Solved Papers

International Mathematics Olympiad - 2010

Section I : Logical Reasoning

1. What
is the sum of the shaded parts if shaded
parts are expressed in fractions?
(b)

11
(a) (b) 11
9 7
11 7 (c)
(c) (d)
18 18
2. A coach asked 3 players on a basketball (d) None of these
team to attempt 25 free throws each during
practice. The given table shows the number of 4. The given table shows the starting and end
free throws each player made in 25 attempts. time of a movie at a theatre. According to
Based on the information in the table, which the information in the table, which of the
is the most reasonable prediction of the following statements is true?
number of free throws Armaan will make out Movie times
of his next 75 attempts?
Start End
Free throws
12:30 P.M. 2:45 P.M.
Player Number of free 3:00 P.M. 5:15 P.M.
throws made
6:45 P.M. 9:00 P.M.
Piysuh 12
9:20 P.M. 11:35 P.M.
Siddharth 18
(a) The end time is exactly 2 hours
Armaan 5 45 minutes after the start time.
(a) 12 (b) 60 (b) The end time is exactly 2 hours
(c) 15 (d) 5 15 minutes after the start time.
3. Which net will make this figure? (c) The end time is exactly 3 hours
30 minutes after the start time.
(d) The end time is exactly 3 hours
45 minutes after the start time.
5. Which of the following shapes do not have a
line of symmetry?

(a)

International Mathematics Olympiad - 2010 3

 (a) P and Q only (b) P and R only 11. Study the diagram and identify the students
(c) Q and R only (d) Q and S only who play all the three games.
6. A truck departs from a distribution center.
From there, it goes 2 blocks east, 3 blocks
south and 3 blocks north. How far and in
which direction must the truck go to get back
to the distribution centre?

(a) P + Q + R (b) V + T
(c) S + T + V (d) S
12. Arrange the words given below in a mean-
ingful sequence.
(i) Fibre (ii) Planet
(a) 4 blocks west (b) 4 blocks east
(iii) Saree (iv) Cotton
(c) 2 blocks west (d) 2 blocks east
(v) Cloth
7. The letters S and T stand for numbers. If S – (a) (ii), (iv), (v), (i), (iii)
100 = T – 100, which statement is true?
(b) (ii), (iv), (iii), (v), (i)
(a) S = T (b) S > T
(c) (ii), (iv), (i), (v), (iii)
(c) S = T + 100 (d) S > T + 100
(d) (ii), (iv), (v), (iii), (i)
8. Class A has higher enrolment than class B.
13. Six friends P, Q, R, S, T and U are sitting
Class C has a lower enrolment than class B. around a hexagonal table, each at one corner
Class A has a lower enrolment than class C. and are facing the centre of the hexagon. P
is second to the left of U. Q is neighbour of
If the first two statements are true, the third
R and S. T is second to the left of S. Who is
statement is ______
sitting opposite to P?
(a) True (b) False
(a) R (b) Q
(c) Uncertain (d) None of these
(c) T (d) S
9. Rahul put his timepiece on the table in such
14. Which letter replaces the question mark?
a way that at 6:00 P.M. the hour hand points
to North. In which direction will the minute
hand point at 9:15?
(a) South – East (b) South
(c) North (d) West
10. Which number will be on the face opposite to
the face which has 2 on it?

(a) M (b) P
(c) E (d) W

(a) 1 (b) 5
(c) 4 (d) 6

4 International Mathematics Olympiad – Class 6

15. Which of the following options can replace 18. The list given below shows the number of
the last grid? students out of 30 who chose different foods
in the cafeteria.
(i) 11 students chose pizza.
(ii) 4 students chose hamburgers.
(iii) 3 students chose tacos.
(a) (b) (iv) __?__ students chose salad.
How many students chose salad?
(a) 18, because 11 + 4 + 3 = 18
(b) 26, because 30 – (11 – 4) – = 26
(c) (d)
(c) 12, because 30 – 11 – 4 – 3 = 12
(d) 20, because 30 – (11 – 4) – 3 = 20
16. Which single transformation is shown below? 19. Look at the graph:

