BOARDS | OLYMPIAD | NTSE

FoUNdaTioN CoUrsE For Classes 8, 9 & 10 Class 8

Class 9

Class 10

Class 7 3rd

Year 2009

3rd IMO - 2009

SECTION  I  :  LOGICAL  REASONING  1. 

2. 

Look  at  the  given  map.  Jay started from Roswell Bridge in a canoe and floats  down  Clear  River  and  Copper  Creek  to  Bird  Park.  What  is  the  distance  that  Jay  travels?  (A)  5.5 m 

(B)  5000 m 

(C)  900 m 

(D)  9000 m 

Bird P ark  Copper C reek  m  k 4  Clear R iver  5 km  Roswell B ridge 

The  three  adjoining  geometric  figures  make  a  pattern.  What  would  the  eighth  figure  in  this  pattern  have?  (A)  8 white squares and 10 shaded rectangles  (B)  8 white squares and 11 shaded rectangles  (C)  8 shaded rectangles and 10 white squares  (D)  8 shaded rectangles and 11 white squares 

3. 

Which  of  the  following  units  best  measures  the  height  of  the  school  flagpole?  (A)  Centimetres 

4. 

(B)  Kilometres 

(C)  Metres 

(D)  Millimetres 

What  is  the  next  number  in  the  series  given  below?  1,  8,  9,  64,  25,  216,  ?  (A)  343 

5. 

(B)  39 

(C)  215 

George's  town  has  a  soccer  league.  Number of players  Sign­up fee  Division  The adjoining table shows the total number  A. (16­18 years old)  49  Rs. 2000 per player  of  players  who  signed  up  this  year.  B. (13­15 years old)  54  Rs. 2000 per player  George needs to figure out the total amount  C. (10­12 years old)  Rs. 3000 per player  67  of  money  from  sign­up  fees.  Which  of  these expressions will give him the correct  amount?  (A)  (49 + 54) ´ Rs.2000 + (67 ´ Rs.3000)  (C)  (49 + 54 ´ Rs.2000) + (67 ´ Rs.3000) 

6. 

(D)  49 

(B)  (49 + Rs.3000) + (54 ´ Rs.2000) + (67 ´ Rs.3000)  (D)  (49 + 54 + 67) ´ (Rs.2000 + Rs.3000) 

Observe  the  pattern  given  below  :  1,  9,  17,  33,  49,  73,  _________  What  will  be  the  next  number  in  the  pattern?  (A)  97 

7. 

(B)  98 

(C)  99 

(D)  100 

Central Jr.  High School's  student  council will  be hosting  a talent show.  Jackie will  be  performing  in a band in the talent show. For this performance, the band members have all agreed to wear long  pants,  a  long­sleeved  shirt,  and  a  vest.  Jackie  has  the  following  choices.  Long pants  Long­sleeved shirts  Vests  1 black  1 white 

1 white  1 red  1 black 

1 red  1 black 

How  many  different  choices  of  outfits  does  Jackie  have?  (A)  12  3 rd  IMO  |  Level­I  |  Class 7 

(B)  7 

(C)  6  2 

(D)  3

3rd IMO - 2009

8. 

In a convex polygon, any two points can be connected by a line segment  that remains entirely within the polygon. The adjoining figure on right  is  an  example  of  a  convex  polygon.  Which  of  the  figures  shown  below  is  another  example  of  a  convex  polygon?  (A) 

9. 

(B) 

(C) 

Convex P olygon 

(D) 

Photocopy  machines  can  be  used  to  make  an  image  larger  or  smaller  on  paper.  Suppose  the  given  triangle  were  reduced  on  a  photocopy  machine  to  80%  of  its  original  size.  Which  of  the  following  gives  the  correct  measures  of  its  sides  and  angles  after  it  was  reduced?  53°  0.6 

(A) 

90° 

53° 

37°  0.8 

48° 

2.4 

1.0 

(B) 

4.0  90° 

2.4 

37°  3.2 

72° 

5.0  90° 

37°  4.0 

48° 3.0 

4.0 

(C) 

53°  3.0 

24°  3.2 

(D) 

5.0  72° 

24°  4.0 

10.  Count  the  number  of  triangles  is  the  adjoining  figure.  (A)  17 

(B)  18 

(C)  19 

(D)  None of these 

11.  What  fraction  of  the  figure  is  shaded?  3  8  4  (C)  8 

(A) 

5  8  7  (D)  8 

(B) 

12.  Mayank  is  writing  a  computer  program  for  basketball  game.  To find the total score he collects the data given in the table.  Given that *stands for multiplication in a computer, F stands for 

For each free throw  For each regular throw  For each long shot 

the  number of free throws made,  R  stands for the number of  regular shots made,  L  stands  for  the  number of  long shots made  and  T  stands  for the total  score a team  has in  a game. Then  the total  score  is  (A)  T = F + (R * 2) + (L *3) 

(B)  T = F * (R + 2)* + (L + 3) 

(C)  T = (F + R + L)* (1 + 2 + 3) 

(D)  T = (1 + F)* (2 + R)* (3 + L) 

13.  All of Mrs. Neha's students are reading poetry by Wordsworth. Smita is in Mrs. Neha's class. John  is  not  in  Mrs.  Neha's  class.  Lisa  is  reading  poetry  by  Wordsworth.  If  all  the  statements  above  are  true,  which  conclusion  below  is  definitely  true?  (A)  Lisa and Smita are in the same class 

(B)  John and Lisa are not in the same class 

(C)  John is not reading poetry by Wordsworth 

(D)  Smita and Lisa are reading poetry by Wordsworth 

14.  Look at  the adjoining  pictures.  64  80  45  Except for the  number 64, half of the  numbers in this  set are greater than 64, and half of the numbers in this  set  are  less  than  64.  Which  of  the  following  statements  about  the  number  64  is  also  true?  (A)  The number 64 would be the mean of this set of numbers  (B)  The number 64 would be the median of this set of numbers  (C)  The number 64 would be the mode of this set of numbers  (D)  The number 64 would be the range of this set of numbers 3 

98 

37 

22 

80 

53 

70 

3 rd  IMO  |  Level­I  |  Class 7 

3rd IMO - 2009

15.  If A is the brother of B and K; D is the mother of B and E is the father of A. Which one of the following  statements  is  definitely  not  true?  (A)  A is the son of D 

(B)  A is the father of K 

(C)  D is the wife of E 

(D)  D is the mother of K 

16.  Which  set  of  numbers  in  the  options  is  like  the  set  given  below?  121,  81,  9  (B)  64, 9, 4 

(C)  168, 15, 3 

17.  Use  the  line  graph  to  answer  the  question.  How  many  children  sold  more  than  200  magazines?  (A)  3 children  (B)  1 child  (C)  2 children 

(D)  10, 6, 5  Total magazine sales 

No. of magazines 

(A)  95, 24, 5 

350  300  250  200  150  100  50 

(D)  7 children 

Sue Joe Kan Sam Vic Ann 

18.  Divya  is  building  a  fence  around  her  18  m ´ 24  m  rectangular  garden.  She  will  •  Put  a  post  at  each  corner 

Divya’s Garden  18 m 

•  Put  some  posts  along  the  sides  and  •  Space  the  posts  equally  around  the  garden. 

24 m 

What  is  the  greatest  possible  distance  between  each  post  and  the  next  post?  (A)  8 metres 

(B)  6 metres 

(C)  3 metres 

(D)  2 metres 

19.  The  given  chart  shows  the  target  heart  rate  for  people  of  different  ages.  When  a  person's  age  increases  by  one  year,  by  how  much  does  the  target  heart  rate  decrease?  (A)  0.8 

(B)  1.25 

(C)  8 

(D)  10 

Target  Heart R ate  Age (in years)  20  30  40  50  60  Target 

160 152 144 136 128 

20.  Look  at  these  number  sentences  given  below  :  +  +  = 11  +  +  = 9 

Each 

and 

(A)  5 

represents  the  same  number.  What  is  the  value  of  (B)  6 

+ 

(C)  7 

?  (D)  8 

SECTION  II  :  MATHEMATICAL  REASONING  21.  Some  adult  humming  birds  weigh  as  little  as  28.36  g.  What  is  the  value  of  6  in  28.36?  (A)  Six 

(B)  Six tenths 

(C)  Six hundredths 

(D)  Six thousandths 

22.  A sequence of mathematical operations was performed on the number 0.882 to  get  an  answer  of  8.67.  Which of  the following  operations was  first  performed on the  number 0.882 to  complete  the  given  sequence?  (A) 

Add 2 

(B) 

Subtract 2 

?  Add 0.008  Multiply by 3 

(C)  Divide by 2  (D)  Multiply by 2 3 rd  IMO  |  Level­I  |  Class 7 

0.882 

8.67 

4 

3rd IMO - 2009

23.  1100  boys  and  700  girls  are  examined  in  a  test.  42%  of  the  boys  and  30%  of  the  girls  pass.  The  percentage  of  the  total  who  failed  is  _______  (A)  58% 

2  (B)  62 %  3 

(C)  64% 

(D)  78% 

2  24.  Deepak keeps all his hockey cards in a special book that holds 6 cards on each page. If  3  pages  3  of  the  book  are  full,  then  how  many  cards  has  Deepak  collected?  (A)  14  (B)  18  (C)  22  (D)  36 

25.  If  the  angles  of  a  triangle  are  in  the  ratio  4  :  5  :  6,  then  the  largest  angle  measures  ________  (A)  60°  (B)  72°  (C)  80°  (D)  90°  5(2 x - 9)  - 8 = 2 x  from  a  study  guide.  3  For  this  equation,  which  of  the  following  must  be  true? 

26.  Sonali  copied  the  equation

(A)  x =

47  2 

(B)  x =

23  2 

(C)  x =

21 4 

(D)  x =

69  4 

27.  The  figures  shown  on  the  right  are  congruent.  What  is  true  about  their corresponding  sides  and  corresponding  angles?  (A)  The corresponding angle measures are equal, but not the corresponding side lengths  (B)  The corresponding side lengths are equal, but not the corresponding angle measures  (C)  The corresponding angle measures and corresponding side lengths are not equal  (D)  The corresponding angle measures and the corresponding side lengths are equal  28.  Prem designed a rectangular garden with a width of 15 cm. The area of the garden is 300 square cm.  What  is  the  length  of  the  garden?  (A)  15 cm  (B)  20 cm  (C)  135 cm  (D)  285 cm  29.  The temperature at 1:00 p.m. on Tuesday was – 13°C. There was an increase of 6°C per hour starting  at 1:00 p.m. Which of the following best represents the Celsius temperature n hours after 1:00 p.m.  on Tuesday?  (A)  –13 + 6n  (B)  (–13) – 6n  (C)  (–13n) + 6  (D)  (–13n) – 6  30.  Which  of  the  following  operations  will  solve  the  equation  given  below  in  one  step? n  = 81  3  n  n  (A)  Add 3 to  and 81  (B)  Subtract 3 from  and 81  3  3  n  n  (C)  Multiply  by 3 and 81 by 3  (D)  Divide  by 3 and 81 by 3  3  3  31.  A number  m  is divided by  5 and added to 8, the result is equal to 3m  subtracted  from 4. Which of  the following  represents  the sentence?  (A) 

m  = 3m - 4  5 

(B) 

8 - m  = 3m + 4  5 

(C)

m  + 8 = 4 - 3 m  5 

(D)

m  + 8 = 3m - 4  5 

1  1  32.  Nupur wants  to run  7  km.  The track  she  runs  on  is  of a  km  in length.  How  many times  does  2  4  1  Nupur  have  to  run  the  length  of  the  track  to  run  a  total  of  7  km  ?  2  3  (A)  2  times  (B)  8 times  (C)  17 times  (D)  30 times 4 

