Nico and his little sister play with shells and marbles. Each shell is worth 6 and each marble is worth 1 (shell = 6, marble = 1). Which picture shows the value 16?
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Answer: E
Show hints
Hint 1 of 2
Each shell counts as 6 and each marble counts as 1 - add up each picture's total.
Still stuck? Show hint 2 →
Hint 2 of 2
You need a total of exactly 16, so look for two shells plus four marbles.
Show solution
Approach: add the shell and marble values in each option
A shell is worth 6 and a marble is worth 1.
Two shells give 12, and you need 4 more to reach 16, so 4 marbles.
The picture with two shells and four marbles totals 12 + 4 = 16.
Simona writes the numbers 2, 0, 2 and 5 in the boxes, one number per box (see picture). In what order can she write them so that the calculation gives the biggest result?
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Answer: E — 5, 2, 0, 2
Show hints
Hint 1 of 2
The third box is the one that gets subtracted, so put the smallest number there.
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Hint 2 of 2
Put the 0 in the subtracted (third) box and add everything else.
Show solution
Approach: minimise what is subtracted, maximise what is added
The calculation is first + second minus third + fourth.
To make it biggest, subtract the smallest number, which is 0.
Then the other three (5, 2, 2) are all added: 5 + 2 - 0 + 2 = 9.
The order 5, 2, 0, 2 does this, which is option E.
The two markers with a question mark have the same value: \(20 + 10 + 10 + ? + ? + 1 = 51\). Which value do you have to use instead of the question mark so that the calculation is correct?
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Answer: C — 5
Show hints
Hint 1 of 2
Add up the numbers you can already read.
Still stuck? Show hint 2 →
Hint 2 of 2
Subtract that running total from 51, then split the leftover between the two equal markers.
Show solution
Approach: fill the known values, then split the remainder
The known markers add to 20 + 10 + 10 + 1 = 41.
The two equal question marks must make up 51 − 41 = 10.
On every birthday Maria gets as many teddies as the age she turns: 1 teddy on her first birthday, 2 teddies on her second birthday, and so on. How many teddies does Maria have in total the day after her sixth birthday?
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Answer: C — 21
Show hints
Hint 1 of 2
On each birthday she gets a number of teddies equal to her age that day.
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Hint 2 of 2
Add up the teddies from birthday 1 through birthday 6.
Show solution
Approach: add the gifts from each birthday
Birthdays 1 to 6 give 1, 2, 3, 4, 5 and 6 teddies.
Add them up: 1 + 2 + 3 + 4 + 5 + 6 = 21.
So the day after her sixth birthday she has 21 teddies (choice C).
Denise fired a silver and a gold rocket at the same time. The rockets exploded into 20 stars in total. The gold rocket exploded into 6 more stars than the silver one. How many stars did the gold rocket explode into?
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Answer: D — 13
Show hints
Hint 1 of 2
The two rockets together make 20 stars, and the gold makes 6 more than the silver.
Still stuck? Show hint 2 →
Hint 2 of 2
Take the 6 extra off the 20 first, split what is left evenly, then give the gold its extra back.
Show solution
Approach: split the total after removing the difference
Remove the 6 extra gold stars: 20 - 6 = 14 shared equally.
Each rocket's base share is 14 / 2 = 7, so the silver has 7.
On the 24th of February 2012 Grandfather's chicks hatched. There are 29 days in February in 2012. How old are the chicks today, on the 15th of March 2012?
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Answer: D — 20 days
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Hint 1 of 2
Count the days from 24 February up to 15 March, using that February has 29 days.
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Hint 2 of 2
Find how many days from the 24th to the end of February, then add the March days.
The bell of a clocktower rings every full hour (8:00, 9:00, 10:00 etc.) and rings as many times as the number of hours. It also rings once on every half hour (8:30, 9:30, 10:30 etc.). How often will it ring between 7:55 and 10:45?
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Answer: D — 30 times
Show hints
Hint 1 of 2
List every full hour and every half hour strictly between 7:55 and 10:45.
