Section A
Multiple Choice — 15 Questions
(+2 / -1)
1
counting
easy
What is the total number of hearts below?
Answer: C
Divide the drawing into 3 parts. The left part has 1 + 2 + 3 + 4 + 5 = 15 hearts, the middle part has 1 + 3 + 5 + 7 + 7 = 23 hearts, and the right part has 1 + 2 + 3 + 4 + 5 = 15 hearts. Total = 15 + 23 + 15 = 53. (Counting by row also gives 17 + 15 + 11 + 7 + 3 = 53.)
2
measurement
easy
Which of the following is the same as 2018 cm?
Answer: C
1 metre = 100 cm and 1 km = 100 000 cm. Checking each: A = 218 cm, B = 200 018 cm, C = 2000 + 18 = 2018 cm, D = 20 108 cm. So 2018 cm = 20 metres and 18 centimetres.
3
data-analysis
easy
The table below shows the scores of Tiffany, Ursula, Vincent and Warren in the "Mathcraft Game". Who received the highest score?
Answer: D
Add each player's four round scores: Tiffany = 7 + 56 + 8 + 43 = 114, Ursula = 37 + 24 + 36 + 13 = 110, Vincent = 27 + 41 + 23 + 21 = 112, Warren = 27 + 38 + 23 + 27 = 115. Warren has the highest total (115).
4
logic
medium
Ducklings are walking in a queue when they are following the mother duck. Joey the duckling is the 6th from the front and 8th from the back (including the mother duck). Some of the ducklings at the back moved away from the queue making Joey the middle duckling in the queue. How many ducklings moved away from the queue?
Answer: A
The queue has 6 + (8 − 1) = 13 in it. If 2 at the back move away, 13 − 2 = 11 remain, and the middle one is the 6th from the front — exactly Joey's position. So 2 ducklings moved away.
5
rate-problems
medium
George takes 4 minutes to go from the 1st floor to the 3rd floor. He just realized that he forgot his water bottle on the 5th floor. He is now on the 2nd floor. How long would it take him to get his water bottle?
Answer: C
From the 1st to the 3rd floor is 3 − 1 = 2 gaps, taking 4 minutes, so 1 gap takes 2 minutes. From the 2nd to the 5th floor is 5 − 2 = 3 gaps, so 3 × 2 = 6 minutes.
6
sequences
medium
What is the next number below?
3, 5, 6, 10, 9, 15, 12, 20, …
Answer: B
Two sequences are interleaved. The odd-position terms are 3, 6, 9, 12, … (adding 3 each time) and the even-position terms are 5, 10, 15, 20, … (adding 5 each time). The missing number is in the 9th (odd) position, so it is 12 + 3 = 15.
7
combinatorics
medium
Hansel wants to buy 2 dice of different colours. The available colours in a store are red, blue, green, yellow, pink and white. How many different combinations of 2 dice are there in the store? (Example: 1 combination is yellow and white.)
Answer: C
Choosing 2 different colours out of 6, where order does not matter, gives 6 × 5 ÷ 2 = 15 combinations.
8
number-theory
medium
A palindrome is a number that can be read the same forward and backward. For example, the numbers 99, 252 and 4884 are palindromes. How many 3-digit palindrome numbers are there?
Answer: C
A 3-digit palindrome has the form ABA. The first digit A can be 1–9 (9 choices, not 0) and the middle digit B can be 0–9 (10 choices); the last digit must equal A. So there are 9 × 10 = 90 three-digit palindromes.
9
geometry
medium
Which of the following CANNOT form a rectangle?
Answer: E
Two identical right triangles join along their hypotenuse to form a rectangle; two or five identical squares line up in a row to form a rectangle; four identical right triangles also combine into a rectangle. But an odd number of identical triangles cannot tile a rectangle — the triangles must pair up — so five identical triangles cannot form a rectangle.
10
spatial-reasoning
medium
Find the correct shadow of the animals shown on the right.
Options A–E are the silhouettes shown below the picture.
Answer: E
Compare each silhouette with the original picture. Options A–D each have a circled object or spot that differs from the original (a wrong tail, head/ears, or the goat's position). Option E is the only silhouette that matches the original outline exactly.
11
calendar
medium
Elmo visits the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February had 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park?
Answer: B
Since 1 January was Sunday, the Wednesdays of January were the 4th, 11th, 18th, 25th. January has 31 days, so the first Wednesday of February was 1 February, giving 1, 8, 15, 22 February. February had 28 days, so the first Wednesday of March was 1 March, giving 1, 8, 15, 22, 29 March. The last Wednesday of March 2017 was the 29th.
12
spatial-reasoning
hard
The diagram shows some cubes of the same size stacked at a corner of a room. How many cubes are there altogether? (Note: The floor is horizontal and the two walls are vertical. There are no gaps or holes behind the visible cubes.)
Answer: E
Count the cubes by level: Level 1 (bottom) = 18, Level 2 = 7, Level 3 = 5, Level 4 = 3, Level 5 (top) = 1. Total = 18 + 7 + 5 + 3 + 1 = 34 cubes, which is not among the listed options, so the answer is None of the above.
13
geometry
medium
The figure is made up of 6 identical rectangles with breadth of 1 cm. What is the perimeter of the figure?