5 

3 rd  IMO  |  Level­I  |  Class 7 

3rd IMO - 2009

16 m  8 m 

33.  Bobby wants to paint a rectangular wall that measures 16 m ´ 9 m. The wall  contains  a  window  with  the dimensions  shown  in  the  adjoining  figure.  If  Bobby  does  not  paint  the  window,  what  is  the  total  shaded  area  he  will  paint ?  (A)  144 sq metres 

(B)  104 sq metres 

(C)  50 sq metres 

(D)  40 sq metres 

5 m 

9 m 

34.  What  type  of  polygon  is  represented  by  the  adjoining  diagram?  (A)  Pentagon  (B)  Heptagon  (C)  Hexagon  (D)  Decagon  35.  Choose  the  correct  order  of  operation  needed  to  evaluate  the  following  expression:  22  –  6 ´ (4  +  7)  (A)  Multiply 6 by 4. Add the product to 7. Subtract the sum from 22  (B)  Add 4 and 7. Subtract 6 from 22. Multiply the difference by 6  (C)  Subtract 6 from 22. Add 4 and 7. Multiply the difference by the sum  (D)  Add 4 and 7. Multiply the sum by 6. Subtract the product from 22.  36.  The track team  was surveyed for  a story in  the school paper. The reporter asked how many times  each  team  member  won  a  race  last  year.  Here  is  the  data  he  collected:  8,  7,  6,  10,  9,  4,  3,  7,  12,  14,  6,  6,  5  What  is  the  mode  of  the  races  won?  (A)  6 

(B)  7 

(C)  7.5 

(D)  14 

37.  What  is  the  correct  value  of  the  expression  given  below? 1 2  42  ´ 8 ¸ + 2 3  (A)  32 

1  (C)  128  3 

(B)  48 

2  (D)  256  3 

38.  Which  of  the  following  expressions  is  equal  to  1?  (A)

0.015 +

85  100 

(B)

6  + 0.4  100 

(C) 0.75 +

1  25 

3  + 0.7  10 

(D)

39.  Javed  drew  the diagram  to  show  how the  area  of  a parallelogram  is  related  to  the  area  of  a  triangle.  If  he  knows  that  the  area  of  the  parallelogram  is  45  cm 2 ,  how  can  he  find  the  area  of  one  of  the  triangles? 

40. 

(A)  Divide 45 cm 2  by 2 

(B)  Multiply 45 cm 2  by 2 

(C)  Find the square root of 45 cm 2 

(D)  Recognize that 9 ´ 5 = 45 

Look  at  the  adjoining  figure.  If  l  ||  m. ÐABO  =  55°  and ÐOCD  =  20°,  find  the  value  of  x.  (A)  75° 

(B)  285° 

(C)  105° 

(D)  360° 

A  x 

B  55°  O  20° 

D 

l 

C 

m 

SECTION  III  :  EVERYDAY  MATHEMATICS  41.  Vikram's age in 20 years will be four less than three times his age now. Which of the following could  be  Vikram's  age  now  and  in  20  years?  (A)  12, 32  3 rd  IMO  |  Level­I  |  Class 7 

(B)  15, 35 

(C)  18, 38  6 

(D)  20, 40

3rd IMO - 2009

42.  Thirty  boys and  twenty  girls attended  the  rally last  Friday.  What was  the  ratio  of  girls  to  the  total  number  of  students  at  the  rally? 

(A)  2:5 

(B)  3:2 

(C)  3:5 

(D)  2:3 

43.  Sound  travels  in  sea  water  at  the  rate  of  1.5  km  per  second.  Scientists  can  figure  out  the  depth  of  the  ocean  floor  by  using  a  method  called  sonar.  Sonar measures the time it takes for sound waves to travel from a ship  Ship  to  the  ocean  floor  and  back  to  the  ship.  Suppose a ship has a sonar sounding of 6 seconds. What would be the  Ocean  approximate  depth  of  the  ocean  floor  below  the  ship?  floor 

(A)  6 km 

(B)  0.5 km 

(C)  9 km 

(D)  4.5 km 

44.  Students  are  using  string  to  make  projects  in  art  class.  •  There  are  200  students  •  Each  student  needs  75  centimetres  of  string  How  many  metres  of  string  are  needed  in  all?  (A)  1.5 metres 

(B)  15 metres 

(C)  150 metres 

(D)  1500 metres 

45.  Sunny started a new business. The table given below shows the  profit or loss each month for  six  months.  Sunny  uses  positive  numbers  to  show  a  profit  and  negative  numbers  to  show  a  loss.  Month 

January  February  March  April  May  June  –1980 

–280 

3870 

–770  –910  1030 

How  much  profit  or  loss  did  Sunny  have  after  being  in  business  for  six  months?  (A)  Loss of Rs. 8840 

(B)  Loss of Rs. 960 

(C)  Profit of Rs. 960 

(D)  Profit of Rs. 8840 

46.  One cup of milk has the same amount of calcium as 16 oranges. Two oranges have the same amount  of  calcium  as  4  eggs.  How  many  eggs  have  the  same  amount  of  calcium  as  one  cup  of  milk?  (A)  20 eggs 

(B)  16 eggs 

(C)  18 eggs 

47.  The  distance  between  the  bases  on  a  baseball  diamond  is  90  metres,  as  shown  here.  What is the distance (d),  in metre, between home plate  and  second base? Round your answer to the nearest whole number.  (A)  90 metres 

(B)  127 metres 

(C)  135 metres 

(D)  180 metres 

(D)  32 eggs  Second base  90 metres  Third base 

90 metres  d 

90 metres 

First base  90 metres  Home plate 

48.  While taking Vidhi's pulse rate on her wrist, Kajal counted 9 beats in 10 seconds. Which statement  best  represents  Vidhi's  pulse  rate?  (A)  9 beats per minute 

(B)  54 beats per minute 

(C)  90 beats per minute  (D)  540 beats per minute 

49.  A  scientist  was  tracking  a  whale. At  noon,  the whale  was  5  metres  below  the  surface  of  the  body  of  water.  The  whale's  movements  over  the  next  several  hours  are  recorded  below.  •  Dove  down  3  more  metres 

•  Rose  up  8  metres  •  Dove  down  15  metres  •  Rose  up  3  metres  After all of the movements described above, which statement best describes the position of the whale  in  relation  to  the  surface  of  the  water?  (A)  12 metres above the surface of the water 

(B)  2 metres below the surface of the water 

(C)  2 metres above the surface of the water 

(D)  12 metres below the surface of the water 7 

3 rd  IMO  |  Level­I  |  Class 7 

3rd IMO - 2009

50.  A  survey  was  done  with  250  women.  Each  woman  was  asked  how  many  children  she  had.  The results showed that 28% of the women had 3 or more children. How many surveyed women have  less  than  3  children?  (A)  78 

(B)  70 

(C)  72  SPACE FOR ROUGH WORK

3 rd  IMO  |  Level­I  |  Class 7 

8 

(D)  180 

Class 7 4th

Year 2010

4th IMO - 2010

SECTION  I  :  LOGICAL  REASONING  1. 

2. 

Rohan plans to make a display by stacking cans. The top 3 rows  are shown  here. The display will be a total of 7 rows. How many cans in all will Rohan  need  to  make  the  display  ?  (A)  49 

(B)  28 

(C)  7 

(D)  22 

There  are 8  girls in  a  dance class.  The girls  are  represented in  the  diagrams shown  below by  the  numbers 1 to 8. If each girl needs a dance partner, which list shows all the possible combinations  of  girls  in  the  dance  class ? 

(A) 

(C) 

1  2  3  4  5  6  7 

1 

2  3  4  5  6  7  8 

1 

(B)  2  3  4  5  6  7  8 

2 

(D) 

1 

2  3  3  4  3  4  4  5 

2  3  4  5  2  6  7  8 

4  5  5  6  5  6  6  7 

6  7  7  8  7  5  8  1 

3  4  5  3  6  7  8 

8  1  2  1  2  3 

4  4  5  6  7  8  5 

5  6  7  6  8  6  7  7  8 

7  8  8 

3. 

A parent group is planning an awards dinner for students, teachers and parents. The parent group  plans to  seat the guests around  a circular table that has seating for 30. The  guests will  be seated  in  the  order  of  student,  teacher,  parent  in  a  repeating  pattern.  Who  will  be  the  20 th  guest  ?  (A)  Student  (B)  Teacher  (C)  Parent  (D)  Cannot be determined 

4. 

Rahul bought 4 packets of notebook paper for school last year. Each packet contained 500 notebook  papers.  He  used  about  20  notebook  papers  each  week.  What  information  is  needed  to  find  the  approximate  number  of  notebook  papers  Rahul  had  left  after  the  school  year  was  over?  (A)  The number of hours Rahul did homework every day  (B)  The number of classes Rahul had  (C)  The number of students in Rahul's grade 

5. 

Which  pair  of  eagle  pictures  shows  translation? 

(A) 

6. 

(D)  The number of weeks in the school year 

(B) 

(C) 

(D) 

The  top,  side  and  front  views  of  a  solid  figure  made  of  cubes  are  shown  below. 

Top 

Side 

Front 

Which  solid  figure  is  best  represented  by  these  views? 

(A) 

4 th  IMO  |  Level­I  |  Class 7 

(B) 

(C) 

2 

(D)

4th IMO - 2010

7. 

A soccer league has 64 teams competing in a tournament. In each round, pairs of teams compete.  The team that wins advances to the next round. The table given below shows the results of the first  2 rounds.  At  the  end  of  which  round  will  there  be  only  2  teams  remaining,  assuming  there  are  no  ties?  Soccer League Tournament  (A)  Round 4  Number of Teams  Number of Teams  Round  (B)  Round 5  Competing  Remaining  (C)  Round 6  1  64  32  (D)  Round 7 

2 

32 

16 

Text messages received by Samira 

Read  the  graph  and  answer  the  given  question. On which day did Samira receive  exactly  60  text  messages  ? 

100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10  5  0 

Number of messages 

8. 

(A)  Monday  (B)  Thursday  (C)  Friday  (D)  Sunday 

Sunday 

Monday 

Tuesday 

Wednesday 

Thursday 

Friday 

Saturday 

Days 

9. 

Priyanka is  taller than  Shikha and shorter  than Sneha.  If  Sneha  is shorter than Yogita,  who  is the  shortest  among  them?  (A)  Priyanka 

(B)  Shikha 

(C)  Sneha 

(D)  Yogita 

10.  A community swimming pool is open on different days depending on the air temperature. The given  table  shows  the  air  temperature  on  different  days.  Swimming Pool  The dates listed in the table show that the pool was closed on  Air Temperature  Date  May  1,  June  1  and  October  1.  If  the  pool  was  open  on  all  the  May 1  68°F  other dates listed, which of the following statements best describes  73°F  June 1  the  air  temperature  when  the  pool  is  open  ?  82°F  July 1  (A)  The air temperature must be between 74°F and 90°F  87°F  August 1  (B)  The air temperature must be lower than 91°F  92°F  September 1  (C)  The air temperature must be higher than 75°F 

October 1 

75°F 

(D)  The air temperature must be between 68°F and 91°F  11.  The given table shows  the ticket  prices at an amusement  park.  Five people in Nick's family paid a total of ` 80 for tickets. If they purchased  2  adult  tickets,  what  were the  other  3  tickets they  purchased  among  the  given options  ?  (A)  2 child and 1 youth 

(B)  3 child 

(C)  3 youth 

(D)  2 youth and 1 child 

Ticket Prices  Type of Tickets  Price  Child  `  10  Youth  `  15  Adult  `  20 

12.  Kishan walks 10 km towards North. From there, he walks 6 km towards South. Then he walks 3 km  towards  East.  How  far  and  in  which  direction  is  he  with  reference  to  his  starting  point?  (A)  5 km West 

(B)  5 km North ­ East 

(C)  7 km East  3 

(D)  7 km West 4 th  IMO  |  Level­I  |  Class 7 

4th IMO - 2010

13.  Which  one  of  the  following  diagrams  best  illustrates  the  three  classes  :  Rhombus,  Quadrilateral,  Polygons ?  (A) 

(B) 

(C) 

(D) 

14.  Which of the following letters in the word 'SELFRIGHTEOUSNESS'  does not change its position when  the  letters  are  reversed?  (A)  E 

(B)  G 

(C)  H 

(D)  T 

15.  If  A  means  'plus',  B  means  'minus',  C  means  'divided  by'  and  D  means  'multiplied  by'  then  18  A  12  C  6  D  2  B  5  equals  ______  (A)  17 

(B)  25 

(C)  27 

(D)  45 

16.  A  shepherd  had  17  sheeps. All  but  nine  died.  How  many  was  he  left  with?  (A)  Nil 

(B)  8 

(C)  9 

(D)  17 

17.  How  many  rectangles  are  there  in  the  given  figure  ?  (A)  6 

(B)  7 

(C)  8 

(D)  9 

18.  Choose the correct mirror­image of Fig. (X), when the mirror is placed along PQ.  (A) 

(B) 

(C) 

(D) 

P 

Q 

Fig.(X) 

19.  A cube is to be coloured in such a way that no two opposite faces have the same colour. The minimum  number  of  colours  required  is  ______  .  (A)  1 

(B)  2 

(C)  3 

(D)  6 

(B)  58 – 50 

(C)  49 – 42 

(D)  25 – 17 

20.  Find  the  odd  one  out.  (A)  83 – 75 

SECTION  II  :    MATHEMATICAL  REASONING  21.  Amit counted the number of people in line for tickets at the movie theatre. Every time he saw 5 people,  he  added  a  tick  mark  on  his  counting  sheet,  as  shown  below. 

