What is the IMO pattern for Class 6?

50 multiple-choice questions for 60 marks in one hour: Logical Reasoning (15), Mathematical Reasoning (20), Everyday Mathematics (10), and 5 Achievers questions worth 3 marks each. There is no negative marking.

Is this a real IMO paper?

No. Every question is written by us in the published pattern, so it is safe to print and share. We are not connected with the Science Olympiad Foundation, which runs the IMO.

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Sit it in one go with a 60-minute timer, then mark it with the answers at the end. Go back over the questions that were missed: the working shows the method for each.

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IMO Sample Paper Class 6 with Answers (Free)

Section	Questions	Marks
Logical Reasoning	15	15
Mathematical Reasoning	20	20
Everyday Mathematics	10	10
Achievers Section	5	15
Total	50	60

Scholar Tests · Sample paper

Maths olympiad sample paper, Class 6

50 questions · 60 marks · 60 minutes · no negative marking

Name ______________________ Date ____________

Section 1: Logical Reasoning

Questions 1 to 15, 1 mark each. Circle the letter of the best answer.

1.
The arrows in this grid follow a rule. Which arrow belongs where the question mark is?
1. A
2. B
3. C
4. D
2.
In a secret code, each digit is always written as the same symbol, in the same order as the digits. 637 is written □ ● ✚ and 692 is written □ ★ ♥. How is 672 written in the code?
1. A♥ ✚ □
2. B● ● ★
3. C□ ✚ ♥
4. D□ ● ♥
3.
If HAT is written in code as KDW, how is PIG written in the same code?
1. AGIP
2. BTMK
3. CMFD
4. DSLJ
4.
Which word does not belong with the others?
1. Aappendix
2. Battic
3. Cglossary
4. Dindex
5.
Three views of the same cube are shown below. Each of its six faces carries a different number from 1 to 6. What is the sum of all the numbers on the faces next to (touching) the face numbered 3?
1. A20
2. B17
3. C16
4. D13
6.
Which letter comes next in this series? K, N, Q, T, …
1. AZ
2. BT
3. CX
4. DW
7.
Which figure is the odd one out?
1. A
2. B
3. C
4. D
8.
Each row of pictures follows the same rule from left to right. Which picture belongs where the question mark is?
1. A
2. B
3. C
4. D
9.
Look at the grid below. The same rule works in every row. What number should replace the question mark?
1. A19
2. B17
3. C10
4. D18
10.
17 April is a Wednesday. What day of the week is 2 May? (April has 30 days.)
1. AThursday
2. BFriday
3. CWednesday
4. DTuesday
11.
Susan and Robert have two children, Mark and Julie. Mark has two children, Maya and Finn.

Julie is Maya's ______.
Which word fits the gap?
1. Acousin
2. Buncle
3. Cniece
4. Daunt
12.
The first shape changes into the second in a certain way. Which shape completes the second pair in the same way?
1. A
2. B
3. C
4. D
13.
The dashed line is a mirror. The square marked P is reflected in the mirror. Which square does its reflection land in?
1. AB1
2. BB2
3. CA1
4. DE6
14.
In a scholarship examination, Rahul ranked 12th and Aisha ranked 8th. Among the girls, Aisha ranked 5th, and among the boys, Rahul ranked 6th. Rahul ranked 30th counting up from the bottom. Among the girls, Aisha ranked 17th from the bottom. How many boys sat the examination?
1. A20
2. B33
3. C21
4. D41
15.
Five friends ran a race. Ruby did not finish fifth. Chloe finished immediately ahead of Priya. Priya did not finish fifth. Tom did not finish first. Chloe finished somewhere ahead of Ruby. Tom finished immediately ahead of Lucas. Who finished third?
1. AChloe
2. BRuby
3. CLucas
4. DPriya

Section 2: Mathematical Reasoning

Questions 16 to 35, 1 mark each. Circle the letter of the best answer.

