2014 Junior Test | Test and Chat

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2014 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. 2014 people stand next to each other in a row. Each person is either a liar (who always lie) or a knight (who always tell the truth). Each person says “to the left of me are more liars than to the right of me there are knights.” How many liars are in the row?

3 points

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Question 1

Q2. ⋅ 5m above the floor. He ties a 2m long string to th e upper corners of each picture (see di a- gram). which picture size (width in cm × height in cm) has its lower edge nearest to the floor?

3 points

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Question 2

Q3. a , b and c show the lengths of the diffe r- ent of pieces of wire pictured. Which of the following inequalities is correct?

3 points

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Question 3

Q4. Which number is an equal distance from 2 and 4 5 on the number line? 3 3 6 5

3 points

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Question 4

Q5. In the year number 2014, the last digit is bigger than the sum of the three other digits. How many years ago did this last happen?

3 points

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Question 5

Q6. The side lengths of the large regular hexagon are twice the leng th of those of the small regular 2 hexagon. What is the area of the large hexagon if the small hexagon has an area of 4 cm ?

3 points

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Question 6

Q7. Which statement is definitely correct if the following statement is false: „Everybody has solved more than 20 problems.“

3 points

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Question 7

Q8. Tom draws a square on the co - ordinate plane. One diagonal sits on the x - axis. Its endpoints are ( − 1,0) and (5,0). Which of the following points is also a corner point of the square?

3 points

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Question 8

Q9. In Kangaroo city there are m men, f women and k children. It is true that m : f = 2 : 3 and f : k = 8 : 1. In what ratio is the number of adults (men and women) to the number of children?

3 points

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Question 9

Q10. The circumference of the large wheel measures 4 ⋅ 2m, and that of the small wheel 0 ⋅ 9m. To begin with the valves on both wheels are at the lowest point, and then the bicycle moves to the left. After a few metres both valves are again at the lowest point at the same time. After how many metres does this happen for the first time?

3 points

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Question 10

Q11. A Grandmother, her daughter and her Granddaughter each have their birthday in February. They can say that they are in total 100 years old and that each persons age is a power of 2. In which year was the granddaughter born?

4 points

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Question 11

Q12. 26 128

4 points

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Question 12

Q13. In a shared apartment where six girls live there are 2 bathrooms. Each morning from 7:00 the girls use the bat h- rooms before breakfast whereby they are 9, 11, 13, 18, 22 and 23 minutes respectively, constantly alone in one of the two bathrooms. What is the earliest time that all six girls can have breakfast together?

4 points

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Question 13

Q14. The shaded part of the regular octagon has an area of 3 cm . How big is the area of the oct a- gon?

4 points

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Question 14

Q15. The length of the tail of the biggest crocodile in a zoo is one third of the total length of the crocodile. The head is 93cm long and makes up one quarter of the length of the crocodile without its tail included. How long is the crocodile?

4 points

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Question 15

Q16. If you add the numbers on opposite faces of this special die, you will get the same total three times. The numbers on the hidden faces of the die are prime numbers. Which number is on the face opposite to 14?

4 points

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Question 16

Q17. Anna walks a distance of 8 km at a speed of 4 km/h. Then she runs for a while at 8 km/h. How many minutes must she run for, so that she has been underway with an overall average speed 5 km/h?

4 points

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Question 17

Q18. Question text unavailable

4 points

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Question 18

Q19. A chess player plays 40 matches and gains from these 25 points, whereby a win gives 1 point, a draw 1 point, and a 2 loss 0 points. How many more matches does he win than he loses?

4 points

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Question 19

Q20. The triplets Meike, Monika and Zita each want to buy equally expensive hats. However, Meike’s savings were 1 , 3 Monika’s 1 and those from Zita 1 5 smaller than the price of a hat. After these hats were reduced by €9 ⋅ 40, the tr i- 4 plets put their savings together and they each bought a hat. Not a single cent was left over. How much had a hat cost originally?

4 points

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Question 20

Q21. p , q und r are positive whole numbers where p += . The value of the product pqr is then equal to; q + 1 19 r

5 points

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Question 21

Q22. In the equation N × U × ( M + B + E + R ) = 33 each letter represents a different digit (0, 1, 2, …, 9) . In how many different ways can the letters, be replaced by different digits?

5 points

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Question 22

Q23. In the diagram Karl wants to add lines joining two of the marked points at a time, so that each of the seven marked points is joined to the same number of other marked points. What is the minimum number of lines he must draw?

5 points

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Question 23

Q24. The diagram shows two different views of the same cube. The cube is made from

5 points

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Question 24

Q25. On an island the frogs are either green or blue. The number of blue frogs increases by 60%, and the number of green frogs decreases by 60%. This has the effect that the new ratio of the number of blue frogs to the number of green frogs, matches the origina l ratio of the number of green frogs to the number of blue frogs. By what percentage has the total number of frogs changed?

5 points

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Question 25

Q26. Tom has written down a few different positive whole numbers which are all smaller than 101. The product of the numbers is not divisible by 18. At most how many numbers could he have written down?

5 points

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Question 26

Q27. Every group of three vertices of a cube form a triangle. How many such triangles are there, such that the vertice s do not all belong to the same face of the cube?

5 points

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Question 27

Q28. PT is the tangent to a circle O , and PB is the angle bisector of the angle TPA (see diagram). How big is the angle TBP ?

5 points

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Question 28

Q29. We consider all 7 digit numbers that result, when for each number you use all the digits from 1 to 7. We write these numbers down in increasing order of size and split the list exactly in the mi d- dle, so that two lists of equal size result. What is the last number of the first of these ordered lists?

5 points

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Question 29

Q30. In triangle ABC, AB = 6 cm, AC = 8 cm and BC = 10 cm. M is the midpoint of the side BC . AMDE is a square and MD intersects AC at point F . 2 What is the area of the quadrilateral AFDE in cm ?

5 points

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Question 30

2014 Junior Test | Test and Chat