* Which of the below is not a cubic number?
344
* There are 512 balls in a box. Half of them are taken out from the box, and this process is repeated
6 times. How many balls are left in the box?
8
* See annex. Calculate by dividing:
2000
* See annex. Calculate by multiplying:
0.08
* See annex. Calculate by multiplying:
0.008
* How many of the following numbers are a prime number? 3, 9, 17, 21, 121, 127, 222, 343,
655, 999
3
* 15 tons of apples have been sold following amounts: 1.5 Dz / 400 kg / 0.75 t / 550 kg / 100
Pfd. How many tons are still left? (Pfd: lbs)
13.1
* Q is a square number and also divisible by 20. Which of the following number is a square
number?
Q/4
* Steven has 85 € and spends 23 €. How much does he have left?
62
* What is the result of: 100 - (70 - (40 - (30 - 20))) ?
60
* See annex. Calculate by subtracting:
-6
* How many of the following numbers are a prime number? 11, 12, 13, 17, 21, 31
4
* How many of the following numbers are a prime number? 11, 12, 13, 17, 21, 27, 31, 45
4
* Q is a square number and also divisible by 20. How many of the following are also a square
number?
I - Q/2
II - Q/4
III - Q/5
IV - Q/8
1
* Which one below gives the greatest value?
1. 222
2. (2x2)2
3. 22 + 22
4. 2(2x2)
There are more than one number which give the greatest value.
* ((6⋅((9+8)⋅2) - 7⋅5) - 3)⋅6 + 4 = ?
1000
* Which of the following numbers is not a cube of an integer?
216 344 1000 125 27
344
* How many prime numbers are there among the following numbers? 2, 3, 21, 27, 29, 37, 39
4
* There are 512 balls in a box. Half of them are taken out from the box, and this process is
repeated 5 times. How many balls are left in the box?
16
* How many prime numbers are there among the following numbers? 2, 3, 11, 13, 17, 19, 23,
27, 31, 39
8
How many of the following equations are correct?
53 = 625
43 = 64
210 = 1028
106 = 1000000
2
* See annex. Calculate by adding:
689
* See annex. Calculate by adding:
17339
* How many of the following are the greatest?
(2x2)2
22 x 22
4 x 22
2 x 22
three
* Which of the following gives the greatest result?
(5 + 2) x 5 - 10 / 5
Xxxxxxxxxxxxxxxxxxxxxxxxxxxx
See annex and enter the result.
1
* See annex. What is the result?
70/33
* See annex. What is the result?
13/60
* See annex and enter the result.
1
* See annex and enter the result.
13
* See annex. Which value will make the following equation a whole number?
7/12
* 50 divided by ½ plus 4 = ?
104
* 50 divided by ½ plus 5 = ?
105
* See annex. How many of the them are incorrect?
1
* ((1 + ½) / ½ + ½) / ½ = ?
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
* 1 kg cheese costs € 18.20. How much does it cost for 318 grams?
€ 5.79
* 85.5 gram of caviar cost € 256.5. How much (€) would it cost for 55 grams?
165
* If 4.5 metres of carpeting cost 90 €, how much 2.5 metres cost?
50
* A bale linen costs 93,75 €. How many meters is the linen if a meter costs 12.50 €?
7.5
* Three buttons cost 5 cents. How many buttons can you buy with 50 cents?
30
* 13.5 kg of seed cost 270 €. How much does 7.5 kg of seed cost?
150
* A motorcycle consumes 11 l gasoline per 100 km. How many litres does it consume
for 350 km?
38.5
* 145g of caviar costs 43.5 €. How much does 75g of caviar cost?
22.5
* An alloy consists of 7 / 8 from gold and costs 840 €. How much would the alloy cost,
if it was 25% of gold?
240
* If 4/12 of a cream cake are missing, the cake costs 24 €. What is the price of a
complete cream cake?
36
* Three candies cost 0.15 €. How many candies you can but with 1.65 €?
33
* A litre of Fanta costs 2.4 €. How much do 2.4 litres of Fanta cost?
5.76
* 3.6 kg of apples cost 12 €. How many kilograms of apple can you get with 10 € ?
3
* A car with a turbo diesel engine consumes 6 litres per 100 km. How much does it
consume on 250 km and how far can it go with 24 litres?
15 litres, 400 km
* A metal wire of 48 cm length expands to 52 cm if heated. How long (in cm) would a
wire of 72 cm length become if heated?
78
* A motorcycle consumes 4/5 of its fuel tank for 3/4 of 400 km. How far (in km) does
the motorcycle go with full tank?
375
* In the holidays, people rent an apartment of 90 m2 for 1200 €. You want to hire an
apartment of 600000cm2. How much money would you pay?
800
* A loom weaves 60 m of X fabric, while the other loom weaves 40 m of Y fabric. How
many meters of X fabric would be weaved, while 60 m of Y fabric are weaved?
90
* A car consumes 6 liters of gasoline per 100 km. How much does it consume at 350
km and how far can it go with 27 liters of fuel?
21 l / 450 km
* A car with 3/5 of fuel can travel 3/4 of the route. How much fuel capacity is
required for the whole route?
4/5 tanks
* A car with 3/5 of fuel can travel 3/4 of the route. How much fuel capacity is
required for the whole route?
12/15 tanks
* A gold bar consists of 7 / 8 of pure gold and has a value of € 840. How much would
it cost, if it consisted from half pure gold?
480
* Five bottles of juice cost 8 €. How many bottles can you buy for 64 €?
40
* 145 grams of caviar cost 43.50 €. What is the price for 75 grams?