(a) Reflection (b) Rotation On which day did Kirti receive the fewest
text messages?
(c) Translation (d) None of these
(a) Tuesday (b) Wednesday
17. Look at the square and the cube shown in
(c) Thursday (d) Friday
figure. Which of the following statements
about both of these figures appears to be true? 20. A coach conducted a survey to determine how
many students plan to tryout tennis and golf.
The results of the survey are shown below.
(i) A total of 30 students plan to tryout tennis.
(ii) A total of 40 students plan to tryout golf.
(iii) 10 students plan to tryout both tennis and
golf.
(a) The square has 4 times as many vertices Which of the following diagrams best
as the cube. represents this information?
(b) The square is congruent to each face on
the cube.
(c) The square has 3 fewer sides than the
(a)
cube has edges.
(d) The square has the same number of right
angles as the cube.

International Mathematics Olympiad - 2010 5

 (b) (d)

(c)

Section II: Mathematical Reasoning

21. Sneha bisects an angle to form two new 24. QS and TV are parallel lines.
angles. If the original angle had a measure of Which angles are supplementary angles?
8°, what is the measure of each new angle?

(a) 8° (b) 20°

(c) 4° (d) 16°
22. Rehan attended a basketball camp for two
(a) ∠VUW and ∠QRP
weeks. His parents paid ` 50.00, which was
1 (b) ∠VUW and ∠SRU
the cost of attending the camp. Rehan (c) ∠VUW and ∠VUR
3
had saved money to pay the rest of the cost. (d) ∠VUW and ∠TUR
Which equation can be used to find c, the
25. A veterinarian weighed all the dogs that
entire cost of attending the camp?
visited her office last month.
1 Use the data to complete the frequency chart
(a) c = 50 × (b) c = 50 × 3
3 shown below.
1 1
(c) c = (d) c = 3× Dog weights (lbs)
(50 × 3) 50
23, 27, 27, 39, 43, 45, 46, 47, 49, 50, 53, 55,
23. Which digit makes the given sentence true? 58, 59, 64, 71, 83, 84, 86, 88, 89, Find the
58, 314, 70 ? is divisible by 5. missing number.
(a) 4 (b) 5
(c) 9 (d) 1

6 International Mathematics Olympiad – Class 6

 Dog weights
Weight (lbs) 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 80 – 89
Number of dogs 3 1 6 1 1 5

(a) 5 (b) 6 30. The given table shows the area, in square
(c) 9 (d) 9 kilometers, of four lakes. Lake E has a greater
area than lake O but a smaller area than Lake
26. Prachi took a total of 2 hours to write 30 party
M. Which could be the area of Lake E ?
invitations. Which of the following equations
can be used to find m, the number of minutes (a) 76,760 km2
Prachi took to write 1 invitation? (b) 57,800 km2
(a) (60 ÷ 30) ÷ 2 = m (c) 25,700 km2
(b) (60 × 30) + 2 = m (d) 18,960 km2
(c) (60 ÷ 2) × 30 = m 31. Sara is counting by 3’s. If she starts counting
(d) (60 × 2) ÷ 30 = m at –30, what are the two missing numbers?
27. Which symbol is located at –3 on the number –30, –27, –24, –21, _?_, _?_, –12
line shown below? (a) –18, –15
(b) –19, –17
(c) –20, –13
(d) –22, –23
32. Which of the following statements about the
(a) (b) 3-dimensional figure appears to be true?

(c) (d)

28. The figure is made of three squares joined

together.
What is the area of the figure in square cm?
(a) It has no congruent faces.
(b) It has 3 congruent rectangular faces.
(c) It has 6 congruent faces.
(d) It has 3 congruent triangular faces.
33. Which equation does this set of algebra tiles
represent?