Answer: B
The length of each small rectangle is 5 cm, so the breadth of the whole figure is 5 cm and its length is 5 + 1 = 6 cm. The perimeter is 5 + 6 + 5 + 6 = 22 cm.
14
spatial-reasoning
medium
What is the missing piece '?' in the diagram?
Options A–E are the five squares shown, each containing a single star in a different position.
Answer: C
Combining the stars from all the given squares into one square, every position is filled except the middle-left. So the missing piece must be the square with a star at the middle-left, which is option C.
15
logic
hard
A toy store has 43 yoyos in the first box and 23 yoyos in the second box. After a week, an equal number of yoyos from each box were sold. The number of yoyos in the first box were then five times as many as the number of yoyos in the second box. How many yoyos were left?
Answer: E
Selling an equal number from each box keeps the difference unchanged: 43 − 23 = 20. In the end the first box has 5 units and the second has 1 unit, so the difference is 4 units = 20, giving 1 unit = 5. The second box ends with 5 yoyos and the first with 5 × 5 = 25, so 5 + 25 = 30 yoyos are left. This is not among the options, so the answer is None of the above.
Section B
Integer-type — 10 Questions
(+4)
16
arithmetic
easy
Find the sum: 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31
Answer: 231
Pair terms from the ends: (11 + 29) + (13 + 27) + (15 + 25) + (17 + 23) + (19 + 21) + 31 = 40 × 5 + 31 = 200 + 31 = 231.
17
geometry
medium
How many rectangles are there in the picture below?
Answer: 15
The figure is a rectangle split into 5 horizontal strips. Rectangles made of a single strip: 5; of 2 adjacent strips: 4; of 3: 3; of 4: 2; of all 5: 1. Total = 5 + 4 + 3 + 2 + 1 = 15.
18
word-problems
medium
In a classroom, Kevin wrote 30 more letters than Sara, and James wrote 40 more letters than Sara. Altogether, they wrote 160 letters. Find the number of letters Kevin wrote.
Answer: 60
Let Sara's letters be 1 unit. Then Kevin = 1 unit + 30 and James = 1 unit + 40. The total is 3 units + 70 = 160, so 3 units = 90 and 1 unit = 30. Sara wrote 30, so Kevin wrote 30 + 30 = 60.
19
number-theory
medium
Find a two-digit multiple of 6 which is one more than a multiple of 13.
Answer: 66
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, … Multiples of 13: 13, 26, 39, 52, 65, … The number 66 is a multiple of 6 and is 1 more than 65, which is a multiple of 13.
20
logic
medium
Andy shows a number to Zach, then they have the following conversation. Andy: "Subtract 17 from it, then divide the result by 6. After that, add 39 to the new number and then multiply the resulting number by 4. Finally, add 29." Zach: "Not hard, the final answer is 209 and I'm very sure it is the correct answer." What is the number that Andy showed to Zach?
Answer: 53
The operations are −17, ÷6, +39, ×4, +29. Work backwards from 209: 209 − 29 = 180, 180 ÷ 4 = 45, 45 − 39 = 6, 6 × 6 = 36, 36 + 17 = 53.
21
patterns
hard
Study the pattern below. Find the value indicated by the last figure (a triangle containing 24).
Answer: 84
The shapes are rules: a circle doubles the number, a square adds 2 to the number, and a triangle switches (reverses) the digits of the number. So 24 is doubled to 24 × 2 = 48, and reversing 48 gives 84.
22
logic
medium
Jeremy has the same size toy cars in his box in which 5 are red, 9 are blue and 4 are white. How many cars does he need to pick from the box without looking to be sure he will get 3 toy cars of the same colour?
Answer: 7
Consider the worst case: he could pick 2 red, 2 blue and 2 white (6 cars) without yet having 3 of one colour. The next car, whatever its colour, gives 3 of a colour. So he needs 2 + 2 + 2 + 1 = 7 cars.
23
logic
hard
Given the three picture equations shown, find the value of the diamond (the last shape).
Answer: 6
The second equation contains the same diamond and hexagon as the third equation, so the remaining shape in the second equation equals 17 − 13 = 4. Then from the first equation the hexagon is 15 − 4 − 4 = 7. Finally, from the third equation the diamond is 13 − 7 = 6.
24
cryptarithm
hard
In the following subtraction, all the different letters stand for different digits. Find the value of A + B + B + A.
Answer: 12
In the ones place, 2 − A ends in 7, so we borrow: 12 − A = 7, giving A = 5. In the tens place (after borrowing), (B − 1) − 5 must end in A = 5, which forces B − 1 = 10, so B = 1 (carrying a borrow to the hundreds). In the hundreds place, (A − 1) − 3 = 1, consistent with A = 5. The subtraction is 512 − 355 = 157, so A + B + B + A = 5 + 1 + 1 + 5 = 12.
25
logic
hard
Fill the figure with numbers so that each shaded square in the figure is surrounded by all digits from 1 to 8. How many times will the digit '8' appear in the filled figure?
Answer: 6
Each shaded square must be surrounded by the digits 1–8, so an 8 must sit in one of the neighbouring cells of every shaded square. Marking the squares that cannot hold an 8 and testing the two possible placements for the central shaded square, only one consistent arrangement works. Counting the 8s in that completed figure gives 6.