22.50 €
* A wire of 4.5 m cost 90 €. How much does a wire of 2.5m cost?
50
* A factory produces 304 bicycles in 8 hours. How many bicycles are produced in half
an hour?
19
* 7/8 of a barrel is filled with whiskey and it costs 84 €. How much does it cost when
it is half full?
48
* The 20 seconds of call costs € 0,50. How much does 5 minutes cost?
7.50 €
* In a factory 288 tables are produced in 8 hours. How many tables are produced in a
quarter?
9
* A "cupric" equals 16 "Auri". How many cuprics is equal to 10000 Auri?
625
* An alloy consists of 7 / 8 from silver and costs 940 €. How much would the alloy
approximately cost, if it was 25% of silver?
268 €
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* Two pipes with a diameter of 4 cm and a radius of 6 cm can fill the pool. The smaller pipe
can fill the pool in 18 minutes. How many minutes does it take the larger pipe to fill the
pool?
2
* Two pipes with a radius of 1 cm and a diameter of 6 cm can fill the pool. The
smaller pipe can fill the pool in 1.5 hours. How many minutes does it take the larger pipe to
fill the pool?
10
* A swimming pool has a capacity of 5000 liters. Through a tube, it will be filled with 5
liters per second but through a hole it loses 50 liters per minute. How many minutes does it
take the pool to be completely full?
20
* A large pipe fills a tub in 2 hours, and a small tube fills it in 3 hours. How many
minutes do they fill the tub together?
72
* 4 workers need 9 days to finish a work. How many workers are needed to finish this
work in half a day?
72
* A water supply is sufficient for 12 people for 15 days. How many days can 4 people
use this supply?
45
* 18 painters need 4 hours to finish a work. How many hours do 24 painters need?
3
* A keeper at a zoo has enough meat to feed 7 lions for 78 days. How long would the
food last for 21 lions?
26
* Seven people finish a work in 6 days. How many people can finish the work in half a
day?
84
* Four bricklayers need six days to build a wall. How many bricklayers would be
necessary to finish the wall after only half a day?
48
* A pile of sand has to be removed by trucks. Two trucks would need eight days to
complete the work. In order to finish earlier an additional truck is delegated to the task as
from day four. When is the sand removed completely?
after 6 1/3 days
* Frank, Julia and Annette want to repair their car. Together they would need 10
days. How many friends should help them to finish the repair in 6 days?
2
* Three people are living in a small village. They want to prepare sausage and fries to
the villagers. Annette needs 2 hours, Julia needs 3 hours and Frank needs 6 hours to prepare.
How long does it take them to prepare the meal together?
1
* Frank and Annette drink 6 liters of sangria in 4 hours. How many customers would
drink 18 liters of sangria in 2 hours?
12
* Frank and Annette drink 6 liters of sangria in 4 hours. How many drinks can three
people drink between the hours 18:00 and 02:00?
18
* A lion, a cheetah and hyena eat a prey animal together. The lion eats the prey alone
in one hour, the cheetah needs three hours and the hyena needs six hours. How many
minutes does it take the three to eat the prey together?
40
* Tom renovates a room of 18 sq meters in 8 hours in one working day. Peter works
at 1/3 performance of Tom. Fritz works 25% faster than Tom. What is the difference in m²
between the worst and the best after 1 1/2 working days?
24.75
* 9 bricklayers need 8 hours on each of the 2 working days to build 3 walls which are
5 m in length. How many bricklayers are needed to finish the same work in 12 hours?
12
* Ten workers need 2 days to build a wall of 3 km in length. How many workers are
needed to build a wall of 90 km long in 10 days?
60
* 3 construction workers need 4 days to build a wall of 12 km in length. How many
days are needed to build a wall of 10 km in length with 5 workers?
2
* Three workers require 6 days to build a 2 km long road. How many workers are
needed to build a 10 km long road in 9 days?
10
* A fodder is enough to feed 7 horses for 78 days. For how many days is it enough for
21 horses?
26
* Ten workers dig a hole 5 yards deep in 2 days. How deep (in yards) is the hole if 5
workers are digging for 10 days?
12.5
* Worker A needs 2 days to finish a task while worker B needs 3 days. How many
days do they need to finish the task together?
1.2
* 2 workers are working for 10 days to dig a hole which is 5m deep. How many
workers are needed to dig a hole which is 8 m deep in 4 days?
8
* A worker needs 2 hours to finish a work while the other needs 3 hours. How many
minutes do they need to finish the work together?
72
* A large pipe fills a tub in 2 hours, and a small tube fills it in 3 hours. How many
hours do they need to fill the tub together?
1.2
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* A helicopter travels 175 meters in 15 seconds. How long does it travel (in km) in 2 hours?
84
* A girl can run 1.75m in 1/4 seconds. How far (in metres) can she run in 10 seconds?
70
* Car A travels at 105 km/h, and car B at 15 km/h. If B travels 13 km, how far does car
A travel?
91
* A ship travels 17.5 kilometes in 12 minutes. How far (in km) does it travel in 9
hours?
787.5
* The large gear rotates 18 times and makes a small cog rotate 54 times. While the
small cog rotates 216 times, how many times does the large gear rotate?
72
* The distance between A and B is 240 km. On the road map, this route appears 40
cm long. What is the scale of the road map?
1 : 600000
* A car leaves the town at 8:51 and reaches City B at 16:31. How long does the actual
journey take if the car gives a break for three quarters?