(a) 9 square cm (b) 18 square cm

(c) 27 square cm (d) 81 square cm
29. Which of the following squares would you
shade to make the figure symmetrical ?
(a) B and D (b) A and C
(c) D and C (d) B and C

International Mathematics Olympiad - 2010 7

 (a) X + 1 = 10 38. Which relationship between units of time is
(b) X + 6 = 10 correct?
(c) X + 1 = 3 1
(a) One hour is of one year
(d) X + 6 = 3 365
1
34. Find the value of (24 – 16) × 8 – 64 ÷ (10 – 2) (b) One hour is of one hour
+ 4. 365
(a) 60 (b) 56 1
(c) One second is of one minute
(c) 16 (d) 24 60
1
35. Karan is k years old. Rahul’s age, r, is 6 (d) One minute is of one second
more than 2 times Karan’s age. Which of the 60
following equations best represents Rahul’s 39. Rohan rolled 3 fair number cubes, and the
age? numbers shown below came out on top. If
(a) r = (6 + 2) k (b) k = 2r + 6 each number is used only once, which group
(c) r = 2k + 6 (d) k = (6 + 2) r shows all the 3-digit numbers that can be
36. Abhay found the perimeter of a square to be made with these digits?
12 metres. Which of the following could be 4 5 6
used to find the length (l) of one edge of the
square? (a) 456, 565, 654, 544, 655, 645
(a) l = 4 × 12 (b) l = 12 ÷ 4 (b) 456, 546, 654, 645, 556, 664, 555
(c) l = 4 + 12 (d) l = 4 – 12 (c) 456, 465, 564, 564, 546, 444
37. Vikas Electronics Store is having a sale. To (d) 456, 465, 564, 546, 645, 654
advertise the sale, the store manager wants
40. Look for the pattern of the three sequence of
to outline the store window with colourful
numbers given below.
ribbon.
2, 4, 6, 8, 10
How many metres of ribbon will be needed to
outline the 4 sides of the window? 7, 14, 21, 28, 35
11, 22, 33, 44, 55
Each sequence is an example of what kind of
numbers?
(a) Even numbers (b) Multiples
(c) Primes (d) Odd numbers

(a) 35 m (b) 24 m
(c) 19 m (d) 32 m

8 International Mathematics Olympiad – Class 6

 Section III: Everyday Mathematics
41. Ms. Neha needs to replace the batteries in 20 Deposit Rs. 24
calculators. Each calculator uses 4 batteries.
The batteries are sold in packages of 16. How First hour Rs. 12
many packages of batteries does Ms. Neha Every additional hour and Rs. 10
need to buy? part there of
(a) 64 (b) 4 Ashmit intend to hire the buggy from 8 : 15 a.m. to
(c) 80 (d) 5 2 : 30 p.m. how much does he has to pay?
7 (a) ` 86 (b) ` 96
42. Sasha is using a wooden strip m long to (c) ` 56 (d) ` 76
8
make a picture frace. If she cuts off a piece 47. Coach kabir needs to buy 12 T.shirts for girl’s
3 basket ball team. The list below shown the
that is m long. Which fraction best
4 prices of T-shirt’s at two stores.
represents the portion that is left of the (i) Store X: one T-shirt costs Rs. 250
original strip? (ii) Store Y: A package of 6 T-shirts costs Rs.
13 1200
(a) m (b) 1 m
8 What is the amount of money coach Kabir
1 1 will save if he buys 12 T-shirts from store Y.
(c) m (d) m
4 8 (a) ` 600 (b) ` 400
43. It takes 90 minutes to wash 20 vehicles at (c) ` 1650 (d) ` 375
a car wash. At this rate, how many minutes 48. There were 180 members in the club last year
does it takes to wash 5 vehicles? the membership decreased by 15% this year.
(a) 22 mins (b) 14 mins How many members are there this year?
1 1 (a) 27 (b) 135
(c) 22 mins (d) 7 mins
2 2 (c) 153 (d) 207
44. The weekly milk order of Aryan’s shop 49. Armaan received ` 2800 as a gift. He wanted
includes 40 litres of low – fat milk and 15 to use the money to go to the movies and to
litres of chocolate milk. What is the ratio of buy a book. He wanted to save the money he
the litres of low fat milk to chocolate milk in had left. Which is the correct order of steps
Aryan’s weekly milk order? to find the amount of money Armaan would
(a) 3 : 1 (b) 5 : 1 have left to save?
(c) 5 : 3 (d) 8 : 3 Step K: Find the sum of the costs of the movie
and the book.
45. Sneha earns ` 110 each week taking care
of pets. Which of the following is the best Step L: Find the difference between ` 2800
estimate of how much money she will earn in and the sum of the costs of the movie and the
28 weeks while taking care of the pets? book.
(a) ` 1000 (b) ` 500 Step M: Identify the cost of the movie and the
(c) ` 9000 (d) ` 3080 cost of the book.
46. At a park, Ashmit intends to hire a buggy to (a) L, K, M (b) M, K, L
help him get around more easily. The table (c) L, M, K (d) K, L, M
shows the rate for hiring a buggy.

