xi. pangea matematika verseny 2019 . évfolyam · xi. pangea matematika verseny 2019. döntő 4....

XI. PANGEA Matematika Verseny 2019. Döntő 4. évfolyam

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1. The air distance between Budapest and New York is about

7000 km. An airplane has already covered one quarter of the

journey heading out from Budapest. How many kilometres

does the plane have to fly until it reaches New York?

A) 1750 km

B) 3500 km

C) 2000 km

D) 5250 km

E) 5000 km

2. Nine girls started to make yarn pompoms. One of these nice,

fluffy toys requires 23 dm of yarn to make. After everybody got

the yarn needed for the toy, only 3 cm was left from the ball of

yarn. What was the original length of the yarn in the ball?

A) 210 cm

B) 21 m

C) 2073 cm

D) 2073 dm

E) 2079 cm



3. The ages of the members of a family are the following: Dad is

38, Mom is 36, Dani is 13, Márti is 10 and the youngest child,

Panni is 3 years old. What was the sum of the ages of the family

members 5 years ago?

A) 95 years

B) 100 years

C) 75 years

D) 77 years

E) 78 years

4. How many squares are there in the diagram?

A) 4 B) 8 C) 12 D) 16 E) 20



5. Panna was going to a summer camp. When she walked one

third of the way, 4 kilometres, she realised that she had left her

backpack at home. She went home to pick up the backpack and

then she set out again. She met Zita halfway to the camp and

then they went together to the camp from there. How many

kilometres did they walk together?

A) 12 km B) 8 km C) 6 km D) 4 km E) 2 km

6. George is preparing for the Pangea mathematics competition.

He solved two questions on Monday and then each day

afterwards he did three more questions than on the previous

day. How many questions did he do altogether from Monday to

Friday?

A) 14 B) 26 C) 40 D) 41 E) 42



7. Find the cube whose net is drawn here.

A) B) C) D) E)

8. Three buses are leaving a bus station at the same time. The first

bus returns to the station every hour, the second returns every

two hours and the third one every three hours. In how many

hours will these three buses return to the station at the same

time?

A) 12 hours

B) 10 hours

C) 8 hours

D) 6 hours

E) 4 hours



9. A knight is looking for the princess in a castle but he cannot find

his way. Finally, one of the guards helps out the knight telling

him the following: “There is an algebraic operation written on

each door. If the result of one of these operations is the number

on your shield then that is the door you have to enter.”

Which door shows where the princess is?

A) 515·3

B) 6160:4

C) 9258:6

D) 4626:3

E) 385·4



10. Last summer Tomi went to Sátoraljaújhely with his family

and they tried the bob-track. Tomi was very brave and he did

three rides. Zita, Tomi’s younger sister, rode the bob only once.

Their father also had three rides, but their mother did it only

once. Zita and her mother preferred the donut slide instead,

which they both rode once. The Donut slide is a huge rubber

tyre people slide down in on a snowy hillside. The table below

shows the ticket prices. How much money did the family pay

altogether?

A) 6125 Ft

B) 5825 Ft

C) 8075 Ft

D) 7275 Ft

E) 5275 Ft

Adults - 1 ride 800 Ft

Adults - 3 rides 1950 Ft

Children - 1 ride 650 Ft

Children - 3 rides 1500 Ft

Donut: Adults - 1 ride 820 Ft

Donut: Children - 1 ride 405 Ft

Donut: Adults - 3 rides 1040 Ft

Donut: Children - 3 rides 860 Ft



11. Pastry-cooks are making a four-tier cake for a wedding. All

layers are going to be of a different flavour: blueberry,

strawberry, raspberry and chocolate. How many different cakes

could the pastry-cooks make if the top layer must be blueberry-

flavoured?

A) 3 B) 6 C) 8 D) 10 E) 24

12. The nurse service either vaccinates babies or examines them

to follow their growth. Today 23 babies visited the nurse

service. Twelwe of them were measured and the others got

vaccinated. There were 11 boys at the nurse’s. Today 5 girls got

vaccinated. How many boys were measured?

A) 5 B) 6 C) 7 D) 11 E) 12



13. Tomi bought pancakes for his friends and himself at the

beach. Everybody wanted the same kind of pancake which cost

570 Ft each. Tomi paid with a 5000 Ft bill. He got some money

back, but if he had bought one more pancake then his 5000 Ft

bill would not have been enough. How many forints did Tomi

get back?

A) 440 Ft

B) 4560 Ft

C) 130 Ft

D) 4430 Ft

E) 540 Ft

14. An ice-cream parlour sells 3 cones of ice-cream every

minute. Each cone of ice-cream contains 2 scoops. The parlour

opens at 10 o’clock in the morning, there is a lunch break

between 12:45 and 13:30, and closes at 8 o’clock in the

evening. How many scoops are sold in the parlour from the

time they open at 10 a.m. to the time they close at 8 p.m. if

they sell the ice-cream this rate all day?

A) 1665

B) 2340

C) 3330

D) 4320

E) 3240



15. Süsü, the dragon, has got one head. Süsü’s children are also

one-headed dragons. One of Süsü’s children invited his friends

to his birthday party. All of his friends are seven-headed

dragons. His one-headed siblings were also there at the party.

All dragons have got two legs. Süsü noticed that the dragon

kids had 54 heads and 24 legs altogether. How many kids does

Süsü have?

A) 3 B) 4 C) 5 D) 6 E) 7



Questions 16-20. must be solved on the "Solutions" sheet. (Show

your work, giving the final solution only is not enough.)

Where there is a diagram included, work within the diagram.

16. When I got on the tram, there were 35 passengers on it, 36

including me. While I was travelling on the tram, I noticed at

the first stop that eight passengers got off and five new

passengers got on. Interestingly enough, exactly the same thing

happened at every stop. How many passengers were there on

the tram when it left the ninth stop?

17. A farmer has 345 cows. Each cow gives 28 litres of milk every

day. The farmer delivers three quarters of the milk to a

creamery. He gives one third of the rest of the milk to his

family, relatives and friends. He makes butter from one half of

the remaining milk and cheese from the other half. How many

kilograms of cheese can he make if 7 litres of milk is required

for one kilogram of cheese?

18. A pen and three bottles of correction fluid cost as much as

four notebooks. At the price of one notebook and five erasers

you can buy four bottles of correction fluid. One notebook

costs as much as three erasers. How many erasers could you

buy at the price of one pen?

19. What is the result of the following operation? Give the

answer in Roman numerals, too.

MCDXXV + DXCIV = ?

20. Olívia takes her puppy for a walk twice a day, each day of

the week. She walked a total of 18 hours and 40 minutes in

four weeks. How many minutes did each walk take if it took the

same time every day?

xi. pangea matematika verseny 2019 . évfolyam · xi. pangea matematika verseny 2019. döntő 4....

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