Amit saw 2 more people after he added his last tick mark. Which could be used to find p, the total  number  of  people  he  saw?  (A)  14 ÷ 2 + 5 = p 

(B)  14 × 2 × 5 = p 

(C)  14 × 5 + 2 = p 

(D)  14 + 5 – 2 = p 

22.  A  triangle  has  angle  measurements  of  32°,  43°  and  105°.  What  kind  of  triangle  is  it?  (A)  Equilateral 

(B)  Isosceles 

(C)  Scalene 

(D)  None of these 

23.  What  is  the  value  of  the  expression  given  below  ?  5  +  5(9  ÷  3) 2  (A)  35  4 th  IMO  |  Level­I  |  Class 7 

(B)  90 

(C)  50  4 

(D)  230

4th IMO - 2010

24.  Which  of  the  following  are  corresponding  parts  of  the  two  given  congruent  figures ? 

  W   km 97°  17

R 

(B)  ST @ XY (C)  TQ @ WX

S 

(D)  ÐQ @ ÐY

X 

26  km 107°   

108°  Q  17 km  48°  97°  T  46 km 

25.  Which  of  the  following  figures  are  obtuse  isosceles  triangles  ?  (A)  P and R only  (B)  Q and R only  (C)  P, Q and R only  25°  (D)  P, R and S only  P 

108°  46 km 

  26  km

36  k m  

(A)  TQ @ XY

107°  Y 

48°  V 

36 km 

35° 

110° 

Q 

R 

S 

26.  Which  of  the  following  digits  makes  the  given  statement  true ?  (A)  3 

(B)  6 

6,06,19?  is  divisible  by  10.  (C)  5 

(D)  0 

27.  Shalini  shaded  3/5  of  her  design  given  on  the  right.  Which  decimal  number  represents  the  shaded  part  of  her  design?  (A)  0.6  (B)  0.06  (C)  0.006  (D)  0.0006  2 3 4 5  1  , , and  are each equivalent to  . Which of the following statements represents  s  4 6 8 10  2  the  relation  between  the  numerator  and  denominator  of  the  fractions  given  above  ? 

28.  The fractions 

(A)  The numerator is twice the denominator  (C)  The numerator is 2 more than the denominator 

(B)  The denominator is twice the numerator  (D)  The denominator is 2 more than the numerator 

29.  Which  group  shows  all  the  numbers  that  are  common  factors  of  36  and  48  ?  (A)  1, 2, 3, 4, 6 

(B)  1, 2, 3, 4, 6, 12 

(C)  1, 2, 3, 4, 6, 9, 12, 18  (D)  1, 2, 3, 4, 6, 8, 12, 24 

30.  Which  of  the  following  figures  has  10  vertices  ?  (A)  Figure U 

(B)  Figure V 

(C)  Figure W 

(D)  Figure X 

U

V

W

X 

31.  Which  two  angles  in  the  given  figure  are  NOT  complementary  ?  T 

(A) ÐRXS and ÐTXU 

S 

(B) ÐSXT and ÐTXU 

30°  60°  60°  30° 

(C) ÐRXS and ÐSXT  (D) ÐTXU and ÐUXV 

V 

X 

R 

32.  Mr.  Raghav  installed  a  triangular  piece  of  stained  glass  above  his  front  door. 

U 

35° 

35° 

Which  of  the  following  best  describes  the  triangle  with  the  given  measures?  (A)  Acute equilateral triangle  (B)  Obtuse isosceles triangle  (C)  Right scalene triangle  (D)  Right isosceles triangle 5 

4 th  IMO  |  Level­I  |  Class 7 

4th IMO - 2010

33.  Which  model  best  represents  the  expression  (A) 

1 2  × ?  2 3 

(B) 

(C) 

(D) 

34.  Mr.  Sameer  was  trying  to  find  a  tablecloth  for  his  rectangular  dining  table.  He  knew  the  area  and  perimeter  of  the  tabletop.  Area  =  36  square  metres,  Perimeter  =  26  metres  Which  of  the  following  best  represents  the  width  and  length  of  the  tabletop?  (A)  Width = 2 m, Length = 18 m 

(B)  Width = 3 m, Length = 12 m 

(C)  Width = 6 m, Length = 6 m 

(D)  Width = 4 m, Length = 9 m 

35.  Leela  looked  at  several  different  flower  arrangements  before  purchasing  one.  The  arrangements  varied in price from ` 15.62 to ` 37.50. Which measure of data can be used to describe the variation  in  price  of  the  different  arrangements  ?  (A)  Mean 

(B)  Mode 

(C)  Range 

(D)  Median 

36.  Which  list  of  integers  is  in  order  from  least  to  greatest  ?  (A)  – 42, –39, – 4, 40, 41  (B)  – 42, 41, 40, – 39, – 4  (C)  – 4, – 39, 40, 41, – 42(D)  41, 40, – 4, – 39, – 42  37.  The  factor  tree  for  the  number  24  is  shown  here.  According  to  the  factor  tree,  which  of  the  following  statements  is  true? 

24  2  12 

(A)  The number 24 is prime. 

6 

2 

(B)  The only prime factor of the number 24 is 12.  (C)  The numbers 24, 12 and 6 are composite. 

2  3 

(D)  The numbers 2, 3, 6 and 12 are prime factors of 24.  38.  Ashwin  used  the  rule  listed  below  to  rewrite  the  expression  10 2  ×  10 5  =  10 7 .  10 m  ×  10 n  =  10 m  +  n  Based on this rule, which of the following is equivalent to the expression 8 –4  × 8 6  ?  (A)  8 –10 , because 8 –4  × 8 6  = 8 –4–6 

(B)  8 10 , because 8 –4  × 8 6  = 8 4+6 

(C)  8 –2 , because 8 –4  × 8 6  = 8 4–6 

(D)  8 2 , because 8 –4  × 8 6  = 8 –4+6 

39.  A ladder that is 13 m long leans against a building. The bottom of the ladder is 5 m away from the  base  of  the  building.  How  far  up  the  side  of  the  building  does  the  ladder  reach  ?  (A)  18 m 

(B)  16 m 

(C)  12 m 

(D)  8 m 

40.  A  mistake  was  made  in  simplifying  the  expression  given  below.  Simplify  :  5  +  2(6  +  4)  –  2 3 ,  Step  1:  5  +  2(10)  –  2 3 ,  Step  2:  7(10)  –  2 3 ,  Step  3:  70  –  2 3 ,  Step  4:  70  –  8,  Step  5:  62.  In  which  step  did  the  first  mistake  appear  ?  (A)  Step 1 

(B)  Step 2 

(C)  Step 3 

(D)  Step 4 

SECTION  III  :    EVERYDAY  MATHEMATICS  41.  Mr.  X  packs  boxes  for  an  appliance  company.  He  can  pack  a  large  box  in  10  minutes  and  a  small  box in 4  minutes. He  needs to pack 10 large boxes and 20  small boxes. If 2.5 hours remain before  closing time, will Mr. X have time to finish the work before closing time if he works without stopping?  (A)  Yes, Mr. X will finish the work in 1.8 hours. 

(B)  No, it will take Mr. X 4 hours to finish. 

(C)  Yes, Mr. X will finish the work in 0.5 hour. 

(D)  No, it will take Mr. X 3 hours to finish.

4 th  IMO  |  Level­I  |  Class 7 

6 

4th IMO - 2010

42.  Tarana  has  4  old  coins  :  W,  X, Y  and  Z.  Coin Y  is  worth  `  2.  Coin  Z  is  worth  3  times  the  value  of  Coin  Y.  Coin  X  is  worth  4  times  the  value  of  Coin  Y.  The  4  coins  are  worth  `  30  altogether.  What  is  the  value  of  Coin  W?  (A)  ` 14 

(B)  ` 18 

(C)  ` 9 

(D)  ` 19 

43.  In a factory, one machine makes flashlights at a rate of 150 flashlights per hour, and another machine  makes the same flashlights at a rate of  135 flashlights per hour. Which of the following equations  can  be  used  to  find  t,  the  total  number  of  flashlights  both  machines  will  make  in  8  hours?  (A)  t = (150 + 135) ÷ 8 

(B)  t = 150(8) – 135(8) 

(C)  t = (150 + 135)8 

(D)  t = 150(8) + 135 

44.  The total length of all songs on a CD, Mohammed bought is about 80 minutes. Each song is between  4  to  6  minutes  long.  Which  is  a  reasonable  number  of  songs  that  could  be  on  the  CD?  (A)  10 

(B)  40 

(C)  74 

(D)  16 

1  45.  Sonal  needed  to  make  2  costumes  for  a  school  play.  The  larger  costume  required  4  metres  of  4  3  material, and the smaller costume required  metres less than the larger one. Which of the following  4  equations can be used  to find  n,  the number of  metres  of  material  needed for the  smaller costume ?  1 3  (A)  n = 4  + 4 4 

1 3  (B)  n = 4  × 4 4 

1 3  (C)  n = 4  ¸ 4 4 

1 3  (D)  n = 4  4 4 

46.  Arun  can  run  100  metres  in  20  seconds.  If  he  competes  in  the  400­metres  race,  about  how  many  seconds  will  it  take  him  to  run  the  race  ?  (A)  50  secs 

(B)  40  secs 

(C)  80  secs 

(D)  20  secs 

47.  Which  of  the  following  statements  represents  the  greatest  percent  of  change  ?  (A)  A tree grew from 6 feet to 12 feet in 1 year.  (B)  An aquarium that was originally priced at ` 80 is now ` 140.  (C)  A person whose salary was ` 1000 per week is now earning ` 1200 per week.  (D)  A baby who weighed 7 pounds at birth now weighs 16 pounds.  48.  Malini  answered  75%  of the  40 problems  on  her  history  homework correctly.  How many  problems  on  her  homework  did  she  answer  correctly  ?  (A)  19 

(B)  30 

(C)  28 

(D)  10 

49.  It took Abhilasha 15 minutes to apply a coat of paint to a piece of pottery. After each coat she waited  close to 60 minutes for the  paint to dry. Which is a reasonable amount of time it could  have taken  for  Abhilasha  to  have  applied  3  coats  of  paint  and  for  the  pottery  to  be  completely  dry  ?  (A)  105 minutes 

(B)  225 minutes 

(C)  195 minutes 

50.  Isha  and  Shivani raced  their  toy  cars.  The given  diagram shows the distance the cars travelled  during  the race.  How much  farther  did  Isha's  car  travel  than  Shivani's  car  ?  (A) 

34  m  100 

(B) 

44  m  100 

Isha 

7 

53  metres  100 

Shivani 

(C) 

(D)  903 minutes 

72  m  100 

19  metres  100 

(D) 

62  m  100 4 th  IMO  |  Level­I  |  Class 7 

Class 7 5th

Year 2011

2

5th IMO - 2011

Section I : Logical Reasoning 1.