Still stuck? Show hint 2 →
Hint 2 of 2
A full hour rings as many times as the hour number; each half hour rings once.
Show solution
Approach: count rings by occasion
Full hours in the window: 8:00 rings 8, 9:00 rings 9, 10:00 rings 10, total 27 rings.
Half hours 8:30, 9:30, 10:30 each ring once, adding 3.
In a cafe the soup costs €4, the main course €9 and the dessert €5. The three courses ordered together cost €15. How many euros cheaper is this than ordering the same three courses separately?
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Answer: A — €3
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Hint 1 of 2
First add up the three separate prices.
Still stuck? Show hint 2 →
Hint 2 of 2
Then compare that total with the combined price of 15.
Show solution
Approach: compare separate total with bundle price
Eva is a centipede with exactly 100 feet. Yesterday she bought 16 pairs of shoes and put them on right away. Even so, she still had 14 feet with no shoes. On how many feet was she already wearing shoes before she went shopping yesterday?
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Answer: C — 54
Show hints
Hint 1 of 2
Each pair of shoes covers 2 feet; first find how many feet have shoes now.
Still stuck? Show hint 2 →
Hint 2 of 2
Subtract the feet she put new shoes on today from the total now wearing shoes.
Show solution
Approach: count shod feet, then remove today's new shoes
She has 100 feet and 14 are bare, so 100 − 14 = 86 feet wear shoes now.
Today she put on 16 pairs = 32 shoes, covering 32 feet.
So before shopping she already wore shoes on 86 − 32 = 54 feet.
Rudi feeds six sheep in the petting zoo. The six sheep get a total of 210 g of food. Each of the five large sheep gets the same amount, and the small sheep gets twice as much as a large sheep. How much food does the small sheep get?
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Answer: C — 60 g
Show hints
Hint 1 of 2
The small sheep eats as much as two large sheep, so count it as two large sheep.
Still stuck? Show hint 2 →
Hint 2 of 2
Then the 210 g is shared into 7 equal large-sheep portions.
Show solution
Approach: count everything in equal large-sheep portions
The small sheep eats as much as two large sheep, so pretend it is two large sheep.
Now there are 5 + 2 = 7 equal large-sheep portions sharing 210 g.
Each portion is 210 ÷ 7 = 30 g.
The small sheep gets two portions: 30 + 30 = 60 g, option C.
Lucy weighs building blocks two at a time and reads these scale values: 200 g, 100 g and 240 g (see picture). How much do the three different building blocks weigh all together?
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Answer: A — 270 g
Show hints
Hint 1 of 2
Each reading is the weight of two of the three blocks together.
Still stuck? Show hint 2 →
Hint 2 of 2
Add the three known readings — that counts every block twice.
Show solution
Approach: add the pair-weights and halve
The three readings 200, 100, 240 each weigh two blocks, so together they count all three blocks twice.
Sum: 200 + 100 + 240 = 540 grams.
Half of that is the weight of the three blocks once: 540 ÷ 2 = 270.
In a queue in front of a ferry there are 8 cars with 19 people in total. There are either 2 or 3 people in each car. How many cars are there with exactly 2 people?
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Answer: D — 5
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Hint 1 of 2
If every car held 2 people there would be only 16; you need 3 more.
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Hint 2 of 2
Each car upgraded from 2 to 3 people adds exactly one person.
Show solution
Approach: start from all-twos and account for the extra people
Eight cars with 2 people each would carry 16 people, but there are 19.
The 3 extra people come from 3 cars holding 3 instead of 2.
Each of the 5 boxes contains either apples or bananas, but not both. The total weight of all the bananas is 3 times the weight of all the apples. Which boxes contain apples?
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Answer: E — 1 and 4
Show hints
Hint 1 of 2
If the bananas weigh 3 times the apples, then for every 1 kg of apples there are 3 kg of bananas — so apples are 1 part out of 4 equal parts of the whole.