6 hours 55 minutes
* Two bicyclists meet at 14:55. They give a break for 5 minutes and then they begin
to ride in opposite directions. How far (in km) is the distance between them at 16:20 if one
goes at 12 km/h and the other at 7.5 km/h?
26
* How many kilometers does a motorcycle go in 9 hours if its average speed is 70
km/h?
630
* At 12:00, car A starts to travel at 80 km/h. Car B starts to travel at 13:00 at 120
km/h. When does car B catch car A?
15:00
* A car travels at 60 km/h from A to B, then it travels back at 40 km/h. What is the
car’s average speed in km/h?
48
* City A and B are located 90 km apart. A car goes from A to B with 60 km / h and
back with 120 km / h. How many minutes does it take for the whole trip?
135
* Two cars meet at 8.30 o’clock. How far (in km) are they at 8:50 o’clock if one of
them travels at 90 km/h, while the other at 135 km/h?
75
* A special bicycle has a front wheel with 10 cm size and a rear wheel with size 80 cm.
If the front wheel rotates 7000 times, how many times does the rear wheel rotate?
875
* Gear A with 20 teeth is connected with gear B with 50 teeth. How many revolutions
does gear B make, if gear A rotates 20 times?
8
* A car travels at 60 km/h from A to B and it should arrive B in 5 hours. But after 3
hours and 10 minutes, the car breaks down and stops. How many kilometers are there left
from target B?
110
* A person wearing roller blades needs 35 minutes for a distance of 12 km. What is
her speed in km/h?
20 4/7 km/h
* Two places A and B are 300 km apart. At 8:00 a.m. a freight train leaves A towards B
at the speed of 30 km/h. A passenger train leaves B towards A at 11:00 a.m. at the speed of
60 km/h. Where and when do the two trains meet?
At 1:20 p.m. 160 km from A
* The reaction time of a car driver is 1 second. At a speed of 96 km/h the driver
suddenly notices a red traffic light. Which distane does the car cover until the driver starts
breaking?
26.6 metres
* A train needs 9 hours for a certain distance at the speed of 72 km/h. How long
would the train take for the same trim if it went 8 km/h faster?
8 hours and 6 minutes
* A student normally needs 15 seconds for a 100 m sprint. One day favourable wind
conditions help her to increase her speed by 2 km/h. What is her time now?
approximately 13.8 sec
* At Frankfurt Airport a passenger wants to get from Terminal A to Terminal B.
Walking would take 3 minutes. Standing on the conveyer belt would take 2 minutes. How
long will it take him if he walks on the conveyer belt?
1.2 minutes
* At Frankfurt Airport a passenger wants to get from Terminal A to Terminal B.
Walking would take 3 minutes. Standing on the conveyer belt would take 2 minutes. How
many seconds will it take him if he walks on the conveyer belt?
72
* Two wheels with diameters of 80 cm and 70 cm are rotating together. If the small
wheel rotates 1000 times, how many times does the large wheel rotate?
875
* A student normally needs 15 seconds for a 100 m sprint. One day favourable wind
conditions help her to increase her speed by 2 km/h. What is her new speed in km/h?
26
* A car goes from A to B at 80 km/h and turns back at 100 km/h. What is the total trip
time in minutes if the distance between A and B is 90 km?
2 h 02 mins
* The diameters of the two wheels of a bicycle are in 4:5 ratio. If the large wheel
rotates 1000 times, how many times does the small wheel rotate?
1250
* The diameters of the two wheels of a bicycle are in 4:5 ratio. If the small wheel
rotates 1000 times,
how many times does the large wheel rotate?
800
* At 10:00, car A starts to travel at 80 km/h. Car B starts to travel at 12:00 at 120
km/h. When does car B catch car A?
16:00
* The front gear with 50 teeth is connected to the rear gear with 20 teeth. How many
times does the front gear rotate if the rear gear rotates 20 times?
8
* A special bicycle has a front wheel with 50 teeth size and a rear wheel with 20
teeth. If the front wheel rotates 40 times, how many times does the rear wheel rotate?
100
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* Out of 50 screws, 8% of them are too small, and 24% of them are too large. How many
bolts have the correct size?
34
* 3% of milk is produced as fat. How many kilograms of milk are needed to produce 1.5 kg of
fat?
50
* After a price increase of 25%, the Hoover costs € 100. What was the price before the
increase?
80
* A student has 21 correct answers out of 30 questions . How many percent did he answer
correctly in the exam?
70
* There are 61 boys in a group of 100 children. What is the percentage of girls?
39
* In a hospital, 900 children are born per year and 495 of them are boys. What is the
percentage of boys?
55
* How much percent wage increase did Mr. X get, if his salary is increased from € 1476 € to €
1549.80?
5
* After the certification exam, 10% of males and 15% of females recieved a journeymen
letter. What percentage receivedthe letter if 60% of the group are females?
13
* A hotel charges an off-peak price of 98 € for a single room. During peak season the hotel
charges an extra 15%. What is the room rate during peak season?
112.70 €
* A certain amount of money is lent at interest of 4% annually. How many years later will the
money be doubled if there is no taxation?
25
* A dealer sells stationery pens. For each 4 pens he sells, he can afford 6 pens. What is his
profit in percentage?
50
* An accountant writes an invoice in an average of 40 minutes. Since he has a headache
today, he spends an average of 1 hour and 20 minutes. How much extra time does he spend
in percentage?
100%
* 1/3 of the tasks are difficult, 1/6 of them are easy. What percentage of the tasks are
neither difficult nor easy?
50
* How much is the monthly rate at an annual interest burden of 9.5% for a loan of €
150,000?