If the letters of the word IMPORTANCE are arranged from left to right in alphabetical order, then



which letter will be fifth from the left? (A) O (B) N

2.

If RESCUE is coded as 372057 and PROBLEM as 9348176, how will PROCURE be coded? (A) 9340537 (B) 9340357 (C) 3840537 (D) 3904537

3.

Rohit left home and cycled 10 km towards South, then turned right and cycled 5 km and then again

(C) M

(D) K

turned right and cycled 10 km. After this he turned left and cycled 10 km. How many kilometres

will he have to cycle to reach his home straight? (A) 10 km (B) 15 km (C) 20 km

4.

Find the odd one out.



(A)

5.

Which of the following is the mirror image of Fig. (X), if the mirror is placed



(B)



(C)

(D) 25 km



(D)

along MR ?

(A)



(B)



(C)



(D)

6.

What number will replace the question mark in the given series?





(A) 33

7.

Find the figure from the options which when placed in the blank space of figure (X) would completes

(B) 24

18, 24, 21, 27, (?), 30, 27 (C) 30

(D) 21

the pattern.

(A)



(C)





(B)





(D)

? Fig. (X)

SPACE FOR ROUGH WORK

3

5th IMO - 2011 8.

Vijay is 17th from the left end of a row of 29 boys and Manish is 17th from the right end in the



same row. How many boys are there between them in the same row? (A) 5 (B) 6 (C) 3

9.



(D) Data inadequate

Pratik remembers that his brother's birthday falls after 18th April but before 22nd April while his sister Sakshi remembers that her brother's birthday falls after 20 th April but before 25th April. On what date does her brother's birthday fall? (B) 21st April (A) 20th April

(C) 19th April

(D) 22nd April

10. Mohit went to sleep at 6:45 p.m. If he rose at 12 noon, for how many hours did he sleep? (A) 17 hours 15 mins (B) 5 hours 15 mins (C) 12 hours (D) 6 hours 45 mins 11. Figures (i), (ii), (iii) and (iv) constitute the Problem set. There is a definite relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a



suitable figure from the options that would replace (?) in figure (iv). Problem Set (A) (B)



(C)



(i)

(D)

(ii)

(iii)

? (iv)

12. A square transparent sheet with a pattern is given. Find out from the options as to how the pattern would appear when the transparent sheet is folded along the dotted line PQ.

(A)









(C)

(B)





(D)

P

Q



13. Arrange the given words in a meaningful sequence and find the correct answer from the options. 1. Income 2. Status 3. Education 4. Well-being 5. Job (A) 3, 1, 5, 2, 4 (B) 1, 3, 2, 5, 4 (C) 1, 2, 5, 3, 4 (D) 3, 5, 1, 2, 4 14. Find the figure from the options which will continue the series established by the Problem Figures.



(A) (C)





(B)

Problem Figures



(D) SPACE FOR ROUGH WORK

?

4

5th IMO - 2011

15. Find a figure from the options which contains Fig. (X) as its embedded part.

Fig. (X)



(A)



(B)

(C)



(D)





16. Which number will replace the question mark in the given pattern? 3 4 8



(A) 8

4

2 5 4

(B) 9

6

4 5 9

?

(C) 10

(D) 11

17. Five persons with names P, M, U, T and X live separately in any one of the following : a palace, a hut, a fort, a house and a hotel. Each one likes two different colours from among the following : Blue, Black, Red, Yellow and Green. U likes red and blue. T likes black. The person living in a palace does not like black or blue. P likes blue and red. M likes yellow. X lives in a hotel. M lives in a ______. (A) Hut (B) Palace (C) Fort (D) House 18. Find out from the given options, a figure which when placed in place of question mark will continue the series established by the Problem Figures.

(A)





(B)



(C)



(D)



19. Five girls are sitting on a bench to be photographed. Shweta is to the left of Richa and to the right of Pia. Misha is to the right of Richa. Reeta is between Richa and Misha.

Who is second from the left in the photograph ? (A) Reeta (B) Misha

(C) Pia

(D) Shweta

20. Pointing towards a girl, Abhishek says, "This girl is the daughter of the only child of my father." What is the relation of Abhishek's wife with the girl ? (A) Daughter (B) Mother (C) Aunt (D) Sister

Section II : Mathematical reasoning 21. Find the number of factors of 75. (A) 4 (B) 6

(C) 8 SPACE FOR ROUGH WORK

(D) 10

5

5th IMO - 2011

22. A diver was diving 100 metres below sea level. He went down 20 metres more and came up

35 metres. How far below sea level did he dive ? (A) + 85 metres (B) – 85 metres (C) + 55 metres

(D) – 55 metres

23. There are three drums with 1653 litres, 2261 litres and 2527 litres of petrol. The greatest possible size of the measuring vessel with which we can measure the petrol of any drum while every time the vessel must be completely filled is _____.

(A) 31

(B) 27

24. A drum of kerosene oil is of the drum is ____.

(A) 45

(C) 19

(D) 41

3 7 full. When 15 litres of oil is drawn from it, it is full. The capacity 4 12

(B) 90

(C) 60

(D) Can't be determined

25. Find the value of the given expression :

(22 + 23 + 2–2 + 2–3) (A) 95 8

(B) 97 8

(C)

99 8

(D)

98 8

Direction (Q. 26-27) : Study the graph carefully to answer the following questions.

Number of Girls Enrolled

Number of Girls Enrolled in Different Hobby Classes in Various Institutes in a Year 450 400 350 300 250 200 150 100 50 0

Painting Stitching Dancing

A

B

C Institutes

D

E

26. What is the difference between the total number of girls enrolled in stitching and dancing from all

institutes together ? (A) 50

(B) 25

(C) 75

(D) 85

27. What is the total number of girls enrolled in painting from all the institutes together ? (A) 1150 (B) 1200 (C) 1275 (D) 1100 SPACE FOR ROUGH WORK

6

5th IMO - 2011

28. Divide 14 toffees between Ankita and Anshul in the ratio 5 : 2 respectively.

(A) 2, 5

(B) 4, 10

(C) 10, 4

(D) 40, 8

29. Mr. Arvind spends 30% of his money on education and he has total ` 15,000. How many rupees

does he spend on his education? (A) ` 5000 (B) ` 4500

(C) ` 1000

(D) ` 5500

30. By selling a shirt for ` 285 a shopkeeper loses 5%. At what price should he sell the shirt so as

to gain 15% ? (A) ` 295

(B) ` 325

(C) ` 300

(D) ` 345

31. In the given figure, AB || GH || DE and GF|| BD || HI, ∠ FGC = 80°. Find the value of ∠ CHI. A

G

F



(A) 80°



(B) 120°



(C) 100°

B

C

D



(D) 160°

I

H

E

32. Solve for x :

(A)

1 3

6x − 2 3x + 5 1 + = 9 18 3 2 (B) 3

(C)

3 5

(D)

8 3

33. In the given figure, BC is produced to D and ∠ BAC = 40° and ∠ ABC = 70°.

Find the value of ∠ ACD. (A) 130° (B) 140° (C) 170° (D) 110°

A

B

C

D

34. A rectangular field has length and breadth in the ratio of 16 : 9. If its perimeter is 750 cm. What

is its area ? (A) 75000 cm2

(B) 32400 cm2

(C) 14400 cm2

(D) 14000 cm2

35. In our office there are 60% female employees. 50% of all the male employees are computer literate. If there 62% employees are computer literate out of the total 1600 employees, then the number of female employees who are computer literate is _____.

(A) 690

(B) 672

(C) 960 SPACE FOR ROUGH WORK

(D) Can't be determined

7

5th IMO - 2011 36. How many numbers are there from 100 to 200?

(A) 100

(B) 101

(C) 99

(D) None of these

(C) CLVIII

(D) XCII

37. Write down the Roman numeral for 92.

(A) LCII

(B) CXXI

38. Which of the following statements is INCORRECT?

(A) Every number is a factor of itself.



(B) Number of factors of a given number are finite.



(C) Every multiple of a number is less than or equal to that number.



(D) 4 and 15 are co-prime numbers.

39. The number of edges in the given figure is ______.

(A) 8

(B) 9



(C) 10

(D) 12

40.

In the given figure, find the value of ∠ BOC. (A) 101° (B) 149° (C) 71° (D) 140°

C A

F 40°

O

31°



B D

E

Section III : Everyday Mathematics 41. Aman's mother was 21 years old when his sister was born. His father is 8 years older than his mother. Now Aman is 17 years old and his sister is 3 years older than him. What is the present age of Aman's father?

(A) 50 years

(B) 47 years

(C) 46 years

(D) 49 years

42. I was sitting alone in a park. After a while there came an old man followed by an old lady. They were followed by two couples who were accompanied by a child each. What was the number of total persons present in the park ?

(A) 10

(B) 9

(C) 11

(D) 8

43. In how many parts can a rod of length 19.5 m be broken into equal lengths of 65 cm ?

(A) 20

(B) 30

(C) 3 SPACE FOR ROUGH WORK

(D) 130

8

5th IMO - 2011

44. Three bells toll at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start

ringing together at a particular time. They next toll together after _______. (A) 6 minutes (B) 12 minutes (C) 18 minutes (D) 24 minutes

45. Mohan has certain amount in his account. He gives half of this to his eldest son and one third of

the remaining to his youngest son. The amount left with him now is ______. (A) 1/3 of the original (B) 2/3 of the original (C) 3/4 of the original (D) 1/6 of the original

46. There are 8 marbles in a box with numbers 1 to 8 marked on them. What is the probability of drawing a marble with number 2 ?

(A)

1 8

(B) 1 6

(C)

1 4

(D)

1 5

1 47. The selling price of a watch is ` 3200 and the profit per cent is 33 %. Find the cost price of the 3 watch.

(A) ` 200

(B) ` 2000

(C) ` 2400

(D) ` 3000

48. If the circumference of a circle is 704 cm, then its area is ______.

(A) 49324 m2

(B) 39424 m2

49. When Sarvesh travelled 33 km he found that

the total journey is (A) 66 km

(B) 132 km

(C) 3672 cm2

(D) 39424 cm2

2 rd of the entire journey was still left. The length of 3 (C) 99 km

(D) 100 km

50. Two equal containers are filled with a mixture of milk and water. The concentration of milk in each of the containers is 20% and 25% respectively. What is the ratio of water in both the containers

respectively? (A) 15 : 16

(B) 16 : 15

(C) 4 : 5

SPACE FOR ROUGH WORK

(D) 5 : 4

Class 7 6th

SET A Year 2012

2

6th IMO - SET A Section I : Logical Reasoning

1. In the question, some letters are given which are numbered 1, 2, 3, 4 and 5. Below are given four options containing combinations of these numbers. Find that combination of numbers so that letters arranged accordingly form a meaningful word. A R E G R

(A) 5, 4, 3, 1, 2

1 2 3 4 5

(B) 5, 1, 4, 3, 2

(C) 4, 5, 1, 3, 2

(D) 2, 4, 3, 5, 1

2. In the given arrangement, how many such symbols are there, each of which is preceded by a letter which is from the first half of the English alphabet and followed by a digit?

9 V @ S 2 G R A o3 Q £ B Z 7 C Y D T 4 8 P F 6 @ $ 5 E H B K d



(A) 2

(B) 4

(C) 3

(D) 1

3.

Find the figure from the options which will continue the series established by the Problem Figures. Problem Figures ?