International Mathematics Olympiad - 2010 9

50. Mohit sliced an orange into circular pieces to put into a bowl of punch. The piece shown below had
a radius of 4 centimetres. Which expression can be used to find the approximate circumference of
this piece of orange?
(a) π × (4)2 (b) 4 × π
(c) 2 × π × 7 (d) 2 × π × 4

Answer Key
1. (a) 2. (c) 3. (b) 4. (b) 5. (b) 6. (c) 7. (a) 8. (b) 9. (d) 10 (d)
11. (d) 12. (c) 13. (d) 14. (a) 15. (d) 16. (c) 17. (b) 18. (c) 19. (b) 20. (a)
21. (c) 22. (b) 23. (b) 24. (c) 25. (a) 26. (d) 27. (a) 28. (c) 29. (b) 30. (c)
31. (a) 32. (b) 33. (b) 34. (a) 35. (c) 36. (b) 37. (b) 38. (c) 39. (d) 40. (b)
41. (d) 42. (d) 43. (c) 44. (d) 45. (d) 46. (b) 47. (a) 48. (c) 49. (b) 50. (d)

Hints and Solution

21. (c) 34. (a)
1 (24 – 16) × 8 – 64 ÷ (10 – 2) + 4
Measure of each new angle 8° × = 4°
2 = 8 × 8 – 64 ÷ 8 + 4
22. (b) = 64 – 8 + 4
c = 50 × 3 = 68 – 8
26. (d) = 60
(60 × 2) ÷ 30 = m 35. (c)
28. (c) r = 2k + 6
Area of square ABCD + Area of square BDFE 36. (b)
+ Area of square BEHG. l = 12 ÷ 4

= (3)2 + (3)2 + (3)2 39. (d)
=9+9+9 456, 465, 546, 564, 645, 654.
= 27 cm2 41. (d)
31. (a) 20 × 4
Number of packages = =5
–21 + 3 = – 18 16
–18 + 3 = – 15 42. (d)
7 3 7−6 1
Required fraction = − = =
8 4 8 8

10 International Mathematics Olympiad – Class 6

43. (c) 47. (a)
90 × 5 45 1 Required fraction = 12 × 250 – (2 × 1200)
Time taken = = = 22 mins.
20 2 2 = 3000 – 2400 = 600
44. (d)
48. (c)
40 8
Ratio = = = 8:3 15 × 180
15 3 Here, 15% of 180 = = 27; 180 – 27
100
45. (d) = 153
Total earnings = 110 × 28 = ` 3080
46. (b)
Required fraction = 24 + 12 + 60 = 96.

International Mathematics Olympiad - 2010 11

International Mathematics Olympiad - 2011
Section I: Logical Reasoning
1. If husband is called wife, wife is called 5. Figures (i), (ii), (iii) and (iv) constitute the
grandfather, grandfather is called grand- problem set. There is a definite relationship
mother, grandmother is called maternal between figures (i) and (ii). Establish a similar
grandmother, maternal grandmother is called relationship between figures (iii) and (iv) by
maternal grandfather, maternal grandfather is selecting a suitable figure from the options
called maternal uncle and maternal uncle is that would replace (?) in figure (iv).
called maternal aunt, then what will the father
of the mother be called?
(a) Maternal grandmother
(b) Maternal uncle
(c) Maternal grandfather
(d) Maternal aunt
2. Which set is most like the given set?
(a) (4, 9, 20) (a) (b)
(b) (16, 33, 67)
(c) (13, 30, 67)
(d) (5, 12, 25)
3. There are four figures (a), (b), (c) and (d). (c) (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 6. Find the figure from the options which
different from the rest. completes the pattern in fig. (X).