1187.50 €
* A motorcycle costs € 15,000. For the first two years, it loses 20% of its original value for
each year. For the next four years, it loses 10% of its original value per year. Following year,
it loses only 5% of the original price. What does the motorcycle worth after 7 years?
2250 €
* 6 pencils costed € 1.20, and now 5 pencils cost € 1.20. What percentage did the pencils
become more expensive?
20%
* A car consumes 7 liters per 100 km and the tank is completely full. After 600km, one
quarter of the tank is left. What percentage of the original tank will remain at the end of the
trip if there is 184 km to go?
2
* Tom earns 15% less than Peter, Sabine has 10% more income than Peter. What is the total
income if Peter earns 2400 €?
7080
* In an exam, 1/3 of the questions were easy, 1/6 of them were very hard. What is the
percent of the questions at average level?
50
* 66 2/3 % of 12 = ?
8
* Peter drives a car which consumes 7 liters per 100 km and
the tank is completely full. After 600km, the fuel indication shows that 1/4 of the tank is left.
What percentage of the original tank will remain at the end of the trip if there is 184 km to
go?
2%
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* If y divided by 3.4 is equal to 9.2, what is y?
31.28
* A shop which is selling soap bars, makes a promotion: "Buy Three Get Another One Free!"
If you want 23 bars, what is the least number you have to pay for?
18
* A clock shows 12:00. How many minutes later do the hour hand and the minute hand are
on top of each other?
65
* Three racing cyclists are starting on a circular course. How many total rounds does the
cyclists need until all of them cross the starting line at the same time if the first cyclist needs
8 minutes per round, the second cyclist 6 minutes and the third cyclist 15 minutes?
43
* A candle is 1m away from the menu. This distance is shortened to 50 cm. How much
brighter does the menu appear now?
4
* At 08:00 local time, an airplane takes off from Frankfurt (8⁰ East) to fly to an airport
located at 97⁰ West in Mexico. The flight time is 11 hours. What is the local time on arrival at
Mexico?
12:00
* Hamburg is on 53° N latitude and Ottawa is 75° N latitude. If it is 12:00 at Hamburg what
time is it at Ottowa?
Not enough information
* The planet Alpha has exactly the same rotation as the earth. An hour lasts 100 minutes
there, and a day has 10 hours. The day begins at Alpha when it comes to us is the morning
clock 06:00. What time is it on Alpha when it is midnight for us?
07:50
* A car consumes 8 liters per 100 km. The tank has a maximum capacity of 60 liters, and
there are still 32 liters in the tank. After a journey of 250 km, how many liters of fuel are
needed to fill the tank completely?
48
* How many three-digit odd numbers become greater when their digits are reversed?
200
* A number has the digits 1, 2, 3 and 4. How many different combinations are possible if
each digit must occur only once?
24
* How many 4-digit numbers can be formed with the numbers 3, 4, 5, 6 if each number
should occur only once?
24
* 6 passengers are going to be seated in a business jet aircraft. How many ways are there?
720
* How many points of intersection can five straight lines have in one plane maximum?
10
* The digits 2, 4, 6 and 8 can be arranged in different combinations to make a 4-digit
number. How many combinations are possible if each digit must occur only once?
24
* There are 6 women and 4 men in a chess competition. The women are playing between
each other. Then each men are playing with each women. How many games would there be
in total?
39
* A factory exports 3/4 of the products and sells 4/5 of the remainder domestically. How
many percent will remain left?
5
* An area of 333000 m² is shared with the ratio 5:4. How many m² is the smaller area?
148000
* A swimming pool has a capacity of 5000 liters. Through a tube, it will be filled with 250
liters per minute but through a hole it loses 50 liters per minute. How many minutes does it
take the pool to be completely full?
25
* Oliver and Christian are drinking beer worth 72 €. For every three glasses Christian drinks,
Oliver drinks five. The price for one glass of beer is 3 €. How many glasses of beer has Oliver
had?
15
* A man has 5 and 10 cent coins in his piggy bank, a total of 17 coins. Together, the coins
have a value of € 1.20. How many 5-cent coins are in his piggy bank?
10
* Whenever Tom gets € 5, Sabine receives € 3. Together, they have 120 €. How much does
Tom have?
75
* Someone spends 1/10 of his money on stamps, and four times of stamp’s money on
stationery. He still has 60 cents left. How much money did he have before?
1.20 €
* For an alloy you need two parts of silver and three parts of lead. How many grams of silver
are needed to make 15 grams of this alloy?
6
* The ratio of the sum of a number and 19 to 32, is equal to the ratio of 51 to 68. What is the
number?
5
* A trader buys plants for 10.500 €. At each plant sold, he deserves exactly 100 €. After
selling his stock overall, he has received 14.000 €. How many plants did he have?
35
* An alloy consists of 5 parts of silver and 8 parts of titanium. How many grams of titanium is
needed to make 156 g of this alloy?
96
* The ratio of the sum of a number and 46 to 76, is equal to the ratio of 63 to 84. What is the
number?
11
* The difference between seven times a number and 4 is equal to the sum of five
times that number and 2. What is the number?
3
* An alloy consists of 6 parts of silver and 4 parts of titanium. How many grams of titanium is
needed to make 150 g of this alloy?
60
* The captain drinks 5 bottles of water before flight. During the flight, while captain drinks 3
bottles, copilot drinks 2 bottles. After the flight a total number of 30 bottles are finished.
How many bottles did the captain drink?
20
* A grandmother wants to hand out her grandchildren 140,000 €. Annette gets two times as
much as Frank. Frank gets two times as much as Julia. How much money does Annette get?