Still stuck? Show hint 2 →
Hint 2 of 2
Add all five box weights, take a quarter of that for the apples, then find which boxes add up to it.
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Approach: apples are one quarter of the total weight
The five boxes weigh 7, 5, 6, 2, 16, totalling 36 kg.
Bananas are 3 times the apples, so apples make up 36 / 4 = 9 kg.
Boxes summing to 9 kg are the 7 kg and 2 kg ones, i.e. boxes 1 and 4.
A number is written into every square of a 4 × 4 table. Mary is looking for the 2 × 2 table where the sum of the four numbers is greatest. How big is this sum?
1
2
1
3
4
1
1
2
1
7
3
2
2
1
3
1
Show answer
Answer: D — 14
Show hints
Hint 1 of 2
Slide a 2 x 2 window over the table and add its four numbers each time.
Still stuck? Show hint 2 →
Hint 2 of 2
The biggest entry, 7, should sit inside the best window.
Show solution
Approach: check the 2 x 2 block containing the largest numbers
Try 2 x 2 blocks, focusing on the area around the 7.
The block with 7, 3 (its right neighbour) and the 1, 3 below them gives 7+3+1+3.
That total is 14, larger than any other 2 x 2 block.
Five boys share 10 bags of marbles between themselves. Everyone gets exactly two bags (see picture). Alex gets 5 marbles, Bob 7, Charles 9 and Dennis 15. Eric gets the two bags that are left over. How many marbles does he get?
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Answer: E — 19
Show hints
Hint 1 of 2
The ten bags hold 1, 2, 3, ... up to 10 marbles; add them all first.
Still stuck? Show hint 2 →
Hint 2 of 2
Subtract the four known boys' totals from the grand total to get Eric's two bags.
Show solution
Approach: total all bags, then subtract the known amounts
The ten bags hold 1 through 10 marbles, a total of 55.
Alex, Bob, Charlie and Dennis took 5 + 7 + 9 + 15 = 36 marbles.
Kate has four flowers, which have 6, 7, 8 and 11 petals respectively. She now tears off one petal from each of three different flowers. She repeats this until it is no longer possible to tear off one petal from each of three different flowers. What is the minimum number of petals left over?
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Answer: B — 2
Show hints
Hint 1 of 2
Every single round takes away exactly 3 petals (one from each of three flowers).
Still stuck? Show hint 2 →
Hint 2 of 2
Since 3 petals leave each round, the petals removed always count up by threes; think about what is left from 32.
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Approach: petals leave 3 at a time, so the leftover is what 32 has past a count-by-three
There are 6 + 7 + 8 + 11 = 32 petals to start.
Each round takes one petal from three different flowers, so exactly 3 petals leave every round.
Counting by threes (3, 6, 9, ..., 30), the most she can remove is 30, which still keeps three flowers alive long enough to do every round.
Tick, Trick and Track are triplets. Their brother Franz is exactly 3 years older. All four children are having their birthdays today. How old can the four brothers be altogether?
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Answer: B — 27
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Hint 1 of 2
The three triplets are all the same age, and Franz is just 3 more than that.
Still stuck? Show hint 2 →
Hint 2 of 2
If you take Franz's extra 3 years off the total, what is left should split into four equal ages.
Show solution
Approach: take off Franz's extra 3, then split the rest into four equal ages
All four boys would be the same age except Franz, who has 3 extra years, so take those 3 away from the total first.
What is left must split evenly into four equal ages (one for each boy).
Take 3 off each choice and see which splits into 4 equal whole numbers: 27 − 3 = 24, and 24 shared by 4 is 6 each, so the ages are 6, 6, 6 and 9.
So the four brothers can be 27 years old altogether, choice B.
In a magic garden there are magic trees. On each tree there are either 6 pears and 3 apples, or 8 pears and 4 apples. In total there are 25 apples on the magic trees. How many pears in total are hanging on the magic trees altogether?
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Answer: D — 50
Show hints
Hint 1 of 2
Use the apple counts (3 per first kind of tree, 4 per second) to total 25 apples.