(a) (b)

(c) (d)

4. Five girls are standing in a row facing east.

Savita is to the right of Urvashi, Tina and
(a) (b)
Urmila. Urvashi, Tina and Urmila are to the
right of Kanika. Urmila is between Urvashi
and Tina. If Tina is fourth from the left end,
how far is Urvashi from the right end?
(c) (d)
(a) First (b) Second
(c) Fifth (d) Fourth

12 International Mathematics Olympiad – Class 6

 7. I n the given fig. (X), which one of the options (d) Data inadequate
will replace the question mark? 11. A, B, C, D, E, F and G are sitting in a row
facing North.
(i) F is to the immediate right of E.
(ii) E is 4th to the right of G.
(iii) C is the neighbour of B and D.
(iv) Person who is third to the left of D is at
one of the ends.
Who are the neighbour of B?
(a) C and D (b) C and G
(c) G and F (d) C and E
12. Find the figure from the options which will
continue the series established by the problem
figure.

(a) (b)

(c) (d) (a) (b)

8. Complete the number series given below.

1, 4, 2, 8, 6, 24, 22, 88, (?). (c) (d)
(a) 86 (b) 352
(c) 90 (d) 154
9. Find out from the options which is the mirror 13. Find the odd one out.
– image of the given word, if the mirror is
placed vertically right. (a) (b)
CONTENTS
(a) STNETNOC
(b) STNETNO C
(c) STNETNOC (c) (d)
(d) Data Inadequate
10. In a unit test Sonakshi’s marks in Mathematics
are more than her marks in History but not 14. Some letters are given which are numbered 1,
more than her marks in Geography. Her 2, 3, 4 and 5. Find the combination of numbers
marks in Science are more than her marks in from the options so that the letters arranged
History but not as much as in Mathematics accordingly form a meaningful word.
and her marks in English are not as much as ERPIC
in Geography. In which subject did she score 12345
the lowest? (a) 3, 2, 4, 1, 5 (b) 3, 2, 1, 4, 5
(a) History (b) English (c) 3, 2, 4, 5, 1 (d) 3, 2, 1, 5, 4
(c) Science

International Mathematics Olympiad - 2011 13

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

(b)
(a) (b)

(c) (d) (c)

16. Pia walks a distance of 4 metres towards

south. Then she turns to the left and walks
3 metres. after this she turns to the right and
walks 4 metres. Now which direction is she (d)
facing?
(a) North – East (b) South
(c) North (d) South – West 19. Which number will replace the question mark
in the given pattern?
17. If in a certain code 15789 is written as
XTZAL and 2346 as NPSU then how will
23549 be written in the same code ?
(a) NPTUL (b) PNTSL (a) 8 (b) 12
(c) NPTSL (d) NBTSL (c) 16 (d) 20
18. In the given question, out of these four pairs 20. If ‘+’ means ×, ‘–’ means ÷, ‘×’ means –, and
of figures only one pair has a relationship ‘÷’ means +, then
similar to the pair in figure (X). Which is that 16 ÷ 64 – 8 × 4 + 2 = ?
pair?
(a) 12 (b) 16
(c) 18 (d) 24