80000
* Frank and Julia buy a car which costs 20,000 €. Julia is going to drive rarely, so she only
pays 1/4th of the money that Frank pays. How much does Julia pay?
4000
* A group of people decides to place 1/3 of the “giant wine barrel” in the marketplace. They
ask the price of the whole barrel and learn that 4/5 filled barrel costs 1200 €. How much
money do they need to pay?
500
* Two cars drive a total distance of 300 km. The distance that car A drives is 2/3 of the
distance that car B drives. How far (in km) does car B drive?
180
* In two cases there are a total of 43 bottles. One case has 9 bottles more than the other.
How many bottles are there in the smaller case?
17
* A wealth of 52000 € will be divided such that A gets three times the money B gets. How
much money does B inherit?
13000
* A game consists of blue and yellow balls. 1 / 3 of the balls are blue and 18 pieces are
yellow. How many balls are there in total?
27
* At a reading, each speaker has 30 minutes speaking time, and the total time is 3 1/2 hours.
How many speakers can speak in total?
7
* After the purchase, 1/4 of the price has been already paid. If another 200 € is paid, 250 €
will remain. What is the total price of the purchase?
600
* Karl and Fritz drink beer together for a total of 72 €. While Fritz drink 3 beers, Karl drinks 5
beers. A beer costs 3 €. How many beers did Karl drink?
15
* Two brothers together have 42 candies. One has 4 more candies than the other. How
much candy does the one who owns fewer candies have?
19
* A family spends 1/6 of their income for rent and four times the rent money for eating and
drinking. They can reserve 420.00 €. How much is the total income?
2520
* Tom spends 1/8 of his money on stamps, and three times of stamp’s money on stationery.
He still has 80 cents left. How many cents did he have before?
160
* There are balls in a bag. The number of balls are halved and then 4 balls are added. This
process is repeated four times. At the end there are 8 balls remained in the bag. How many
balls were there in the bag at the beginning?
8
* Number ‘x’ is doubled and 1 is added to the result. This process is repeated once again
and the result is 43. What is x?
10
* A succession of € 576000 should be split in 4:5 ratio. How big is the smaller proportion?
256000
* When you subtract 12 from 6 times the requested number, you get 3 times that number.
What is the requested number?
4
* Three numbers have the ratio 2:3:4 and their total value is 45. What is the biggest
number?
20
* A money is halved every 4 days. What was the total amount if 20 € is left after 20 days?
640
* In a family, every daughter has the same number of brothers and sisters, and each son has
twice as many sisters as brothers. How many sons are there in the family?
3
* A 60 m canvas should be cut so that one piece is 2/3 of the other piece. How long is the
shorter piece in metres?
24
* 15 crates of strawberries weigh 250kg, and every empty box weigh 3 kg. How much does
the strawberries weigh?
205
* Tom gets quarter, Peter gets 35% of some money. Sabine gets the rest which is 120 €. How
much does Peter get?
105
* Mr P. gets one fifth from a lottery prize and Mrs N. gets one fourth. How much is the total
lottery prize if Mrs N. gets 4000 € more than Mr P.?
80000
* Two brothers are together 39 years old, one being 7 years older than the other. How old is
the older brother?
23
* A squirrel is 3 years old. It has seen daylight in only 1 / 24 of its lifetime. How many months
is that?
1.5
* Frank, Julia and Annette are totally 77 years old, as their grandmother. Frank is 5 years
older than Julia. Julia and Annette are together 17 years older than Frank. How old is Julia?
25
* If a father is three times as old as his youngest son and twice as old as his oldest daughter
and all three people together are at a total age of 88 years, how old is the daughter?
24
* A father is 20 years older than his son. Two years ago, he was 3.5 times as old as the son.
How old is the son now?
10
* After 15 years, the pilot will be twice as old as the copilot. The copilot will be 25 in 5 years.
How old is the pilot today?
55
* In 2 years, Kosta will be twice as old as George, who is now 10 years younger than Kosta.
How old is Kosta today?
18
* A couple is together 75 years old and the age difference between them is 5 years. How old
is the younger of the two?
35
* Together, a mother and her daughter are 60 years old. The mother is 36 years older than
her daughter. How old are both persons?
daughter 12, mother 48
* 3 hours ago the distance to 10 a.m was as twice as the distance to 1 p.m. What time is it
now?
19:00
* A candle is 2 feet away from the menu. This distance is shortened to 1 foot. How much
brighter does the menu appear now?
4
* There are 500 tickets in a lottery and 100 of them are winning tickets. 24 of them are
already sold. How many tickets should Mr. Jon buy in order to ensure that he wins
something?
401
* The total age of a brother and a sister is 42 and sister is 4 years older than the brother.
How old is the brother?
19
* The amount of alcohol in Peter's blood is 2.50 g/lt and it decreases by 0.25 g/lt per hour.
What is the amount of alcohol left in his blood after 7 hours and 20 minutes?
0.66 g/lt
* x is halved and 4 is added to the result. This process is repeated four times and the result is
8. What is x?
8
* There are 500 tickets in a lottery and 100 of them are winning tickets. 24 of them are
already sold. How many tickets should Mr. Jon buy in order to ensure that he wins
something?
401
* A clock shows 12:00. What is the next time when the hour hand and the minute hand are
on top of each other?
01:05
* At midnight, Peter has a total alcohol content of 1.5g in his blood. The blood alcohol
content reduces by 0.15 g/ml per hour. What is the alcohol concent left in his blood at
07:40?