(A)



(B)



(C)

4. If Z = 52 and ACT = 48 then BAT = ? (A) 39 (B) 41 5.



(C) 44

(D)

(D) 46

The given question consists figures (i), (ii), (iii) and (iv). There is a definite relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace (?) in figure (iv). +

?

+

+

(i)

(iii)

×

(A)

6.

P started from his house towards West. After walking a distance of 25 m, he turned to the right



(C)

(iv)



+

(B)

×

(ii)



×



(D)

and walked 10 m. He then again turned to the right and walked 15 m. After this he has to turn to his right at 135° and to cover 30 m. In which direction should he go ?

(A) West

(B) South

7.

Find the wrong term in the series given below.



(A) 420

(B) 378

(C) South-West

440, 420, 399, 378, 354 (C) 354

(D) South-East

(D) 399

3

6th IMO - SET A 8.

Find out from the options which is the mirror-image of the given combination if mirror is placed along MR. (A)



(B)



(C)



(D)

9.

Rohit earns more than Farhan but not as much as Jay. Krish earns less than Jay but not as little





as Farhan. Mohit earns more than Farhan but not as much as Rohit. If they are arranged according

to their earnings, who will be in the middle ? (A) Krish (B) Rohit

(C) Mohit

(D) Data inadequate

10. Find the figure from the options if placed in place of question mark, which will complete the figure(X). (A)



(B)

(C)



(D)





11. J, K, L, M, N, O and P are seven kids playing in the garden. They are wearing clothes of colours - black, blue, white, green, pink, yellow and brown. Out of the seven kids, three are girls. No girl is wearing either black, yellow or brown. M's sister O is wearing pink, while he is wearing brown. J is wearing blue, while his sister K is not wearing green. N is wearing yellow, while his best friend

P is a boy. What colour is K wearing ? (A) Green (B) Pink

(C) Brown (D)

White

12. Select a figure from the options which contains Fig.(X) as its part. (A)





(C)



(B)

Fig.(X)

(D)



13. If in the following groups of numbers after adding all the digits of each group, are arranged in decreasing order, then which will be the middle group ?

853, 395, 486, 249, 497, 766, 914 (B) 497 (C) 486

(A) 395

(D) 766

14. There is a Problem Figure having two parts I and II. The Problem Figure has some characteristics. Select the figure from the options which has the same commonality.

(A)



(C)

I

II

I

II



(B)



(D)



I

II



4

6th IMO - SET A

15. In the adjoining figure there is one matrix followed by four Answer Figures. In the matrix there are eight designs and one space left blank shown by question mark. Which answer figure will replace the question mark?

(A)



(B)





(C)



(D)



?

16. If P means ÷, R means +, T means – and W means ×, then what is the value of given statement? 24 R 16 P 8 W 6 T 9

1 (A) 15 3

(B) 21

(C) 147

(D) 27

17. In this question, there are four figures as given in options (A), (B), (C) and (D). Out of these four figures, three are similar in a certain way. However, one figure is not like the other three. Choose the figure which is different from the rest.

(A)

(B)





(C)

18. In the given figure, which number will replace the question mark?

(A) 45



(B) 41 (C) 32



(D) 40

(D)



3

6 15

9 31

27

?

56

81

19. If ‘sheet’ is called ‘pillow’, ‘pillow’ is called ‘quilt’, ‘quilt’ is called ‘mosquito net’, ‘mosquito net’ is

called 'scarf' and ‘scarf’ is called ‘saree’, then which is used only in winters? (A) Quilt (B) Pillow (C) Mosquito net (D) Scarf

20. The given three elements are related in some way. Find the diagram in which these three elements fit. Oil, Wick, Lamp

(A)



(B)



(C)



(D)

Section II : Mathematical reasoning 21. Simplify :

[(31 – 19) × {5 – (5 + 2 – 3)} of 3 + (– 2)] × (–1) (A) 24

(B) – 34

(C) – 54

(D) 12

X

22. In the given figure, XYZ is an equilateral triangle and XZQ is an isosceles

triangle. Find ∠QZO. (A) 30° (B) 60° (C) 45° (D) 50°

Y

O 30° Q

Z

5

6th IMO - SET A 23. The given solid (not drawn to scale) is a regular triangular pyramid. The net of the pyramid is wrongly drawn with 1 extra face. Which of the following faces (P, Q, R or S) is not a part of the net ?

(A) P

(B) Q



(C) R

(D) S

9 1 of a number is 45, what is of the same number? 5 5 (A) 5 (B) 25 (C) 30

24. If

(D) 81

25. Find the area of parallelogram PQRS, if PR = 24 cm and QU = ST = 6 cm.

(A) 72 cm2



(B) 100 cm2



(C) 150 cm2



(D) 144 cm2

S

R U T

24

cm 6 cm

P

Q

26. John is n years older than his sister. His sister's age is 12. What is their total age after 4 years ? (A) 28n years (B) 24n years (C) (32 + n) years (D) (28 + n) years A

27. In the given figure, AB and CD are straight lines. Find ∠ y.

D

(A) 97°



(C) 77°



(D) 55°

40°

C

°

(B) 27°

35



48° y

B

28. The descending order of the given fractions is _______. 4/3, 4/7, 7/10 (A) 7/10 > 4/7 > 4/3 (B) 4/7 > 4/3 > 7/10

(C) 4/3 > 7/10 > 4/7

(D) 4/3 > 4/7 > 7/10

29. Find the circumference of the circle that is within a square if the area 22   of the square is 81 cm2.  Take π =   7  2 2 (B) 14 cm (A) 7 cm 7 7

(C) 28

2 cm 7

(D) 63

9 cm 14

A

30. In the given figure, find ∠x.

(A) 120°



(B) 110°



(C) 115°



(D) 125°

E

36° 58° B

F

x G

C

6

6th IMO - SET A

31. Find the value of x. (A) 47.095

(D) 47.95 24.5 cm

32. The length of a rectangular painting with border is 24.5 cm and



of the painting. (A) 111 cm

(B) 100 cm

(C) 133 cm

(D) 294 cm2

2

3 cm

3 cm

its width is 12 cm. The width of the border is 3 cm. Find the area

3 cm



3889 + 12.952 – x = 3854.002 (B) 47.752 (C) 47.932

12 cm

2

2

3 cm

33. Express 25 seconds as a fraction of 1 hour.

(A)

34. If

5 12

1 4

(B)

1 144

(C)

(D)

1 24

1 of a number is 166, then what is 30% of the number? 2

(A) 99.6

(B) 83

(C) 64.5

(D) 49.8



(A) 67°



(B) 113°



(C) 40°



(D) 140°

A

E

35. In the given figure, AB || DE. Find a.

40° a

C

67°

B

D

Direction (36 & 37) : The given bar graph shows the percentage distribution of total expenditures of a company under various expenses heads during 2011.

25

20

15

20 15

12.5

10

17.5

10 5 nt

se

me

or

ve

rti

sp

Tra n

Ad

Inf

ras

tru

ctu

re

0

t

5

Ta xe Re s De sea ve rch lop a me nd nt S Int ala ere ry st on Lo an s

Percent

20

36. The total amount of expenditures of the company is how many times the expenditure on research and development ?

(A) 27

(B) 20

(C) 18

(D) 8

37. If the interest on loans amounted to ` 2.45 crores, then the total amount of expenditure on advertisement, taxes & research and development is _______.

(A) ` 7 crores

(B) ` 5.4 crores

(C) ` 4.2 crores

(D) ` 3 crores

7

6th IMO - SET A

38. A shopkeeper bought 24 chairs at the rate of ` 450 per chair. He sold 16 of them at the rate of ` 600 per chair and the remaining at the rate of ` 400 per chair. Find his gain or loss percent.

(A) 18

14 % 27

(B) 20

3 % 4

5 (C) 31 % 9

(D) 14

8 % 9

39. Dipanshu invested a sum of money for a period from May 2006 to May 2008 at the rate of 12% per annum. If the interest received by him is ` 1620, then find the sum.

(A) ` 5000

(B) ` 6500

(C) ` 6000

(D) ` 6750

40. Which of the following statements is correct ?

(A) All squares are congruent.

(B) All right angles are congruent.



(C) Two obtuse angles are always congruent.

(D) None of these

Section III : Everyday Mathematics 3 full of orange juice. This amount is equal to 6 full glasses. When 1 full glass is drunk, 5 what fraction of the jar is still left with orange juice?

41. A jar is



(A)

1 10

(B)

1 6

(C)

2 5

(D)

1 2

42. Monika mixed orange syrup and water in the ratio 4 : 9. How many litres of orange syrup were required to mix with 324 L of water ?

(A) 36 L

(B) 144 L

(C) 167 L

(D) 198 L

43. The cost of a bag was 55% the cost of a skirt. If Mitika intended to buy both the bag and the skirt, then how much money must she have, if the skirt costs ` 31.50 more than the bag ?

(A) ` 38.50

(B) ` 70

(C) ` 108.50

(D) ` 120.55

44. Jasmine and Sonia had 60 phonecards. Jasmine had thrice as many phonecards as Sonia. How many phonecards did Jasmine have?

(A) 15

(B) 20

(C) 30

(D) 45

45. A bus travelled 18 km in 20 minutes. How far could it travel in 1 hr 20 minutes?

(A) 72 km

(B) 118 km

(C) 360 km

(D) 108 km

46. The side of a square plot is 80 m. A path of 4 m width along the sides of the square are constructed in the middle of the plot. Determine the area of the path.

(A) 1216 m2

(B) 1200 m2

(C) 1360 m2

(D) 624 m2

47. A milkman sells 42 litres of milk at ` 19.75 per litre to a hostel. How much money should he get from the hostel ?

(A) ` 1892

(B) ` 829.50

(C) ` 165.85

(D) ` 122.50

48. By selling an article for ` 660, Pradeep loses ` 60. At what price must he sell the article to

gain 15%? (A) ` 728

(B) ` 628

(C) ` 828

(D) ` 928

8

6th IMO - SET A

49. There are two buildings standing on the opposite sides of a park. A ladder, 17 m long, reaches a point on a building at a height of 15 m from the ground. The ladder is now turned to the other building on the other side of the park keeping its foot at the same point. The ladder now reaches a point on this building at a height of 8 m above the ground. Find the distance between the two buildings.

(A) 32 m

(B) 18 m

(C) 25 m

(D) 23 m

50. A place P is 82 m above the sea-level and another place is 13 m below the sea-level. What is the

distance between the two places? (A) 95 m (B) 69 m

(C) –95 m SPACE FOR ROUGH WORK

(D) – 69 m

Class 7 6th

SET B Year 2012

2

6th IMO - Set B

Section I : Logical Reasoning 1. If 'rat' is called 'dog', 'dog' is called 'lion', 'lion' is called 'wolf', 'wolf' is called 'snake' and 'snake'

is called 'elephant', what will be 'dog' called ? (A) Rat (B) Dog

2.

Mohit ranked 12th in a class of 33 students from the top. What is his rank from the bottom? (B) 21st (C) 23rd (D) 15th (A) 22nd

3.

Which of the following does not fit in the letter number series given below ?

(C) Wolf

(D) Lion

G7M J10S M20P L12W (A) J10S (B) G7M (C) M20P 4.

(D) L12W

In which of the following figures, Fig. (X) is embedded as its part?

Fig. (X)



(A)

(B)

5.

Select a figure from amongst the options which will continue the series established by the given



(C)



(D)



problem figures.



(A)

6.

Rohan is taller than Kartik who is shorter than Sushant. Naman is taller than Arsh but shorter than



Kartik. Sushant is shorter than Rohan. Who is tallest? (A) Rohan (B) Sushant (C) Arsh

7.

Which of the following is the correct mirror image of the given Fig. (X), if mirror is placed vertically



(B)

(C)





(D)

(D) Naman

left?

Fig. (X)



(A)

8.

How many rectangles are there in the given figure?