16.
In the diagram below, what is the size of the angle marked x?
1. A80°
2. B35°
3. C25°
4. D45°
17.
For any two numbers, a ◆ b means (a + b) × a. What is 3 ◆ 2?
1. A6
2. B10
3. C5
4. D15
18.
The dashed line is a line of symmetry. One more square must be shaded so that the pattern matches on both sides of the line. Which square must be shaded?
1. AC5
2. BA5
3. CC3
4. DD5
19.
Two numbers add to 40, and one is 8 more than the other. What is the larger number?
1. A32
2. B16
3. C24
4. D4
20.
This solid rectangular prism has been built from identical cubes. Some of the cubes cannot be seen in the drawing. How many cubes cannot be seen?
1. A9
2. B12
3. C4
4. D14
21.
Which of these is the largest?
1. A60%
2. B1/2
3. C3/4
4. D0.7
22.
A sequence begins 5, 9, 13, 17, … and carries on in the same way. What is the 11th term?
1. A41
2. B49
3. C46
4. D45
23.
Elena stacks three ordinary dice one on top of another on a table. On any die, the dots on opposite faces add to 7. The face on the very top of the stack shows 2. How many dots are on the faces that cannot be seen — the face resting on the table, and the pairs of faces where one die meets the next?
1. A5
2. B63
3. C16
4. D19
24.
In a number code, each shape stands for the same number every time it is used, and a row of shapes means those numbers added together. ■■★★ = 144, ■▲★ = 116 and ▲▲★★ = 192. What number does ★★ stand for?
1. A104
2. B2
3. C452
4. D52
25.
James has ₹50. 20% of it is spent on a book. How much is spent on the book?
1. A₹250
2. B₹100
3. C₹10
4. D₹1
26.
Which of these fractions is not equal to 5/11?
1. A50/110
2. B10/22
3. C20/44
4. D15/22
27.
4 1/3 + ? = 11 1/3. What is the missing value?
1. A8
2. B15 2/3
3. C3 1/2
4. D7
28.
The net below is folded to make a cube. What is the total of the number on the shaded square and the number on the face that ends up opposite it?
1. A25
2. B34
3. C26
4. D29
29.
When a number is multiplied by 6, the answer is the same as multiplying that number by 4 and then adding 16. What is the number?
1. A4
2. B3
3. C9
4. D8
30.
880 students at Marlow Primary were asked how they get to school. The pie chart below shows their answers. How many of them get there by ferry?
1. A704
2. B88
3. C528
4. D176
31.
In the triangle below, what is the size of the angle marked x?
1. A134°
2. B46°
3. C67°
4. D48°
32.
Hugo used a balance to compare the masses of some objects. The results are shown below. Which of these must be true?
1. AOne cube and one cone are heavier than two balls.
2. BTwo balls are heavier than one cone.
3. CTwo cones are heavier than one cube.
4. DOne cube is lighter than one cone.
33.
This is a plan of a netball court. How many of the solid lines in this drawing are parallel to the dashed line?
1. A10
2. B3
3. C6
4. D5
34.
Dev started with a box of cards. Dev handed out 30% to a friend, 25% to a cousin and 15% to a neighbour, each share worked out from the number Dev started with. 120 cards were left. How many cards were there at the start?
1. A400
2. B30
3. C171
4. D267
35.
Each letter of the alphabet stands for a number: A = 1, B = 2, C = 3, and so on to Z = 26. What is the value of E × G + E − C?
1. A26
2. B43
3. C45
4. D37

Section 3: Everyday Mathematics

Questions 36 to 45, 1 mark each. Circle the letter of the best answer.

36.
A box measures 2 cm long, 7 cm wide and 4 cm high. What is its volume?
1. A100 cm³
2. B56 cm³
3. C52 cm³
4. D13 cm³
37.
This picture graph shows the books read. How many more books are there for Thursday than for Tuesday?
1. A7
2. B11
3. C3.5
4. D15
38.
The thermometer below shows the temperature of some water. What is the reading?
1. A16 °C
2. B19 °C
3. C18 °C
4. D20 °C
39.
A box holds 6 yellow counters and 7 green counters. Two counters are taken out one after the other, and the first is not put back. What is the chance that both are yellow?
1. A36/169
2. B5/26
3. C137/156
4. D6/13
40.
Grace is marking out a straight fence that is 84 metres long. Grace puts a post at the very start, another at the very end, and one every 12 metres in between. How many posts are used altogether?
1. A8
2. B9
3. C7
4. D6
41.
Anika spins the arrow on this spinner once. Which word best describes the chance that it lands on a part marked M?
1. Aunlikely
2. Ban even chance
3. Clikely
4. Dimpossible
42.
A cyclist rides at an average speed of 80 km/h for 15 minutes. How far does it go?
1. A22 km
2. B320 km
3. C20 km
4. D1200 km
43.
A bus trip leaves at 11:44 am and takes 2 hours 35 minutes. What time does it finish?
1. A2:19 pm
2. B3:19 pm
3. C2:19 am
4. D3:39 pm
44.
The same rule turns every number in the top row into the number directly below it. What number belongs in the cell marked with a question mark?
1. A74
2. B109
3. C14
4. D53
45.
Grace collected data on the juice cartons in a shop and graphed the results. Which statement about the cartons is not true?
1. AOne sixth of the orange cartons are small.
2. BThere were 12 more large than small altogether.
3. CAltogether 44 cartons were counted.
4. DThere were more orange cartons than apple cartons.

