2012 Kadett Test | Test and Chat

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2012 Kadett (Grade 7 - 8)

Questions: 30 | Answered: 0

Q1. Three bars of choc olate cost 6 € € . How much h is one bar o f f chocolate?

3 points

ABCDE

Question 1

Q2. 11.11  1.111 

3 points

ABCDE

Question 2

Q3. A wri s s twatch lies o o n the table w w ith its face u u pwards. Th e minute han d d points tow a a rds north ‐ e a a st. How ma n n y minutes h a a ve to pass f o o r the minut e e hand to poi n t towards n o orth ‐ west for the first tim e e ?

3 points

ABCDE

Question 3

Q4. Eva h a a s a pair a sci ssors and fiv e e letters ma d d e from card b b oard. She c u u ts up each l e e tter with a s ingle straight c cut so that a s s many piece s as possible are obtaine d d . For which l etter does s h h e obtain th e most pieces?

3 points

ABCDE

Question 4

Q5. The d i i git sum of a six ‐ digit nu m ber is 5. Ho w w big is the p r r oduct of the digits?

3 points

ABCDE

Question 5

Q6. A dra g g on has 5 he a a ds. Each tim e someone c c hops off on e e head, 5 ne w w heads are g r row back. If 6 6 heads are choppe d d off one afte r the other, h h ow many h e e ads does th e e dragon end up with?

3 points

ABCDE

Question 6

Q7. Each o o f the nine p a a ths in a par k k are 100 m l o o ng. Anna w a a nts to walk f f rom A to B without using the sa m m e path twic e e . How long t t he longest p p ath she can c c hoose?

3 points

ABCDE

Question 7

Q8. One v ertex of the t t riangle on t h h e left is con n n ected to on e e vertex of t h e triangle o on the right u u sing a strai g g ht line so th a a t no connec t t ing line segmen t t dissects eit h h er of the tw o o triangles in t to two parts . . In how man y ways is t t his possible ? ?

3 points

ABCDE

Question 8

Q9. Werner f o o lds a piece o o f paper as s h h own in the d d iagram. Wit h h a pair of scissors he m m akes two st raight cuts i n n to the pape r r . Then is unf o o lds it again. Which on t h h e following s s hapes are n o o t possible fo o r the piece o f paper to show after w w ards?

3 points

ABCDE

Question 9

Q10. A cu b b oid consists of three bui l l ding blocks. Each buildin g g block has a different colour a n n d is made u p of 4 cubes. What does t t he white bui lding block l o o ok like?

3 points

ABCDE

Question 10

Q11. From the digits 1, 2, 3, 4, 5, 6, 7, 8 we form two four ‐ digit numbers so that every digit is used exactly once and the sum of the two numbers is as small as alte Beete neue Beete possible. What is the value of this sum?

4 points

ABCDE

Question 11

Q12. Ms. Green plants peas (“Erbsen”) and strawberries (“Erdbeeren”) only in her garden. This year she has changed her pea ‐ bed into a square ‐ shaped bed Erdbeeren

4 points

ABCDE

Question 12

Q13. Barbara wants to complete the grid shown on the right by inserting three numbers into the empty spaces. The sum of the first three

4 points

ABCDE

Question 13

Q14. The diagram shows a five ‐ pointed star. How big is the angle A?

4 points

ABCDE

Question 14

Q15. Take four cards and on each one write one of the numbers 2, 5, 7, 12. 100° 93° On the back of each card write one of the following properties: “divisible by 7”, 58° ? A “prime number”, “odd”, “greater than 100” so that the number on the other side B does not have this property. Every number and every property is used exactly once. Which number is on the card with the property “greater than 100”?

4 points

ABCDE

Question 15

Q16. How many natural numbers n are there for which n  24 and n  24 are two ‐ digit numbers?

4 points

ABCDE

Question 16

Q17. In which of the following expressions can one exchange each number 8 with 8 different sets of equal positive numbers without changing the result?