0.35
* 3 hours ago, the time until 10 a.m. was as twice as it will be in one hour. What time is it
now?
5
* In 10 years, Max will be twice as old as Fritz is now, who is 2 years younger than Max. How
old is Max now?
14
* Two cars drive a total distance of 300 km. The distance that car A drives is 2/3 of the
distance that the other car drives. How far (in km) does the other car drive?
180
* At midnight, Mike has a total alcohol content of 1.25 g in his blood. The blood alcohol
content reduces by 0.20 g/ml per hour. At what time will he be sober?
06:15
* Number ‘x’ is doubled and 1 is added to the result. This process is repeated once again
and the result is 42. What is x?
9.75
* Three people will start to drink at the bar, but they can not decide the sequence. How
many possibilities are there?
6
* Two cars drive a total distance of 300 km. The distance that car A drives is 2/3 of the
distance that car B drives. How far (in km) does car A drive?
120
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How many functions below do not go through the y-axis?
a) y = 12
b) y = - (5 - x)
c) y = sinx
d) -5/x²
1
* x4 – 6x3 + 5x² + 22x + 55 = 45
What is x = ?
x=-1
* (x + 3)(x - 3)(x - 2) Which of the following answers represents the equation?
x³-2x²-9x+18
* How many of the following equations apply for X = -2 ?
X²-4=0
X²-2X+4=0
X²+4X+4=0
X²+4X-4=0
X²+2X+4=0
2
* Which one is correct about the following equation? x² - 5x + 6 = 0
(x - 2) . (x - 3) = 0
* One sheet (0.1 mm thick) is folded 10 times. How thick is the staple in centimeters?
10.24
* What are the solutions for (x - 0,6)² = 1.96?
2, -0.8
* Which of the values given for the equation lead to a positive result?
x=1
* 2x.x – x2 = 135. What is x?
5
* How many times must a sheet with a thickness of 0.1 mm be folded so that the thickness
can cover the distance between the Earth and the moon?
40
* Number ‘2’ will be used three times. What is the greatest number that can be achieved?
4194304
* Which of the answers form the graph shown in the annex?
x-2
* Which of the answers form the graph shown in the annex?
2x
* How much does f(x) = x² graph shift if it becomes f(x) = (x - 3)² + 5?
3 units right, 5 units up
* For which values does the following equation give real solutions?
log[(x-2)(x-3)(x-3)]
x>2, x≠3
* Which of the answers is the lowest point of this parabola: y = x² - 4x - 1
x = 2, y = -5
* For which values does the following equation give real solutions?
√(x²-3x+2)
x ≥ 2 or x ≤ 1
* If the square roots of the natural numbers from 1 to 200 are written down, how many of
them are whole numbers?
14
* Which number’s square root is equal to two times its cubic root?
64
* Which of the answers form the graph shown in the annex?
x²
* Which graph in the annex represents f(x) = x² - x ?
1
* What is the positive value of x for (x - 0,6)² = 1.96?
2
* How many times must a sheet with a thickness of 0.1 mm be folded so that the thickness
can cover the distance between the Earth and the moon?
42
* (x – 0.3) / (2 – x)
How many of the following values will give a result below 0? x=0 x=0.1 x=0.3 x = 1
2
* (x-6).(x+2).(x+3) = ?
x³ - x² - 24x - 36
* (x - 1) . (x - 0)
For which values of x, the result of the equation is not negative?
x ≥ 1 or x ≤ 0
* (x-3).(x-6).(x+4) = ?
x³ - 5x² - 18x + 72
* (x+3) . (x-5) . (x-3) = ?
x³ - 5x² - 9x + 45
* x³ + 4x² - 11x - 30
(x+2) . (x-3) . (x+5)
* (x+4) . (x-6) . (x+2) = ?
x³ - 28x - 48
* f(x) = x4 – 6x3 + 3x² + 26x - 24
Which of the values below will give a result equal to zero?
1, 3, 4
* f(x) = x6 – 10x5 + 34x4 – 40x3 - 11x² + 50x - 24
Which of the values below will give a result equal to zero?
1, 3, 4
* Which graph in the annex represents f(x) = (x-4)² + 5 ?
1
* (x+3).(x-5).(x+6)
x³ + 4x² - 27x - 90
* (x+5).(x-6).(x+3)
x³ + 2x² − 33x – 90
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* A staircase has 8 steps with a height of 14 cm each. This staircase is to be exchanged by a
new one with only 7 steps. What is the height (in cm) of each of the new steps?
16
* The gate is 15 meters north of the tree, and the tree is 30 meters north of the house.
What is the distance from the gate to the house in metres?
45
* 15 aircraft are performing a formation flight. Only two aircraft are one in front of another,
and the other aircraft are flying side by side as much as possible. The space between two
aircraft is 8 meters. If you neglect the dimensions of the aircraft, how long is the distance
from one end of the formation to the other end in meters?
104
* A guy from Texas has a square shaped farm of 100 km2. How far must he ride to check his
farm’s outer fence in km?
40
* The shaded square has an area of 1. What is the area of the large square?
25
* How long is the diagonal of the square with an edge length of 1 cm? Choose the most
approximate answer.
1.4
* A rectangle has an area of 2193 sq meters and its length is 51 m. How long is the width in
metres?
43
* A rectangle is 12 cm long and 8 cm wide. A second rectangle is identical with respect to
the surface area. How wide (in cm) is the second rectangle if it is 16 cm long?
6
* A rectangle has the edge lengths: a = 10 cm and b = 5 cm. a is enlarged by 20%, b is
reduced by 10%. How many percent is the change in the area of the rectangle?