14 International Mathematics Olympiad – Class 6

 Section II: Mathematical Reasoning
21. What is the value of p + q in the given number 27. If (k – 8) is the highest common factor of 56
line ? and 77, then the value of k is ____.
(a) 7 (b) 11
(c) 15 (d) 16
28. The number of edges in the given figure is
(a) – 9 (b) – 6
______ .
(c) – 3 (d) – 3
22. Fill in the blank:
1 million = --------- hundred thousand.
(a) One (b) Ten (a) 8 (b) 9
(c) Hundred (d) Twenty (c) 10 (d) 11
23. Which of the following statements is 29.
The Hindu – Arabic numeral form for
CORRECT? XCCMXCIX is _____ .
(a) All whose numbers are natural numbers. (a) 1099 (b) 9099
(b) Every natural number has a predecessor. (c) 1089 (d) 999
(c) Division by zero is not defined. 30. Estimate the sum of (21397 + 42505) to
(d) Every whole number has a predecessor. nearest thousand.
24. The sum of the prime factors of 63 is ____. (a) 64000 (b) 65490
(a) 4 (b) 8 (c) 70000 (d) 92000
(c) 10 (d) 14 31. Which of the following numbers is divisible
by 9?
25. How many right angles are there in 3 complete
turns? (a) 9076185 (b) 92106345
(a) 16 (b) 12 (c) 10349576 (d) 95103476
(c) 8 (d) 4 32. Find the value of – 12 – (– 48) – [(–13) + (–
8) – (–3) + 4].
26. An oil tank contains 30 2 litres of oil. It is (a) – 48 (b) 50
5
(c) – 12 (d) 62
then filled with 37 2 litres of oil. Later,
3 33. Which of the following has fractions in
1 ascending order?
56 litres of oil is pumped out from the
9 3 2 7 9 8
2 3 7 9 8
(a) , , , , (b) , , , ,
tank. What is the volume of oil left in the tank 3 5 9 11 9 5 3 9 11 9
in litres? ‘
8 9 7 2 3 8 9 7 3 2
43 43 (c) , , , , (d) , , , ,
(a) 11 (b) 12 9 11 9 3 5 9 11 9 5 3
45 45
34. Find the value of X in the given expression.
8 4
(c) 37 (d) 18 832.58 – 242.31 = 779.84 – X
3 45
(a) 179.57 (b) 199.57
(c) 295.05 (d) 189.57

International Mathematics Olympiad - 2011 15

Direction (Q. 35 – 36): Look at the bar graph and answer the following questions.

35. In which month only 15 cars were sold?

(a) January (b) February
(c) April (d) May
(a)
36. How many cars were sold in the last quarter
of the year?
(a) 280 (b) 130
(c) 140 (d) 105
37. The length of a rectangular hall is 5 metres
more than its breadth. If the breadth of the
hall is 25 metres, then area of the hall is (b)
_____.
(a) 150m2 (b) 225m2
(c) 750m2 (d) 850m2
38. How many minimum squares must be shaded
to make the given figure symmetric?
(c)

(a) 1 (b) 2
(c) 3 (d) 4 (d)
39. Which of the following is an ISOSCELES
triangle?

16 International Mathematics Olympiad – Class 6

40. Count the number of line segments.

(a) 8 (b) 12
(c) 10 (d) 13

Section III: Everyday Mathematics

41. Four different electric devices make a beep 46. A lady parked her car on the 6th floor and took
a lift up 17 floor to the finance department.
after every 30 minutes, 1 hour, 1 1 hour and
2 She then went down 9 floors to the tax
1 hour 45 minutes respectively. All the department. On which floor would you find
devices beeped together at 12 noon. They will the lady?
again beep together at _____. (a) 14th (b) 15th
(a) 12 midnight (b) 3 a.m. (c) 23th (d) 26th
(c) 6 a.m. (d) 9 a.m. 47. Smriti bought 19 boxes of sweets. Each
42. Armaan was asked to multiply a number by box contains 228 sweets. How many sweets
25. Instead he multiplied the number by 52 would be left with her after giving 519 sweets
and got the answer 324 more than the correct to friends?
answer. The number to be multiplied was (a) 766 (b) 3,813
_____. (c) 4,332 (d) 4,851
(a) 12 (b) 15
1
(c) 25 (d) 32 48. Avni completed of her holiday homework
5
43. If one – third of a tank holds 80 litres of water, 3
on Monday and of it on Tuesday. How
then the quantity of water that half of the tank 4
holds is ____. much of her holiday homework did Avani
80 complete in the two days?
(a) litres (b) 100 litres
3
(a) 1 (b) 4
(c) 120 litres (d) 240 litres 9
3 19
44. In a class of 50 students, 15 are girls. 5 girls (c) (d)
20 20
2
and of the boys were chosen to play a 49. Pia, Ridhi and Muskaan divided 11.775 kg
7
of wheat flour equally among themselves.
match. The total number of students chosen
Pia used all her wheat flour equally to bake
to play a match is ____.
5 chocolate cakes. How much wheat flour did
(a) 12 (b) 15 each cake need?
(c) 19 (d) 25 (a) 0.665 kg (b) 3.92kg
45. The number of girls in a class is 5 times the (c) 0.875kg (d) 0.785kg
number of boys. Which of the following
50. If the temperature of city A is –20° C and the
cannot be the total number of children in the
temperature of city B is 10°C, the difference
class?
in the temperatures of the two cities is ____.
(a) 24 (b) 30
(a) –30°C. (b) –10°C
(c) 35 (d) 42
(c) 10°C (d) 30°C