(A) 13



(B)

(B) 14



(C)

(C) 15



(D)

(D) None of these

3

6th IMO - Set B 9. If '÷' means '–', '–' means '×', '×' means '+' and '+' means '÷', then 72 + 9 × 45 – 5 ÷ 42 – 6 = (A) –19 (B) 0 (C) 21

(D) –5

10. Find the missing number in the figure, if the given matrix follows a certain

? 21 (B) 4 1 20 (D) 2

rule row-wise or column-wise. (A) 5 (C) 3

1 22 2 23

2 40 5 43

11. Two positions of a dice has been shown here. What digit will be just opposite of 5?



(A) 4

(B) 2

(C) 6

(D) 1

12. Which of the following alphabets is common to all geometrical figures?

F

L E T D P Q

(A) P

(B) Q

S R



H

(C) L

(D) F

13. In a code language if CROCODILE is coded as ORCDOCELI, how will ELEPHANTS be coded in the

same language ? (A) PHATNELES

(B) ELETAHPSN

(C) ETEPANHTS

(D) ELEAHPSTN

14. Figures (i) & (ii) of the Problem Figures bears a certain relationship. Select a figure (iv) from the options which bears the same relationship with figure (iii).



(A)



(B)



(C)



(D)

15. Vikas walked 10 metres towards North, took a left turn and walked 15 metres; and again took a left turn and walked 10 metres and stopped walking. How far and in which direction is he now

from the starting point? (A) 15 m East (B) 15 m West

(C) 5 m South

(D) 10 m North

16. Find the figure from the options which completes the Fig. (X).

(A)



(B)

?

(C)



(D)

Fig. (X)

4

6th IMO - Set B

17. Pointing towards a person in a photograph, Aashka said, "He is the only son of the father of my sister's brother." How is that person related to Aashka?

(A) Father

(B) Cousin

(C) Maternal Uncle

(D) Brother

18. P, Q, R, S, T, V and W are sitting around a circle facing the centre. R is third to the right of V, who is second to the right of P. T is second to the left of Q, who is second to the left of W. V is sitting between S and W. Who is on the immediate left of R?

(A) Q

(B) T

(C) P

(D) Data inadequate

19. Study the following arrangement of digits, letters and symbols and answer the question given below :

F I 4 K B 5 9 # D R 2 # 7 M G % H V T 3 8 * 1 J A How many such symbols are there in the above arrangement each of which is both immediately preceded and immediately followed by a digit?



(A) None

(B) One

(C) Two

(D) Three

20. Find the next term in the given series below. 4, 6, 12, 14, 28, 30, ___ ?__

(A) 32

(B) 60

(C) 62

(D) 64

SECTION iI : MATHEMATICAL REASONING 1 1 of the money on magazines and of the money on a 3 4 snack. Which of the following fractions represents the part of money he did not spend ?

21. Dhruv earned some money. He spent



(A)

5 12

(B)

1 2

(C)

2 3

(D)

5 7

22. The students in seventh-grade had a dance party. They spent ` 500 for a local band. The equation below can be used to find the total profit y, if the students sold x tickets to the dance party. y = 4x – 500

What does the number 4 represent in the equation?



(A) The price per ticket



(C) The number of tickets sold



(B) The cost of the band (D) The profit made from selling x tickets

23. What percentage of the faces are smiling?



(A) 41.5

(B) 57.5

(C) 62.5

(D) 42.5

24. Solve for x :

(A) 1

15(x – 9) – 2 (x – 12) + 5 (x + 6) = 0 (B)

9 2

(C)

−5 8

(D) 12

5

6th IMO - Set B

25. In the figure (not drawn to scale), ACD is a right-angled triangle, ABC is an isosceles triangle with AB = AC, ACG, EAB and FAD are straight lines. Find the value of x and y respectively.



(A) 70°, 85°

(B) 80°, 75°

(C) 70°, 80°

(D) 75°, 85°

26. There are 54 green apples and 30 more red than green apples in a container. What is the ratio of

the number of red apples to the total number of apples? (A) 5 : 9 (B) 5 : 14 (C) 14 : 23

(D) 23 : 14

DIRECTION (27-28) : The given graph shows the number of books sold by Megha's book store in the first 8 weeks of the year.

27. What was the average number of books sold in 8 weeks? (A) 4875 (B) 4375 (C) 5892

(D) 2945

28. What is the range of the given data? (A) 2000 (B) 1000

(D) 2500

(C) 1500

29. Two figures are congruent, if they have the same ______. (A) Shape (B) Size (C) Both (A) and (B) 30.

How many faces does the given solid have? (A) 8 (B) 10 (C) 12 (D) 14





(D) None of these

31. The rectangle is made of 12 identical squares. It is divided into 4 parts. Which of the following 3 of the rectangle? 2 parts will be removed to form 12



(A) L and N

(B) M and O

(C) L and M

(D) M and N

6

6th IMO - Set B

32. Which rule represents the relation shown in the table ?

(A) y = x – 1



(B) y = x + 3



(C) y = 2x – 3



(D) y = 2x + 3

x 2 3 4 5 6

y 1 3 5 7 9

33. Find the area of the given figure (not drawn to scale).



(A) 200 cm2

(B) 94 cm2

(C) 84 cm2

(D) 100 cm2

34. Find the value of the given expression.

(A) –78

35. If

(–35) – (–15) + 8 – 9 – (–152) – 25 + (–8) (B) 32

(C) –55

(D) 98

6 y − x  x 3 equals _____. = , then the value of  +  7 y + x  y 4

(A)

5 7

(B) 1 1 7

(C) 1

(D) 2

36. The diameter of a scooter wheel is 56 cm. How much distance will it cover in 10 revolutions ?

(A) 1660 cm

(B) 1875 cm

(C) 1560 cm

(D) 1760 cm

37. The largest number which divides 77, 147 and 252 to leave the same remainder in each case, is _______.

(A) 9

(B) 15

(C) 25

(D) 35

38. The side of a square plot is 80 m. Two paths of 4 m width along the sides of the square are constructed in the middle of the plot. Determine the area of the path.

(A) 139 m2

(B) 624 m2

(C) 264 m2

(D) 512 m2

39. Latika is 6 m years old. She is thrice as old as her sister. What will their total ages after six years?

(A) 8m + 6

(B) 8m + 12

(C) 24m + 6

(D) 24m + 12

40. In the given figure l || m and AB = BC, find the value of y.



(A) 45°

(B) 48°

(C) 20°

(D) 30°

7

6th IMO - Set B

SECTION iII : EVERYDAY MATHEMATICS 41. Ishika and her grandfather both had birthdays last week. The sum of their ages is 100 years. Her

grandfather's age is 4 times Ishika's age. How old is Ishika ? (A) 16 years (B) 20 years (C) 22 years

(D) 25 years

42. The ratio of boys to girls in a club is 7 : 4. There are 21 fewer girls than boys. What is the total

number of children in the club? (A) 49 (B) 77

(C) 84

(D) 231

43. Jenny uses 36 beads to make 4 bracelets. How many of the same type of bracelets can Jenny

make with 180 beads ? (A) 20 (B) 27

(C) 432

(D) 972

44. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively.

In 30 minutes, how many times do they toll together? (A) 4 (B) 10 (C) 15

(D) 16

45. 1 litre of water weighs 1 kg. How many cubic millimetres of water will weigh 0.1 g? (A) 0.1 (B) 1 (C) 10 (D) 100 2 3 of the first group and of the second group 3 4 board buses to travel to a museum, how many more people of the first group board buses than

46. Each of two groups of tourists has 60 people. If



of the second group ? (A) 2

(B) 4

(C) 5

(D) 40

47. The temperature of a city at 1 p.m. was 15°C. Every hour it decreases by 3°C. The temperature at

6 p.m. was _____. (A) 3°C

(B) 0°C

(C) –3°C

(D) –6°C

48. A man sells a car to his friend at 10% loss. If the friend sells it for ` 54000 and gains 20%, the

original C.P. of the car was _____. (A) ` 25000 (B) ` 37500

(C) ` 50000

(D) ` 60000

49. The total cost of 3 tables and 2 chairs is ` 745. If one table costs ` 40 more than one chair, find

the price of each table and chair respectively. (A) ` 160, ` 120 (B) ` 165, ` 125

(C) ` 200, ` 160

(D) ` 120, ` 80

50. Equal sums of ` 7200 were lent to Megha and Priya at 5% per annum for a period of 4 years and

5 years respectively. Find the difference of the interest paid by Megha and Priya. (A) ` 140 (B) ` 560 (C) ` 260 (D) ` 360 SPACE FOR ROUGH WORK

Class 7 7th

SET A Year 2013

2

7th IMO - Set A

logical reasoning 1.

Priya remembers that she saw her maternal aunt on Friday after 23rd of a month. If 6th of that month fall on Sunday, then on what day of the week did she meet?



A. B. C. D.

2.

Beena, who is Garima's daughter, says to Latika, 'your mother Aashka is the younger sister of my mother, who is the third child of Rajeev'. How is Rajeev related to Latika?



A. B. C. D.

3.

Which of the following options has the same relationship as that of MJ : QN ?



A. B. C. D.

4.

How many such pairs of letters are there in the word 'DISTURBANCE' which have as many letters between them as there are in English alphabets ?

24th 25th 27th 29th

Brother Uncle Maternal grandfather Father

PK : NP RL : OP BR : FV EF : IM



A. B. C. D.

6 5 8 7

5.

Mohit, Nitin and Raj play cricket, hockey and football. Mohit, Nitin and Tarun play cricket, football and volleyball. Mohit, Raj, Sumit and Nitin play cricket and hockey. Which game is played by all the boys?



A. B. C. D.

6.

Which of the following is the mirror image of the given word, if the mirror is placed vertically to the left?



A.



B.



C.



D.

8.

How many 5's are there in the given series of which is immediately preceded by an even number and immediately followed by a vowel? 2 5 D 4 1 5 I 3 B C 6 2 5 A 6 5 I J 9 3 5 Q 7 F 4 3 8 J K A 6 5 0 4 5 



A. B. C. D.

0 3 4 2

9.

If '+' means '÷', '–' means '×', '÷' means '+' and '×' means '–', then 320 ÷ 225 + 15 × 15 – 85 = ?



A. B. C. D.

180 140 60 –940

10. Find the missing figure in the given figure matrix.

Hockey Cricket Football Volleyball

2REASONING7 A. B. C. D.

The opposite faces of a cube are as shown :

Which of the following options represents the unfolded cube?







7.



A.



B.



C.



D.







3

7th IMO - Set A 11. Five friends Ashu, Andy, Monu, Sonu and Meeku are sitting on a bench facing north. Ashu is sitting next to Monu, Andy is sitting next to Meeku, Meeku is not sitting next to Sonu, who is sitting on left end at the bench. Andy is on the second position from the right, Ashu is second from the left, in which position is Monu sitting?

A. B. C. D.

3 2nd 1st 5th rd

12. Find the figure from the options in which Fig. (X) is embedded as one of its part.



A.



B.



C.



D.



A. B. C. D.



HJTAKCP HKTALCP HKTAKCP HKTAKBP

14. B is the South-West of A, C is to the East of B and South-East of A and D is to the North of C in line with B and A. In which direction of A is D located?

A. B. C. D.

"Vegetable, Fruit, Rotten" ?



A.

B.



D.



16. Arrange the following words in the alphabetical order as arranged in dictionary and choose the word that comes last.

A. B. C. D.

Prominent Prohibition Programme Prolong

17. Which of the following options will complete the series? 3, 2, 11, 4, 35, 8, 107, 16, ? A. 321 B. 323 C. 32 D. 120



A. B. C. D.

12 13 11 10

19. The given question consists of two sets of figure. Figures P, Q, R and S consists of a problem set. There is a definite relationship between figures P and Q. Establish a similar relationship between Figure R and S by selecting a suitable figure from the options that would replace (?) in figure S.

North-West South-West South-East North-East

15. Which of the following Venn diagrams correctly describes the relationship amongst



C.