Still stuck? Show hint 2 →
Hint 2 of 2
Notice each apple comes with a fixed bundle of pears, so the pear total may not depend on the exact mix.
Show solution
Approach: find the tree counts from apples, then total the pears
A '6-pears/3-apples' tree carries 2 pears per apple, and an '8-pears/4-apples' tree also carries 2 pears per apple.
Since every apple is matched by exactly 2 pears on either kind of tree, the 25 apples come with 2 × 25 = 50 pears.
Eva writes seven numbers on a piece of paper, one of which is 201. She adds up these seven numbers and gets 2016. Now she replaces the 201 with the number 102 and again adds up the seven numbers. Which result does she get now?
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Answer: C — 1917
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Hint 1 of 2
Only one number changes, so only the change in that number changes the total.
Still stuck? Show hint 2 →
Hint 2 of 2
Find how much smaller 102 is than 201, and subtract that from 2016.
Show solution
Approach: adjust the sum by the change in the single number
Replacing 201 with 102 lowers that number by 201 − 102 = 99.
Heinzi the kangaroo has bought some toys. For them he gave 150 kangoo-coins (KC) and received 20 kangoo-coins back. Just before leaving the shop he changed his mind and exchanged one of the toys he had bought for another one. Because of this he received a further 5 kangoo-coins back from the shopkeeper. Which of the toys in the picture has Heinzi taken home with him? (The price of each toy is shown on its tag.)
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Answer: A — Carriage and Aeroplane
Show hints
Hint 1 of 3
Work out how many coins Heinzi really spent in the end, after all the change he got back.
Still stuck? Show hint 2 →
Hint 2 of 3
He handed over 150, then got 20 back, then 5 more back, so take both amounts away.
Still stuck? Show hint 3 →
Hint 3 of 3
Now look at the price tags and find the toys that add up to exactly that many coins.
Show solution
Approach: net spending, then match a price pair
He paid 150 and got 20 back, then 5 more back after the exchange: net 150 − 20 − 5 = 125.
The toys he kept must cost 125 together.
Carriage (73) + Aeroplane (52) = 125; no other pair fits.
Chrissi wants to sell 10 glass marbles that each have a different weight. Their weights are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 dag. They are to be packed into bags, two marbles at a time, so that each bag has the same weight. Which two marbles will be put into the same bag?
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Answer: C — 3 and 8
Show hints
Hint 1 of 3
Ten marbles two at a time make 5 bags, and all five bags weigh the same.
Still stuck? Show hint 2 →
Hint 2 of 3
Add all the weights 1 + 2 + ... + 10 = 55, then share that equally among 5 bags.
Still stuck? Show hint 3 →
Hint 3 of 3
Each bag must weigh 11, so find the marble that pairs with 3 to make 11.
Show solution
Approach: equal-sum pairing
The total weight is 1+2+···+10 = 55, and 5 bags means each weighs 11 dag.
Pairs making 11: (1,10), (2,9), (3,8), (4,7), (5,6).
Anna, Bonnie and Caspar have some kangaroo cookies on their plates (see picture). There are 15 more cookies left over. They share these out so that each child ends up with the same number of cookies on their plate. How many cookies are added to Anna's plate?
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Answer: D — 6
Show hints
Hint 1 of 2
First find how many cookies there are altogether, then share them equally among the three children.
Still stuck? Show hint 2 →
Hint 2 of 2
Subtract the cookies Anna already has from her fair share.
Show solution
Approach: find the equal share, then see how many Anna still needs
The plates already hold 3 (Anna) + 4 (Bonnie) + 5 (Caspar) = 12 cookies.
With the 15 extra there are 12 + 15 = 27 cookies in all.
Shared equally, each child should have 27 ÷ 3 = 9 cookies.
Penguin Peter goes fishing every day and brings home 9 fish for his two children. Each day he gives 5 fish to the first child he sees, and the other child gets the remaining 4 fish. Over the last few days, one child has received 26 fish in total. How many fish did the other child get?