International Mathematics Olympiad - 2011 17

 Answer Key
1. (b) 2. (d) 3. (d) 4. (d) 5. (d) 6. (c) 7. (b) 8. (a) 9. (a) 10 (d)
11. (b) 12. (d) 13. (d) 14. (c) 15. (c) 16. (b) 17. (c) 18. (a) 19. (c) 20. (b)
21. (b) 22. (b) 23. (c) 24. (c) 25. (b) 26. (a) 27. (c) 28. (b) 29. (c) 30. (a)
31. (a) 32. (b) 33. (b) 34. (d) 35. (a) 36. (d) 37. (c) 38. (b) 39. (d) 40. (c)
41. (d) 42. (a) 43. (c) 44. (b) 45. (c) 46. (a) 47. (b) 48. (d) 49. (d) 50. (d)

Hints and Solutions

21. (b) 28. (b)

p + q = – 9 + 3 = –6 29. (c)
22. (b) XCCMXCIX
23. (c) 30. (a)
24. (c) Clearly, 21397 + 42505 = 21000 + 43000 = 64000
63 = 3 × 3 × 7 31. (a)

∴ Required sum = 3 + 7 = 10 9076185 = 9 + 0 + 7 + 6 + 1 + 8 + 5 = 36
25. (b) 36 is divisible by 9.
3 × 360° So given number is divisible by 9.
No. of right angles = = 12
90° 32. (b)
– 12 – (–48) – [(–13) + (–8) – (–3) + 4]
26. (a)
= –12 + 48 – [–13 – 8 + 3 + 4]
2 2 1
Required volume = 30 + 37 − 56 = – 12 + 48 + 14
5 3 9
152 113 505 = 50
= + −
5 3 9 33. (b)
1368 + 1695 − 2525 3 2 7 9 8
= < < < <
45 5 3 9 11 9
538 34. (d) Given,
=
45 832.58 – 242.31 = 779.84 – X
43
= 11
⇒ X = 779.84 – 590.27 = 189.57
45
35. (a)
27. (c) We have 36. (d)
56 = 2 × 2 × 2 × 7 Required cars = 35 + 50 + 20 = 105
77 = 7 × 11 37. (c) Given,
Highest common factor = 7 Breadth = 25m
k – 8 = 7 ⇒ k = 7 + 8 = 15 Length = 25 + 5 = 30m
Area of hall = l × b = 30 × 25 = 750 m2

18 International Mathematics Olympiad – Class 6

38. (b) 44. (b)
39. (d) Girls = 15; Boys = 50 – 15 = 35.
40. (c) Total no. of students chosen to play a match
AB, BC, CD, DE, AC, BD, CE, AD, AE, BE. 2
= 5 + of 35
41. (d) 7
LCM of 30, 60, 90, 105 = 1260 = 5 + 10 = 15
1260 45. (c)
1260 minutes = = 21 hours. 24 = 4 + 5 × 4
60
12 noon + 21 hours = 9 a.m. 30 = 5 + 5 × 5
42. (a) 42 = 7 + 5 × 7
Let the number be x. 46. (a)
x × 52 – x × 25 = 324 47. (b) Required no. of sweets =

⇒ 27x = 324 228 × 19 – 519 = 4332 – 519 = 3813
324 48. (d)

⇒x= = 12
27 1 3 4 + 15 19
+ = =
5 4 20 20
43. (c) Here,
l 49. (d)
= 80 litres Required weight = 11.775 ÷ (5 × 3)
3
= 11.775 ÷ 15
l = 80 × 3 = 240 litres

= 0.785 kg
l 240
= = 120 litres 50. (d)
2 2
Difference in temperature = 10° – (–20°)
= 10° + 20° = 30°

International Mathematics Olympiad - 2011 19