Section 4: Achievers Section

Questions 46 to 50, 3 marks each. Circle the letter of the best answer.

46.
A rectangular place mat has an area of 54 cm². One of its sides is 9 cm long. What is the distance all the way round it?
1. A28 cm
2. B54 cm
3. C36 cm
4. D30 cm
47.
A swimming carnival starts at 2:54 pm and lasts 1 hour 15 minutes. What time does it finish?
1. A4:09 pm
2. B5:09 pm
3. C4:49 pm
4. D4:09 am
48.
Jonah is marking out one side of a straight driveway that is 165 metres long. Jonah plants a tree at the very start, another at the very end, and one every 15 metres in between. How many trees are used altogether?
1. A12
2. B11
3. C10
4. D13
49.
Each of these three numbers has one digit hidden by a question mark: ?20, 3?9, ?17. The average of the three numbers is 362. What is the sum of the three hidden digits?
1. A4
2. B11
3. C3
4. D74
50.
Priya is standing in square P. Ruby is standing in square Q. Which one of these squares is the same distance, in a straight line, from both of them?
1. AC2
2. BH1
3. CF4
4. DE4

Answers and working

Logical Reasoning

1.A. Along each row, from left to right, every arrow is the one before it turned a quarter turn anticlockwise, so the missing arrow points down.
2.C (□ ✚ ♥). Read each clue place by place to find every digit's symbol. Coding 672 gives □ ✚ ♥.
3.D (SLJ). Every letter moves 3 places forward in the alphabet, so PIG becomes SLJ.
4.B (attic). All the others are parts of a book; attic is one of the parts of a house.
5.B (17). Faces seen together on a cube cannot be opposite each other, and the three views leave only one possibility: 1–3, 2–4, 5–6. So 3 is opposite 1, and the four faces touching it total 21 − 3 − 1 = 17.
6.D (W). Each letter moves 3 places forward in the alphabet, so after T comes W.
7.B. In every figure but one, the dot is inside the shape. The odd one out is the hexagon with its dot outside it.
8.A. Along every row the shape stays the same and there is one more dot each step, so the missing picture is the hexagon with 3 dots.
9.D (18). In every row, the third number is the first two added together. In the row with the question mark that gives 18.
10.A (Thursday). From 17 April to the end of April is 13 days, plus 2 more into May = 15 days. 15 = 2 weeks and 1 day, so count 1 on from Wednesday: Thursday.
11.D (aunt). Julie is Maya's aunt. Mark is Maya's parent. Mark and Julie are both children of Susan and Robert, so Julie is Mark's sister. A parent's sister is an aunt, so Julie is Maya's aunt and Maya is Julie's niece.
12.B. In the first pair the shape is turned a quarter turn clockwise. Doing the same to the third shape gives the answer.
13.A (B1). P is 3 squares from the mirror, so its reflection is the same distance on the other side. That is B1.
14.A (20). Rahul is 12th from the top and 30th from the bottom, so everyone numbers 12 + 30 − 1 = 41. The same trick on the girls gives 5 + 17 − 1 = 21 girls. Boys = 41 − 21 = 20. (The other two ranks are true but not needed.)
15.B (Ruby). The clues fix one order only: first Chloe, second Priya, third Ruby, fourth Tom, fifth Lucas. So Ruby finished third.