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Answer: D — 28
Show hints
Hint 1 of 3
Every single day the two children together get 5 + 4 = 9 fish.
Still stuck? Show hint 2 →
Hint 2 of 3
Each day a child gets either 5 or 4, so try how many days it takes one child to reach 26.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you know the number of days, the other child's total is 9 per day minus 26.
Show solution
Approach: find the number of days, then take the rest of the daily 9s
Each day one child gets 5 fish and the other gets 4, so together they get 9 fish a day.
For one child to reach 26 (made of 5s and 4s), it takes 6 days: 5 + 5 + 4 + 4 + 4 + 4 = 26.
In all, the children got 9 × 6 = 54 fish over those 6 days.
The 5 balls shown begin to move at the same time in the directions of their arrows. When two balls going in opposite directions collide, the bigger ball swallows the smaller one and grows by the smaller ball's value, then keeps moving in its own direction (see the worked example). What is the final result of the collisions of the 5 balls?
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Answer: C
Show hints
Hint 1 of 2
When two balls bump head-on, the bigger one eats the smaller one and grows by its number, still going the same way.
Still stuck? Show hint 2 →
Hint 2 of 2
No ball ever disappears, so the final ball's number is just every ball's number added together — you only need its direction too.
Show solution
Approach: all the balls merge into one, so add the values and find the direction
Nothing is ever lost in a collision, so the one ball left at the end is worth 10 + 9 + 3 + 7 + 20 = 49.
Following the bumps shows the big left-going 20 keeps winning the head-on hits, so the surviving ball moves left.
Matching '49 moving left' to the pictures gives option C.
In an ice cream shop there is some money in a drawer. After 6 ice creams were sold, there were 70 euros left in the drawer. After a total of 16 ice creams were sold, there were 120 euros left in the drawer. How many euros were there in the drawer at the start?
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Answer: C — 40
Show hints
Hint 1 of 2
Between the two moments, 10 more ice creams were sold and the drawer grew by 50 euros.
Still stuck? Show hint 2 →
Hint 2 of 2
Find the price of one ice cream, then step back to before any were sold.
Show solution
Approach: find the price per ice cream, then work back to the start
From 6 to 16 sold is 10 more ice creams, and the money rose from 70 to 120, i.e. +50 euros.
So each ice cream costs 50 / 10 = 5 euros.
The first 6 brought in 6 x 5 = 30 euros, so the start amount was 70 - 30 = 40 euros.
On a tall building there are 4 fire escape ladders, as shown. The heights of 3 of the ladders are marked at their tops (32, 48 and 36). What is the height of the shortest ladder?
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Answer: D — 20
Show hints
Hint 1 of 2
Each ladder stands on a ledge, and a taller ledge means a taller ladder top — the ledges step up by equal amounts.
Still stuck? Show hint 2 →
Hint 2 of 2
Find the step between two ladders whose tops you know, then step the same amount down to the shortest ladder.
Show solution
Approach: find the equal step between ladder tops and step down to the shortest
The ladders sit on ledges that rise by the same step each time, so their tops rise by that same step too.
Two of the marked tops are 48 and 36, a step of 48 - 36 = 12.
Stepping down 12 from the 32 ladder gives the shortest ladder: 32 - 12 = 20.
Sara has 16 blue marbles. She can swap her marbles in the following way: for 3 blue marbles she gets 1 red marble, and for 2 red marbles she gets 5 green marbles. What is the maximum number of green marbles she can get?
Show answer
Answer: B — 10
Show hints
Hint 1 of 2
First turn as many blue marbles as possible into red ones, then trade reds for greens.
Still stuck? Show hint 2 →
Hint 2 of 2
Watch the leftovers: trades only happen in fixed bundles (3 blue, 2 red).
Show solution
Approach: trade in bundles and track leftovers
16 blue ÷ 3 gives 5 red marbles (1 blue left over).
5 red ÷ 2 gives 2 trades = 10 green marbles (1 red left over).