8
* A rectangle has sides of 5 cm x 10 cm. If both sides are increased by 10%, how many
percent does the area increase?
21
* A paving contractor is required for a space of 500 sq meters area. How many stones must
be ordered if the size of one stone is 10x20 cm?
25000
* A rectangle has the edge lengths: a = 5 cm and b =10 cm. a is reduced by 20%, b is
increased by 20%. What is the change in the area of the rectangle?
reduced by 4%
* Which triangle applies for sinα = sinβ?
equilateral triangle
* Which of the following is correct about a triangle if sinα = sinβ?
Two sides of the triangle are equal.
* The sides of a rectangle and a parallelogram are the same. Which of the following is
correct?
Area of the rectangle is larger
* The circumference of a parallelogram is ….. a square with the same area.
greater than
* A cube house has a sloping roof. The edge lengths of the house is 8 m and the overall
heightl of the house is 11m. How big is the entire surface (in square metres) of the two
slanting roof?
80
What is the area of the shaded part in square metres?
279
* See annex. Which of the following information is correct?
γ is not 90°.
* Which of the following data results in more than one triangle?
one side and one angle
* The sides of a triangle are 3 cm, 4 cm and 5 cm. This is ........
a right triangle
* With which of the following information can you draw infinite number of triangles?
all three angles
* With which of the following information can you draw one specific triangle?
lengths of a and b, and γ
* What is the approximate height in an equilateral triangle with a side of 20 cm?
17 cm
* Which triangle can be drawn in relation with the annex?
a = 4, b = 5, γ = 60°
* With which of the following information is it possible to draw more than one triangle?
only the interior angles
* Which of the following data results in more than one triangle?
α = 80°, β = 60°, γ = 40°
* What is the height in an equilateral triangle with a side of 20 cm? Enter the closest answer
as a whole number.
17
* 3-4-5 triangle is:
a Pythagorean triangle
* Which of the following information is not enough to draw a specific triangle?
all three angles
* What is the approximate height in an equilateral triangle with a side of 12 cm?
10.4 cm
* In a triangle, A is the right angle and the corresponding side is a. Which equation is
correct?
b² + c² = a²
* Which equation is correct?
c² = a² - b²
* Which equation is correct?
b² = a² - c²
* See annex. What is the area of the shaded part?
πa2/4
* A spiral staircase is located on a circle with radius 1 meter. How many stairs with inside
edge length 20 cm and outer edge length about 30 cm fit in this circle?
21
* What is the shaded area in the square with a side length a?
a2(π/2 - 1)
a kare diye
* The circumference of a circle is enlarged by 10 meters. What is the increase in its radius in
meters? Round the answer to one decimal place.
1.6
* Which equation applies to the shaded area?
a2(1 - π/4)
a kare diye
* Two concentric circles are drawn and one is 10 meters longer than the other. How
many meters are there between two circles? Round the answer to one decimal place.
1.6
* A rope is tightly attached around the equator. How many meters should the rope
be extended so that it floats 1 meter above the equator?
6.28
* The circumference of a circle with 10m radius is extended by 10 meters. What is the
approximate radius of the new circle?
11.6 m
* A rope is tightly attached around the equator. How many meters should the rope
be shortened so that it surrounds the equator 1 meter below the soil?
6.28
* A new concentric circle is added outside the first circle shown in the annex. The red
circle's radius is 1m and the black circle's circumference is 10 m. What is the approximate
increase in radius?
0.6 m
* A new concentric circle is added outside the first circle shown in the annex. The
new circle's circumference is 10 m longer than the first one. How far is the new circle from
the first circle?
1.6 m
* Which equation applies to the shaded area?
a2(-1 + π/2)
a kare diye…
* Which equation applies to the shaded area?
a2(π/2 - 1)…a kare diye
* A cube with a total length 96 cm weighs 7.68 kg. What is the density in grams per
cubic decimeter?
15000
* How long is the diagonal of the cube with an edge length of 1 cm? Round the
answer to one decimal place.
1.7
* How many cubes, each with the total length of 36 cm fit into a cube with a total length of
144 cm?
64
* A cube with a total length of 96 cm has a weight of 768 g. What is the density of the cube
in g per cubic centimetres?
1.5
* In a column, the area of the base is doubled and the height is halved. What is the
change in volume?
remains the same
* There is a square column. The height is reduced to half, but width and depth are
doubled. What is the change in the volume of the column?
doubled
* A cube has a total length of 60 cm. Its weight is 250 g. What is the density in g per
cubic centimetres?
2
* A cube with an edge length of 8 cm has a weight of 768 g. What is the density of the
cube in g per cubic centimetres?
1.5
* A silver cube has edge lengths of 5 cm each. A stamp mark ‘800’ indicates that the
cube is made of 800/1000 pure silver. Assume that silver has a density of 10.5 g/cm3 and a
price of 0.68 €/g. Calculate the value of the silver portion.
714
* A pyramid consists of cubes with a side length of 2 cm. What is the volume of the
pyramid in cm³ if it has 4 cube levels?
240
* The bottom side of a square pyramid consists of 6 stones. How many stones are
there in total?
91
* The Picture shows a cross section of a square pyramid. The cubes have a side length
of 2m. What is the volume of the entire pyramid in m3, if it consists of 5 levels?
440
* A square pyramid has 5 levels. The annex shows that first level has 1, second level
has 4 and third level has 9 cubes. What is the total volume of the square pyramid (in m³) if
the cubes have an edge of 2m?