18. Which number will replace the question mark, if the matrix follows a certain rule row-wise or column-wise ?

13. In a certain code language, the word 'DIPLOMA' is written as 'FERHQIC'. How will the word 'FOREIGN' be written in that code?





A.



B.



C.



D.





4

7th IMO - Set A

20. In the given question a piece of sheet is folded and cut and then unfolded. Select this figure from option which exactly resembles the unfolded paper.



B. C.



A.











D.



MATHEMATICAL REASONING 21. The figure is made up of 3 squares. What is the area of the shaded part of the figure? (figure not drawn to scale)



A. B. C. D.

50 24 36 48

cm2 cm2 cm2 cm2

22. In the given figure, PQ || RS, PS || QR and ∠RPT is 1 as much as ∠PTS. What is the value of ∠RPQ ? 4

25. Which of the following will make the expression true? 7 2 1 4 6 3  3 − 6  − 2 +  5 ÷ 8  + 4



A. B. C. D.

84° 63° 42° 52°

23. Which of the following statements is INCORRECT with respect to integers ?

A.



B.



C.



D.

Integers are closed under both addition and subtraction. Commutative property holds in addition but not in subtraction. Associative property holds both in addition and subtraction. 0 is the additive identity of integers.

24. The value of 28 in 528094 is the same as ______.

A. B. C. D.

7000 + 1094 8094 – 90 7094 + 906 28094 – 94

> < = Can't be determined

26. The circumference of the tyre of Radha's bicycle is 2.5 m. She took part in a bicycle race of 1 km. When she had covered 700 m, the tyre burst. If she had to finish the race, how many more times the wheel must go round?



A. B. C. D.

4  6 3 ÷ +  5  8 4 7  3 5 −  +  +1  4 6 3

A. B. C. D.

24 120 125 30

27. Mohit spends ` 7x – 4 for a shirt and ` 2x + 8 for a pair of trousers. If he gives the shopkeeper a 1000 rupee note, how much will he get back ?

A. B. C. D.

1012 – 9x 996 – 9x 992 – 8x 996 – 7x

28. Find the mean and median respectively in this group of test results.

A. B. C. D.

60, 43, 47, 61, 35, 53, 49, 32, 59 49, 47 46.87, 49 48.69, 43 48.77, 49

29. The average of 4 numbers is 25. The average of the first 3 numbers is 22. What is the value of the 4th number ?

A.

23

5

7th IMO - Set A

B. C. D.

34 44 47

33. Simplify :

30. Solve for x : 15 (x – 9) – 2 (x – 12) + 5 (x + 6) = 0

A.



B.



C.



D.

–3 1 2 9 2 4

31. In the given figure, ABC is a straight line. Find y.



A.



B.



C.



D.

5 x 7 y 5 × (10a3 x 2 ) −3 (2 x5 y 3 ) × (6a 2 y ) −2

25 4 xy 6 25 2 3 x y 4 9 2 a xy 100

9  y  ×  100a  xa 

4

Direction (34-35) : A fair dice has faces numbered 0, 1, 7, 3, 5 and 9. If it is thrown, the probability of getting 34. a 1 is _________



A. B. C. D.

50° 80° 100° 130°

32. How many unit cubes are required to make it a cuboid?



A. B. C. D.



A.



B.



C.



D.

2 5 1 6 1 2 3 5

35. an odd number is A. 1 2 B. 3 5 C. 6 1 D. 6

18 30 28 26

EVERYDAY MATHeMATICS 36. By selling a watch for ` 1275, Javed lost 15%. At what price should he sell to make profit of 10%?

A. B. C. D.

` ` ` `

1500 1482 1550 1650

37. A businessman borrowed some money at 1% per month. After some time, he settled the debt by paying ` 14,750. If the total interest was ` 2950, find the time.

A. B.



C.



D.

2 years 1 month 3 years 1 2 years 2 1 year 8 months

38. Four persons step off together during a morning walk. Their steps measure 60 cm, 80 cm, 75 cm and 90 cm respectively. At what distance from the starting point will they again step off together ?

A. B. C. D.

12 m 36 m 4m 72 m

39. Rajesh had a packet of 20 sketch pens. He gave 12 to Kartik and 6 to Meena. What fractions of the packet did he give to Kartik and Meena ?

A.



C.

3 10 9 10

B.

4 5

D.

1 5

6

7th IMO - Set A

40. 20% of the students were absent in an examination. 15% of those who appeared failed. If 340 students passed, what was the total number of students?

A. B. C. D.

550 450 400 500

41. A man is five times as old as his son. He will be three times as old as his son after 10 years. Find their present ages.

A. B. C. D.

10 years, 50 years 8 years, 40 years 12 years, 60 years 6 years, 30 years

42. A park 300 m by 210 m has a path 5 m wide all round it, the path being inside the park. Find the cost of constructing the path at ` 100 per 10 m2 .

A. B. C. D.

` ` ` `

point of alcohol?

A. B. C. D.

–137 °C 137 °C –59 °C 59 °C

44. Nine counters numbered 1 to 9 are placed in a bag. One is taken out at random. The probability that it is divisible by 3 is _______.

A.



B.



C.



D.

1 2 1 3 2 9 4 9

45. In a school, 8a 2 + 4a + 9 students were enrolled. 2a 2 – 9a + 2 students were boys. How many girls were enrolled?

500 5000 50000 500000

43. The melting point of mercury is –39°C. The freezing point of alcohol is –98°C. How much more is the melting point of mercury as compared to the freezing



A. B. C. D.

6a2 4a2 6a2 4a2

– 13a + 7 + 13a + 7 + 13a + 7 – 13a + 7

Achievers Section Direction (46-47) : The line graph shows the number of storybooks Armaan read in the last 4 months of a year.



B.

3 4



C.

1 2



D.

5 12

48. What percentage of the figure is shaded ?

46. The ratio of storybooks he read in September to November is

A. B. C. D.

1 4 2 5

: : : :

4 1 5 2

47. The number of storybooks that he read in October as a fraction of the total number of storybooks read is

A.

1 12



A. B. C. D.

50 60 70 65

% % % %

7

7th IMO - Set A 49. If the 2 unit cubes marked 'X' are removed from the solid, which solid will be obtained?





A.

B.





C.



D.



50. Select the incorrect match.

A. B. C. D.

SPACE FOR ROUGH WORK

Item S.P. (`) Profit / loss C.P. (`) Pen 96 20% profit 80 Sofa 7000 12½% loss 8000 Wooden shelf 6786 13% loss 7812 Tea set 1526 9% gain 1400

Class 7 7th

SET B Year 2013

2

7th IMO - Set B

logical reasoning 1.

The positions of how many letters in the word WONDERFUL will remain unchanged when the letters within the word are arranged alphabetically?



A. B. C. D.

2.

Select a figure from the options which will continue the same series as established by the five problem figures.



A.



B.

None One Two Three



6.

There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the given options, which will replace the (?) in figure 4.

A.







C.











D.

D.

A. B. C. D.

B.

C.

4 4 4 4

× 5 + 9 – 3 ÷ 4 = 15 × 5 × 9 + 3 ÷ 4 = 11 – 5 ÷ 9 × 3 – 4 = 17 ÷ 5 + 9 – 3 + 4 = 18







3.

Rahul told Anand, "Yesterday I defeated the only brother of the daughter of my grandmother." Whom did Rahul defeat?



A. B. C. D.

4.

Which is the third number to the left of the number which is exactly in the middle of the following sequence of numbers?

7.

Select the pair from the given options that has a relationship similar to that in the Figure (X).

Son Father Cousin Brother

1 2 3 4 5 6 7 8 9 2 4 6 8 9 7 5 3 1 9 8 7 6 5 4 3 2 1

A. B. C. D.

3 4 5 6

5.

If '–' stands for 'division', '+' for 'multiplication', '÷' for 'subtraction' and '×' for 'addition', then which one of the following equations is correct?

I

II

Figure (X)



A.

I

II



B.

I

II

I

II

I

II

C.

D.







3

7th IMO - Set B 8.

Select the correct mirror image of Figure (X). a

R N

b

c d

Figure (X)

c

B.



d c

C.



c

D.

b d



9.

d

b

Figure (X)

a

R N

b a

R N

d

A.



B.



In an imaginary language, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are substituted by a, b, c, d, e, f, g, h, i and j & 10 is written as ba. A. B. C. D.







Then, baf ÷ bf × d is equal to

44826 44882 46682 44682



a



R N



c

R N

A. B. C. D.

12. Which of the following shapes is exactly embedded in the Figure (X)?

b

a

A.





C.





D.

13. Find the missing character in the number pattern given below. 25

df cb be d

16 361 1 81

10. Select a figure from amongst the option figures, which will continue the series established by the four problem figures. ?



A. B. C. D.

4

9

64 289 16 9



14. In the following question, find out which of the options completes the figure matrix?



? Figure (X)



C.





D.



11. In a certain code language, 24685 is written as 33776. How is 35791 written in that code?

81

260 269 324 429

B.

? 25

A.

1



A.



B.



C.



D.



4

7th IMO - Set B

15. The given question consists of a set of three figures showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely resemble the unfolded form of paper.

X

Y

Z

A.

A.





















AB7CD9Z4 P2M c KS3 5NT a Which of the following letters is exactly midway between the 4th letter from left end and 6th letter from right end?

A. B. C. D.

K M P Y

17. Select the figure from the options which satisfies the same conditions of placement of dots as in Figure (X).









19. Which of the following statements is correct with respect to the given figure? C D A B



A. B. C. D.

A and B are in all the three shapes. E, A, B, C are in all the three shapes. F, C, D, B, A are in all the three shapes. Only B is in all the three shapes.

20. Select a figure from amongst the options which will continue the same series as established by the five problem figures.

A.





B.





B.



C.

C.







D.

D.



F

E

Figure (X)

A.

D.

16. Study the following arrangement of letters, digits and symbols to answer the question given below :









D.





C.

C.



B.

B.

18. Which of the following options will complete the pattern in Figure (X)?







5

7th IMO - Set B

Mathematical reasoning

Feet above or below sea level

21. The given bar graph shows heights of selected lakes. Find the difference in elevation for Lake E and Lake C. 600 600 512 500 300

26. Find the angles x and y respectively in the given figure.

245

200 100 – 92

0

B

– 52

B

C

D

E

F

G

420 604 504 692



A.



B.



C. D.



−5 −2 −3 1 6 , , , , 10 7 5 4 7 −3 −5 −2 1 6 , , , , 5 10 7 4 7 1 6 −5 −2 −3 , , , , 4 7 10 7 5 −2 −3 −5 1 6 , , , , 7 5 10 4 7

23. In the figure, ABCD is a rectangle, DCEF is an equilateral triangle. Find x.



A. B. C. D.

66º 60º 66º 60º

and and and and

y T x º 35

S

31º

E

R Q

º

A

A. B. C. D.

30º

P

– 100

22. Arrange the following numbers in the ascending order. 1 6 −3 −5 −2 , , , , 4 7 5 10 7



A

144

36



400

25. The triangle ABC and PQR may not be congruent when A. AB = PQ, AC = PR, ∠A = ∠P B. AB = PQ, AC = PR, BC = QR C. AB = PQ, AC = PR, ∠B = ∠Q D. ∠A = ∠P, ∠B = ∠Q, AB = PQ

C

84º 40º 48º 48º

D

27. Which of the following sum is in the simplest form? 4 −5 A. + 9 9 −5 11 + B. 12 −12 −2 13 + C. 5 20 −7 1 2 + + D. 8 12 3 28. Half of 1 percent written as a decimal is

A. B. C. D.

0.005 0.05 0.02 0.2

29. In the given diagram, PQU is an equilateral triangle, QRVU is a square and RSTU is a rhombus. Find the perimeter, in cm, of the whole diagram. P

A. B. C. D.

25º 30º 20º 50° 1 4 + x x −1 23 − x ( x − 8) + + = 7− . 5 4 7 5 7 8 5 9

Q

4 cm

U 5 cm

R

V

24. Solve for x :

A. B. C. D.



A. B. C. D.

17 21 26 27

S

T

6

7th IMO - Set B

30. 40% of 1640 + ? = 35% of 980 + 150% of 850

A. B. C. D.

372 842 962 1052



31. Form an equation of the form ax + b = c, where a, b and c are constants, such that the solution of the equation is x = 4.