Every box shows the result of the addition of the numbers on the very left and on the very top (for example: 6 + 2 = 8). Which number is written behind the question mark?
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Answer: E — 15
Show hints
Hint 1 of 2
Every box is its left number added to its top number; find a box where you already know both to fill in a missing edge number.
Still stuck? Show hint 2 →
Hint 2 of 2
The box showing 10 sits under the top number 2, so its left number must make 10.
Show solution
Approach: use a known box to find the missing left number, then add
Each box is the number at the left of its row plus the number at the top of its column.
The box showing 10 is under the top number 2, so its left number is 8 (because 8 + 2 = 10).
The question-mark box is in that same row, under the top number 7.
There are 10 balls, numbered 0 to 9 in a basket. John and George play a game. Each person is allowed to take three balls from the basket and calculate the total of the numbers on the balls. What is the biggest possible difference between the John and George's totals?
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Answer: E — 21
Show hints
Hint 1 of 2
To make the gap as large as possible, one player grabs the biggest numbers and the other the smallest.
Still stuck? Show hint 2 →
Hint 2 of 2
They draw from the same basket, so the two sets of three balls cannot overlap.
Show solution
Approach: maximise one total and minimise the other
One player can take the three largest balls: 9 + 8 + 7 = 24.
The other is then left to take the three smallest: 0 + 1 + 2 = 3.
Leo writes numbers in the multiplication pyramid. In a multiplication pyramid, you multiply two numbers that are next to each other to get the number directly above them (in the middle). Which number must Leo write in the grey field?
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Answer: E — 8
Show hints
Hint 1 of 3
Each block is found by multiplying the two blocks right under it.
Still stuck? Show hint 2 →
Hint 2 of 3
Start at the bottom row, which you know, and build one row up at a time.
Still stuck? Show hint 3 →
Hint 3 of 3
Keep multiplying neighbouring blocks until you reach the grey one.
Show solution
Approach: build the pyramid upward, multiplying each pair of neighbours
Start with the bottom row 1, 2, 2, 1.
Multiply each neighbouring pair to get the next row up: 1×2 = 2, 2×2 = 4, 2×1 = 2, so that row is 2, 4, 2.
Multiply neighbours again: 2×4 = 8 and 4×2 = 8, so the grey block is 8.
Hubert the rabbit loves cabbages and carrots. In one day he eats either 9 carrots, or 2 cabbages, or one cabbage and 4 carrots. In one week Hubert ate 30 carrots. How many cabbages did he eat during this week?
Show answer
Answer: B — 7
Show hints
Hint 1 of 3
There are 7 days in a week, so Hubert eats one of his three menus on each of the 7 days.
Still stuck? Show hint 2 →
Hint 2 of 3
Only two of the menus give carrots: the 9-carrot day and the 1-cabbage-and-4-carrots day.
Still stuck? Show hint 3 →
Hint 3 of 3
Try a few of each carrot-day until the carrots add up to 30, then count cabbages on every day.
Show solution
Approach: find which days give the 30 carrots, then count cabbages
Only two kinds of day give carrots: a 9-carrot day, or a day of 1 cabbage and 4 carrots.
Two 9-carrot days give 18 carrots, and three of the ‘1 cabbage + 4 carrots’ days give 12 more — that is 18 + 12 = 30 carrots, using 5 days.
Those three mixed days give 3 cabbages, and the 2 days left over are 2-cabbage days, giving 2 × 2 = 4 more.
Vera’s mum has made sandwiches, each using two slices of bread. There are 24 slices in a pack. How many sandwiches can she make with two whole packs and one half pack of bread?
Show answer
Answer: D — 30
Show hints
Hint 1 of 3
First work out the total number of bread slices Vera's mum has.
Still stuck? Show hint 2 →
Hint 2 of 3
A half pack has half of 24 slices, which is 12 slices.
Still stuck? Show hint 3 →
Hint 3 of 3
Each sandwich eats 2 slices, so split the total into pairs to count the sandwiches.