440
* A square pyramid has 5 levels. How many stones are there in total?
55
* The annex shows the first 3 levels of a square pyramid which consists of 5 levels.
What is the total volume of the square pyramid (in m³) if the cubes have an edge of 2m?
440
* A cube has edge lengths of 5 cm each. The cube weighs 0.54 kg. What is its specific
weight?
4.32 g per cubic centimetre
* The edge length of a cube is doubled. How many times is the new surface area
compared to the old surface area?
4
* A woman slices a cube with an edge length of 8 cm into little cubes with an edge
length of 2 cm. How many cuts are needed at least?
9
* The edge length of a cube is doubled. How many times is the new volume
compared to the old volume?
8
* The bricks are 10 cm long, 5 cm high and 8 cm deep. Some bricks are removed from the
wall as shown in the picture. What is the total volume removed from the wall in cm³?
1600
* The bricks are 4 cm x 5 cm x 6 cm. The blue bricks are removed from the wall as
shown in the picture. What is the total volume of the current wall in cm³?
1920
* The dimensions of a rectangular prism are 4 m in length, 20 cm in width and 15 cm
in height. What is the volume of the prism in cubic decimeter?
120
* All edges of a rectangular prism are doubled. How many times is the new volume
compared to the old volume?
8
* All sides of a rectangular prism are doubled. Which one is correct about the
volume?
It is increased eightfold.
* A rectangle has sides of 12 cm and 8cm. The short sides are enlarged by 1/3. What
is the new area in sq. cm?
128
* A container holds 21 cubic metres of water maximum. The rectangular base of this
container has the side lengths 3.5 m and 3 m. What is the height in metres?
2
* A wall will be built which is 3m in length, 10m in width and 5m in height. The bricks
to be used are 3cm in width, 5cm in height and 10cm in length. How many bricks are
needed?
1000000
* The bricks are 1 cm x 3 cm x 4 cm What is the volume (cm³) of the shaded area in
the picture?
48
* What is the total volume of the wall in the annex in liters if the bricks are 15cm x
30cm x 45cm ?
324
* A wall will be built which is 10 m in length, 10 cm in width and 30 cm in height. The
bricks to be used are 10 cm in length, 5 cm in width and 3 cm in height. How many bricks are
needed?
2000
* What is the total volume of the wall in the annex in liters if the bricks are 5cm x 3cm
x 8cm ? (without seens)
1.92
* What is the total volume of the wall in the annex in cm³ if the bricks are 1cm x 3cm
x 4cm ?
192
* A wall will be built which is 10 m in length, 10 cm in width and 300 cm in height.
The bricks to be used are 5cm in width, 10cm in height and 20cm in length. How many bricks
are needed?
3000
* All points in a space have the same distance to a straight line. Which shape results?
a cylinder
* Half of a cone shaped paper cup (in height) can be filled in 30 minutes. How long
does it take (in hours) to fill the complete cup?
4
* Frank’s doctor tell him that his liver’s diameter has quadrupled. How many times
larger did his liver become by volume?
64
* The radius of a sphere is halved. What is the new surface area?
25% of the original area
* The radius of a sphere is doubled. What is the change in its surface area?
more than 300%
* Sphere : Circle.
Dice: ?
square
* A sphere is inscribed in a cube. What is the difference between their surface areas?
somewhat less than 100% of the area of the sphere
* How many large circles can be formed by passing the poles of the Earth?
an infinite number
* How many great circles can be drawn from the North Pole to the South Pole?
an infinite number of
* Kerosene has a specific weight of 0.8. If an aeroplane is refueled with 4000 kg
kerosene, how many litres are inside its tank?
5000
* A rope is tightly attached around the equator. How long should the rope be
extended so that it floats 1 meter above the equator?
6.28 m
* All edges of a rectangular prism is doubled. How many times is the new surface
area compared to the old surface area?
4
* The two corners of a cube are cut off. Which of the following do we obtain?
18 edges
* Half of a cone shaped paper cup (in height) can be filled in 30 minutes. How long
does it take to fill the complete cup?
4h
* 15 aircraft are performing a formation flight. They are arranged so that behind each
aircraft there are two aircrafts. The horiztontal space between two aircraft is 8 meters. If you
neglect the dimensions of the aircraft, how long is the horizontal distance from one end of
the formation to the other end in meters?
32
* A parallelogram has the same base line and the perimeter with a rectangle. How is
the area of the rectangle compared to the parallelogram?
Greater
* Over the top of a mast, a 98
meter rope is drawn to the
opposite sides of the mast. The
angle between the ground and
the rope is 30°. How high is the
mast in meters?
24.5
76974
* What is the tangent of alpha?
b/a
76973
* What is sine of alpha?
b/c
76975
* Which angle applies sinα = cosα?
45
76972
* Which of the following equation
represents the graph shown in the
annex?
sinα
76782
* Lisa’s kite has been stick on the
top of a tree. The string of the kite
is 54 m long. The angle between
the string and the ground is 30
degrees. How high is the tree in
meters?
27
76216
* Which triangle applies for sinα =
sinβ?
Isosceles triangle
81157
* What is cosine of alpha?
a/c
81158
* The graph in the annex shows:
sinα
81159
* The graph in the annex shows:
cosα
81160
* The graph in the annex shows:
tanα
81161
* The graph in the annex shows:
cotanα
81181
* Which triangle applies for sinα =
sinβ?
α=β
81272
* Which of the following applies for
sinα = sinβ?
α = 180 - β
81835
* What is sine of alpha?
a/b
81631
* What is sine of alpha?
a/b