A. B. C. D.

2x 7x 5x 3x

+ + + +

33. Which of the following statement do not hold in the process of solving the equation 15 + 3x = 3?

5 2 4 4

= = = =



A. B. C.

D.

3x = 3 – 15 15 – 3 = – 3x 3x 15 + =3 3 15 3 x 3 + = 3 3 3

34. Simplify, the expression by removing brackets.

15 10 16 16

32. In the given figure, if PR = QR, ∠SRP = ∠TRQ and ∠SQP = ∠TPQ, then S T



a − 2b − [4a − 6b − {3a − c + (5a − 2b − 3a − c + 2b)}] A. 5a + b B. 4a – c C. 3a + b + c D. 2a

35. In the given figure, the given lengths of DPQR are in centimetres. If PQ = PR, find the length of QR. Q

P



A. B. C. D.

DSQR DSQR DRQS DQRS

@ @ @ @

R

2x – 3

5x + 1

Q

DPTR & SR = TR DTPR & SR = TR DTPR & SR = TR DPRT & SR = TR

P 2x + 13



A. B. C. D.

3 4 5 6

cm cm cm cm

R

everyday Mathematics 36. A man buys an article for ` 27.50 and sells it for ` 28.60. Find his gain percent.

A. B. C. D.

4% 5% 12 % 8%

37. A sum of money invested at simple interest triples itself in 8 years. How many times will it become in 20 years time?

A. B. C. D.

8 times 7 times 6 times None of these

38. The price of a watch is ` 50 more than twice the price of a gold ring. Let the price of the ring be ` x. If the price of the watch is ` 208, find the price of the ring.

A. B. C. D.

` ` ` `

85 79 88 75

39. Anish borrowed ` 15000 at the rate of 12% and another amount at the rate of 15% for two years. The total interest paid by him was ` 9000. How much did he borrow?

A. B. C. D.

` ` ` `

31000 33000 28000 18000

40. A car was purchased for ` 80,000. Its value depreciates every year by 20%. Find the value of the car at the end of 2 years.

A. B. C. D.

` ` ` `

51,600 51,200 52,100 52,400

41. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

A. B. C. D.

14 18 16 15

times times times times

7

7th IMO - Set B 42. The price of a table is `100 less than 6 times the price of a chair. A similar set of one table and 4 chairs is priced at `1400. Find the price of a chair.





44. A bag contains an equal number of one rupees, 50 paise and 25 paise coins respectively. If the total value is ` 35, how many coins of each type are there?

A. B. C. D.

` ` ` `

140 150 148 145

43. A rectangular grass plot 80 m × 60 m has two roads, each 10 m wide, running in the middle of it, one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at `2 per m2 .



A.

` 2600



B. C. D.

A. B. C. D.

` 2700 ` 2750 ` 2800

20 15 25 18

1 45. A car is moving at an average speed of 3 km/hr. 9 1 How much distance will it cover in 5 hours? 7 A. 15 km B. 16 km C. 17 km D. 18 km

ACHIEVERS SECTION 46. The diagram shows a rectangle. Which rectangle, A, B, C or D, has a shaded area which is the same as the shaded area in diagram? (The length and breadth of rectangle PQTU and each of the rectangles A, B, C and D are the same). 11 cm

P

U

6 cm

Q 3 cm

P

R

U

A.



T

Q P 6 cm V

U



T

Q P 5 cm V





P

T

R V

U

D.



Q

T



What is the principal sum? I. The sum amounts to ` 690 in 3 years at S.I. II. The sum amounts to ` 750 in 5 years at S.I. III. The rate of interest is 5% p.a.



A. B. C. D.

I and III only II and III only I and II only Any two of the three

If Mrs. Kapoor buys 3 mangoes and uses the rest of the money to buy apples, then

U

C. Q

T

48. Mrs. Kapoor has certain sum of money to buy fruits. She can buy n mangoes at ` 1.60 each and have ` 0.80 left. Alternatively, she can buy (n + 10) apples at ` 0.70 each and have ` 0.10 left.

B.

S

47. In the given question, a question is asked and is followed by three statements. While answering the question, you may or may not require the data provided in all the statements. You have to read, the question and the three statements and then decide whether the question can be answered with any one or two of the statements or all the three statements are required to answer the question. Select the correct option.



(a) Find the value of n. (b) How much money does Mrs. Kapoor have for buying fruits? a b A. 10 ` 10.02 B. 10 ` 14.20 C. 6 ` 14 D. 7 ` 12

8

7th IMO - Set B

49. Select the incorrect match.

A. B. C. D.

Cube Cylinder Triangular Pyramid Cuboid

Faces 6 1 4 6

Edges Vertex 12 1 6 12

8 1 4 8

50. Statement I : If four quantities a, b, c and d are such that the ratio a : b is equal to the ratio c : d, then we say a, b, c and d are in ratio and a:b:c:d. Statement II : If a : b = 5 : 9 and b : c = 4 : 7, then a : b : c = 20 : 36 : 63. A. Both statements I and II are true. B. Statement I is true and statement II is false. C. Statement I is false and statement II is true. D. Both statements I and II are false.

SPACE FOR ROUGH WORK

ANSWER KEYS 3 rd  IMO  (2009)  1.  (D)  11.  (A)  21.  (C)  31.  (C)  41.  (A) 

2.  (B)  12.  (A)  22.  (A)  32.  (D)  42.  (A) 

3.  (C)  13.  (D)  23.  (B)  33.  (B)  43.  (D) 

4.  (D)  14.  (B)  24.  (C)  34.  (C)  44.  (C) 

5.  (A)  15.  (B)  25.  (B)  35.  (D)  45.  (C) 

6.  (A)  16.  (B)  26.  (D)  36.  (A)  46.  (D) 

7.  (A)  17.  (A)  27.  (D)  37.  (D)  47.  (B) 

8.  (C)  18.  (B)  28.  (B)  38.  (D)  48.  (B) 

9.  19.  29.  39.  49. 

(B)  (A)  (A)  (A)  (D) 

10.  20.  30.  40.  50. 

(D)  (C)  (C)  (B)  (D) 

7.  (B)  17.  (D)  27.  (A)  37.  (C)  47.  (C) 

8.  (A)  18.  (C)  28.  (B)  38.  (D)  48.  (B) 

9.  19.  29.  39.  49. 

(B)  (B)  (B)  (C)  (B) 

10.  20.  30.  40.  50. 

(C)  (C)  (D)  (B)  (A) 

7. 17. 27. 37. 47.

(A)  (B)  (D)  (D)  (C) 

8. 18. 28. 38. 48.

(C)  (A)  (C)  (C)  (D) 

9. 19. 29. 39. 49.

(B)  (D)  (B)  (D)  (C) 

10. 20. 30. 40. 50.

(A)  (B)  (D)  (B)  (B) 

7. 17. 27. 37. 47.

(B)  (C)  (B)  (C)  (B) 

8. 18. 28. 38. 48.

(B)  (A)  (C)  (A)  (C) 

9. 19. 29. 39. 49.

(D)  (C)  (C)  (D)  (D) 

10. 20. 30. 40. 50.

(C)  (D)  (C)  (B)  (A) 

7.  (B)  17.  (D)  27.  (B)  37.  (D)  47.  (B) 

8.  (D)  18.  (B)  28.  (A)  38.  (B)  48.  (C) 

9.  19.  29.  39.  49. 

(A)  (C)  (C)  (B)  (B) 

10.  20.  30.  40.  50. 

(D)  (B)  (A)  (D)  (D) 

7.  (C)  17.  (B)  27.  (B)  37.  (A)  47.  (A) 

8.  (D)  18.  (C)  28.  (D)  38.  (B)  48.  (B) 

9.  19.  29.  39.  49. 

(D)  (D)  (B)  (C)  (D) 

10.  20.  30.  40.  50. 

(C)  (C)  (C)  (D)  (C) 

7.  (D)  17.  (C)  27.  (A)  37.  (C)  47.  (D) 

8.  (B)  18.  (B)  28.  (A)  38.  (B)  48.  (D) 

9.  19.  29.  39.  49. 

(B)  (D)  (D)  (B)  (B) 

10.  20.  30.  40.  50. 

(B)  (D)  (C)  (B)  (C)

4 th  IMO (2010)  1.  (B)  11.  (D)  21.  (C)  31.  (A)  41.  (D) 

2.  (D)  12.  (B)  22.  (C)  32.  (B)  42.  (A) 

3.  (B)  13.  (A)  23.  (C)  33.  (A)  43.  (C) 

4.  (D)  14.  (D)  24.  (C)  34.  (D)  44.  (D) 

5.  (B)  15.  (A)  25.  (A)  35.  (C)  45.  (D) 

6.  (C)  16.  (C)  26.  (D)  36.  (A)  46.  (C) 

5 th  IMO (2011)  1. 11. 21. 31. 41.

(C)  (C)  (B)  (A)  (D) 

2. 12. 22. 32. 42.

(A)  (B)  (B)  (A)  (B) 

3. 13. 23. 33. 43.

(B)  (D)  (C)  (D)  (B) 

4. 14. 24. 34. 44.

(D)  (D)  (B)  (B)  (B) 

5. 15. 25. 35. 45.

(B)  (B)  (C)  (B)  (A) 

6. 16. 26. 36. 46.

(B)  (D)  (B)  (B)  (A) 

6 th  IMO (2012)  SET A  1. 11. 21. 31. 41.

(B)  (D)  (B)  (D)  (D) 

2. 12. 22. 32. 42.

(D)  (B)  (B)  (A)  (B) 

3. 13. 23. 33. 43.

(B)  (A)  (D)  (C)  (C) 

4. 14. 24. 34. 44.

(D)  (B)  (A)  (A)  (D) 

5. 15. 25. 35. 45.

(C)  (A)  (D)  (C)  (A) 

6. 16. 26. 36. 46.

(C)  (D)  (C)  (B)  (D) 

SET B  1.  (D)  11.  (C)  21.  (A)  31.  (D)  41.  (B) 

2.  (A)  12.  (D)  22.  (A)  32.  (C)  42.  (B) 

3.  (C)  13.  (D)  23.  (D)  33.  (D)  43.  (A) 

4.  (B)  14.  (D)  24.  (B)  34.  (D)  44.  (D) 

5.  (C)  15.  (B)  25.  (B)  35.  (C)  45.  (D) 

6.  (A)  16.  (C)  26.  (C)  36.  (D)  46.  (C) 

7 th  IMO (2013)  SET A  1.  (B)  11.  (A)  21.  (C)  31.  (B)  41.  (A) 

2.  (C)  12.  (C)  22.  (B)  32.  (A)  42.  (C) 

3.  (C)  13.  (C)  23.  (C)  33.  (D)  43.  (D) 

4.  (A)  14.  (D)  24.  (D)  34.  (B)  44.  (B) 

5.  (B)  15.  (D)  25.  (A)  35.  (C)  45.  (C) 

6.  (B)  16.  (A)  26.  (B)  36.  (D)  46.  (C) 

SET B  1.  (B)  11.  (B)  21.  (B)  31.  (D)  41.  (C) 

2.  (D)  12.  (C)  22.  (B)  32.  (B)  42.  (B) 

3.  (B)  13.  (C)  23.  (A)  33.  (C)  43.  (A) 

4.  (B)  14.  (D)  24.  (B)  34.  (D)  44.  (A) 

5.  (A)  15.  (D)  25.  (C)  35.  (C)  45.  (B) 

6.  (D)  16.  (C)  26.  (C)  36.  (A)  46.  (B)