Show solution
Approach: count slices, then divide by 2
Two whole packs and one half pack give 24 + 24 + 12 = 60 slices.
Each sandwich uses 2 slices, so 60 ÷ 2 = 30 sandwiches.
Pinocchio’s nose is 9 cm long. Each time he lies, his nose grows by 6 cm. Each time he tells the truth, it shrinks by 2 cm. He tells three lies and twice tells the truth. How long is Pinocchio’s nose now?
Show answer
Answer: D — 23 cm
Show hints
Hint 1 of 3
Each lie adds 6 cm to the nose; each truth takes 2 cm away.
Still stuck? Show hint 2 →
Hint 2 of 3
There are three lies and two truths, so work out the total growing and the total shrinking.
Still stuck? Show hint 3 →
Hint 3 of 3
Start at 9 cm, add all the growing, then take away all the shrinking.
Show solution
Approach: add the lies, subtract the truths
Three lies add 3 × 6 = 18 cm; two truths take off 2 × 2 = 4 cm.
At the London 2012 Olympic Games the USA won the most medals: 46 gold, 29 silver and 29 bronze. China was second with 38 gold, 27 silver and 23 bronze. How many more medals did the USA win than China?
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Answer: C — 16
Show hints
Hint 1 of 3
Add up all of the USA's medals, then add up all of China's medals.
Still stuck? Show hint 2 →
Hint 2 of 3
The lighter way is to compare gold to gold, silver to silver, and bronze to bronze.
Still stuck? Show hint 3 →
Hint 3 of 3
Find each of those three differences and add the three differences together.
Show solution
Approach: compare each colour separately so the numbers stay small
Gold: the USA had 46 and China had 38, that is 8 more gold.
Silver: 29 against 27 is 2 more, and bronze: 29 against 23 is 6 more.
Adding the three extras, 8 + 2 + 6 = 16 more medals, which is answer C.
15 tables were set for a party. 5 plates were laid on 6 of the tables. 3 plates were laid on the rest of the tables. How many plates were needed in total?
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Answer: C — 57
Show hints
Hint 1 of 2
Find how many tables get 3 plates after 6 tables get 5 plates.
Still stuck? Show hint 2 →
Hint 2 of 2
Work out each group's plates and add them.
Show solution
Approach: split into two groups of tables
6 tables get 5 plates each: 6 x 5 = 30 plates.
The other 15 - 6 = 9 tables get 3 plates each: 9 x 3 = 27 plates.
During a party, two identical cakes were each cut into four identical pieces. Each of these pieces was then cut into three identical pieces. Each person at the party got a piece of cake, and there were three pieces left over. How many people were at the party?
Show answer
Answer: B — 21
Show hints
Hint 1 of 2
Work out how many small pieces the two cakes are cut into altogether.
Still stuck? Show hint 2 →
Hint 2 of 2
Each person ate one piece, and three pieces were left.
Show solution
Approach: count pieces, then subtract leftovers
Two cakes × 4 = 8 quarters, and each quarter × 3 = 24 small pieces in all.
Three pieces were left over, so the number of people = 24 − 3 = 21, answer B.
Matthias and Klara live in a tower block. Klara lives 12 floors above Matthias. One day Matthias climbs the stairs to visit Klara. When he is halfway there he is on the 8th floor. On which floor does Klara live?
Show answer
Answer: B — 14th
Show hints
Hint 1 of 2
Halfway up the climb, Matthias has gone up half of the 12 floors.
Still stuck? Show hint 2 →
Hint 2 of 2
Find Matthias's floor first, then add 12 for Klara.
Show solution
Approach: use the halfway floor to find the start
Half of the 12-floor climb is 6 floors, and that point is the 8th floor.
A ferry boat can carry, in one trip, either 10 cars or 6 lorries. Yesterday the boat crossed the river 5 times. It was always full and carried 42 vehicles in all. How many of these were cars?