Mathematical Reasoning

16.B (35°). OA and OD lie in a straight line, so the angles between them come to 180°. The ones printed on the diagram take up 80° + 65° = 145°, which leaves 180° − 145° = 35°, so x = 35°.
17.D (15). Put 3 where a is and 2 where b is, keeping them in that order — this rule gives a different answer the other way round. That makes it (3 + 2) × 3, which comes to 15.
18.A (C5). Every shaded square needs a partner the same distance on the other side of the line, in the same row. H5 has none, so its partner C5 must be shaded.
19.C (24). Take the difference off the total first: 40 − 8 = 32. That is what TWO of the smaller one come to, so the smaller is 16 and the larger is 16 + 8 = 24.
20.C (4). Three faces are showing, so peel one layer off each of them. What is left is a 2 by 2 by 1 block entirely inside, which is 4 cubes.
21.C (3/4). As decimals: 60% = 0.6, 1/2 = 0.5, 3/4 = 0.75, 0.7 = 0.7. The largest is 3/4.
22.D (45). Each term is 4 more than the last, so the nth term is 5 + (n − 1) × 4. For n = 11: 5 + 10 × 4 = 45.
23.D (19). Each of the two touching places hides a pair of opposite faces, which is 7 dots, so that is 14. The face on the table is opposite the 2, so it is 5. Altogether 19.
24.A (104). The three clues give ■ = 20, ▲ = 44, ★ = 52. So ★★ is 52 + 52 = 104.
25.C (₹10). 20% means 20 out of every 100. So the amount is ₹50 × 20 ÷ 100 = ₹10.
26.D (15/22). Multiplying the top and the bottom by the same number leaves a fraction unchanged. In 15/22 the top has been multiplied by 3 but the bottom by 2, so it is not equal to 5/11.
27.D (7). Turn the sentence round to get at the missing part: 11 1/3 − 4 1/3 = 7. Put 7 back into the sentence and it works out to 11 1/3.
28.B (34). Two squares that are joined along an edge, or that meet at a corner, always end up side by side on the cube, so none of those can be opposite 15. Pairing all six squares up under that rule, and keeping the ends of every straight line of three together, leaves 15 with 19. So 15 + 19 = 34.
29.D (8). Multiplying by 6 rather than by 4 adds 6 − 4 = 2 lots of the number. Those 2 lots come to 16, so the number is 16 ÷ 2 = 8.
30.D (176). The Ferry slice is 20 per cent of the chart. And 20 per cent of 880 is 880 ÷ 100 × 20 = 176.
31.B (46°). The two ticked sides are the same length, so the two angles at the ends of the third side are equal. Each of them is 67°, and the three angles come to 180°, so x = 180° − 67° − 67° = 46°.
32.B (Two balls are heavier than one cone.). The pictures say one cone is lighter than one cube and one ball; one cube is lighter than one ball; one ball and one cone are heavier than two cubes. Put together, they make it certain that two balls are heavier than one cone, whatever the objects weigh.
33.D (5). Counting the two outside edges of the plan, 6 lines run the same way as the dashed one. A line is not parallel to itself, so that leaves 5.
34.A (400). The shares add to 70%, so the 120 left over are the other 30%. One per cent is 120 ÷ 30 = 4, so the whole is 400.
35.D (37). The letters stand for E = 5, G = 7, E = 5 and C = 3. Do the multiplying first, then the adding and subtracting, and the answer is 37.

Everyday Mathematics

36.B (56 cm³). Volume multiplies all three edges: 2 × 7 × 4 = 56 cm³.
37.A (7). One circle stands for 2 books. Thursday has 5.5 circles, which is 11; Tuesday has 2 circles, which is 4. The difference is 7.
38.C (18 °C). The printed numbers are 10 apart with a small mark every 2 degrees. The liquid stands 1 mark below 20, so the reading is 18 °C.
39.B (5/26). The first draw is 6 out of 13. One yellow is now gone, so the second is 5 out of 12. Both must happen, so multiply: 6/13 × 5/12 = 5/26.
40.A (8). 84 ÷ 12 = 7 gaps, and a row of gaps has one more post than gaps because both ends carry one. So 7 + 1 = 8.
41.C (likely). Four of the six equal parts are marked M, so landing on M is likely.
42.C (20 km). In one hour it covers 80 km, so in one minute it covers 80 ÷ 60 km. Over 15 minutes that is 80 × 15 ÷ 60 = 20 km.
43.A (2:19 pm). Add the hours first: 11:44 am plus 2 hours is 1:44 pm. Then the 35 minutes. That takes the minutes past 60, so an hour carries, and it finishes at 2:19 pm.
44.A (74). The rule is: multiply by 7, then add 4. It works on every column — 7 × 4 + 4 = 32 — so the missing number is 7 × 10 + 4 = 74.
45.D (There were more orange cartons than apple cartons.). Checked against the columns, three of the four statements hold. "There were more orange cartons than apple cartons" does not. There were more apple cartons than orange cartons, not the other way round.

Achievers Section

46.D (30 cm). The other side is 54 ÷ 9 = 6 cm. Round the edge is 9 + 6 + 9 + 6 = 30 cm.
47.A (4:09 pm). Add the hours first: 2:54 pm plus 1 hour is 3:54 pm. Then the 15 minutes. That takes the minutes past 60, so an hour carries, and it finishes at 4:09 pm.
48.A (12). 165 ÷ 15 = 11 gaps, and a row of gaps has one more tree than gaps because both ends carry one. So 11 + 1 = 12.
49.B (11). The total is 3 × 362 = 1086. The visible parts make 346, so the hidden digits are worth 740. Whatever way they fit, the digits add to 11.
50.A (C2). From C2 to P is 3 across and 4 up or down; to Q it is 5 across and 0 up or down. Both give the same straight-line distance, so C2 is the square.

Written by Scholar Tests in the published IMO pattern. Not an SOF paper; we are not connected with the Science Olympiad Foundation.

IMO sample paper for Class 6, with answers