Show answer
Answer: E — 30
Show hints
Hint 1 of 2
Each of the 5 full trips carries either 10 cars or 6 lorries.
Still stuck? Show hint 2 →
Hint 2 of 2
Start by pretending every trip was lorries, then see how far short of 42 you are.
Show solution
Approach: start from all-lorry trips and swap until the total is right
If all 5 trips were lorry trips, that would be 6 + 6 + 6 + 6 + 6 = 30 vehicles, which is 12 short of 42.
Changing one lorry trip (6) into a car trip (10) adds 4 vehicles, and 12 needs three such changes.
So 3 trips were car trips: 10 + 10 + 10 = 30 cars, choice E.
Hans started a chain e-mail. He sent an e-mail to his friend Peter, who sent it on to 2 more people. Each person who gets the e-mail sends it on to 2 more people. After 3 rounds, 1 + 2 + 4 = 7 people have received the e-mail. How many people have received the e-mail after 5 rounds?
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Answer: C — 31
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Hint 1 of 2
Each round doubles the number of new people: 1, 2, 4, then 8, 16.
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Hint 2 of 2
Add up the new people from all five rounds.
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Approach: sum the doubling rounds
Each round the number of new people doubles: 1, 2, 4, then 8, then 16.
Jana writes down how much her toys weigh: 22 g, 23 g, 25 g, 34 g and 36 g. She wants to share all her toys into two boxes so that both boxes weigh the same. Which two toys do not go in the same box?
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Answer: C
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Hint 1 of 2
Add all five weights and split into two equal boxes.
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Hint 2 of 2
Find which toys sum to half the total; the two that land in different boxes are your answer.
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Approach: split the weights into two equal halves
The weights 22, 23, 25, 34, 36 add to 140 g, so each box holds 70 g.
One box is 22 + 23 + 25 = 70 (balloon, car, boat); the other is 34 + 36 = 70 (helicopter, plane).
So the balloon and the plane end up in different boxes.
Adam has 9 marbles and Brenda also has 9 marbles. Together they have 8 white and 10 black marbles. Brenda has twice as many black marbles as white marbles. How many black marbles does Adam have?
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Answer: B — 4
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Hint 1 of 2
Brenda has 9 marbles, and her black pile is twice as big as her white pile.
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Hint 2 of 2
Once you know how many black marbles Brenda has, the rest of the 10 black ones must be Adam's.
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Approach: split Brenda's 9 into equal groups, then give the rest of the black marbles to Adam
Brenda's black pile is twice her white pile, so think of 1 white group and 2 matching black groups: that is 3 equal groups making 9, so each group is 3.
Brenda then has 3 white and 6 black marbles.
There are 10 black marbles altogether, so Adam has the leftover 10 − 6 = 4 black marbles.
The teacher wrote the numbers 1 to 8 on the board. Then he covered the numbers with triangles, squares and one circle (see picture). The sum of the numbers covered by the triangles equals the sum of the numbers covered by the squares, and the number covered by the circle is a quarter of that sum. What is the sum of the numbers covered by the triangles and the circle?
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Answer: C — 20
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Hint 1 of 3
First add up all the hidden numbers: 1 + 2 + 3 + ... + 8.
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Hint 2 of 3
The triangle pile and the square pile weigh the same, and the circle is just a small extra equal to a quarter of one of those piles.
Still stuck? Show hint 3 →
Hint 3 of 3
Try to split the total into two equal big piles plus a small piece that is a quarter of one big pile.
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Approach: split the total 36 into two equal piles plus a quarter-size circle
The hidden numbers are 1 through 8, and 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
The triangles and the squares make two equal piles, and the circle adds a quarter of one of those piles, so 36 splits as one pile + one equal pile + a quarter-pile.
That is the same as four-and-a-quarter quarter-piles making 36, so each quarter-pile is 4; one full pile (the triangles) is four of them, which is 16, and the circle is one quarter-pile, which is 4.
The triangles cover 16 and the circle covers 4, so together they cover 16 + 4 = 20, choice C.