4 points

ABCDE

Question 17

Q18. Three equally sized equilateral triangles are cut from the vertices of a large equilateral triangle of side length 6cm . The three little triangles together have the same perimeter as the remaining grey hexagon. What is the side ‐ length of one side of one small triangle?

4 points

ABCDE

Question 18

Q19. The lazy tomcat Garfield observes some mice stealing cheese. Each mouse carries away at least one piece of cheese but less than ten pieces. Each mouse steales a different amount of cheese pieces. No mouse steals exactly twice as many pieces as another mouse. What is the maximum number of mice Garfield can have observed?

4 points

ABCDE

Question 19

Q20. At an airport there is a “rolling pavement” which is 500 m long and transports people with a speed of 4 km/h. Anna and Peter step onto the rolling pavement at the same time. While Peter is standing still, Anna continues to walk with a speed of 6 km/h. How big is Anna’s head start on Peter when she leaves the rolling pavement after 500 m?

4 points

ABCDE

Question 20

Q21. Initi a a lly the side l e e ngth of a ta l l king magic s q quare is 8 c m m . Every time it speaks th e e truth its sid e e s each decreas e e by 2 cm. If i t lies its peri m m eter doubl e e s. It says fo u u r sentences, two of whic h h are true an d d two are false, in w which order is unknown. W hat is the b b iggest possi b b le perimete r it can have after those f o o ur sentenc e e s?

5 points

ABCDE

Question 21

Q22. The d d iagram sho w w s the 7 posi t t ions 1, 2, 3, 4, 5, 6, 7 of t t he bottom s ide of a die which is rolled aroun d its edge in t his order. W W hich two of t t hese positio ns were take e n up by th e same face o o f the die?

5 points

ABCDE

Question 22

Q23. Stef a a n has 5 dice in different s s izes. If he pl a a ces them in order next t o o each other f from smalle s s t to biggest then th e e height of t w w o neighbour i i ng dice each h differ by 2 c m. The bigg e st die is as bi i g as the tow e e r build by the two smallest dic e e . How high i s s a tower ma d de up of all 5 5 dice?

5 points

ABCDE

Question 23

Q24. In a s s quare ABCD M is the mi d d point of AB. . MN is perp e e nticular to A C. Determin e e the rati o o of the area o o f the grey t r r iangle to th e e area of the s s quare ABCD .

5 points

ABCDE

Question 24

Q25. Tan g g o is being da nced in pair s s , a man with a woman. N o more than 50 people attend a dance eveni ng. At a cert a a in moment 3 3 /4 of the m e e n were dan c c ing with 4/5 A M B B of the w omen. How m m any people were dancin g at this mo m m ent?

5 points

ABCDE

Question 25

Q26. Davi d d wants to pl ace the twel v v e numbers f f rom 1 to 12 in a circle so that two adj a a cent numb e e rs always differ b y y 2 or 3. Whi c c h numbers a re therefore adjacent?

5 points

ABCDE

Question 26

Q27. Wan ted are all th ree ‐ digit nu m m bers from 1 1 00 to 999 th a a t have the f o o llowing pro p p erty: If you r r emove the first digi t t a square n u u mber remai n n s and if you remove the l ast digit agai n a square n u u mber rema i ns (e.g. 16 4 4 – (1)64 – 1 6 6 (4)). How bi g g is the sum o o f all number s with this s p p ecial proper t t y?

5 points

ABCDE

Question 27

Q28. Ther e are 30 cha p p ters in a bo o o k. Each cha p p ter has a dif f f erent length , i.e. 1, 2, 3, … … , 30 pages. Each chapter starts on a n e e w page. Th e e first chapte r r starts on p a a ge 1. At mo s t how many c chapters sta r r t on a page with an o o dd page nu m m ber?

5 points

ABCDE

Question 28

Q29. A pi e e ce of string i s folded as s h h own in the d d iagram by f o o lding it in th e middle, th e e n S S chnitt folding i t t in the midd le again und finally foldin g g it in the mi d d dle once m o o re. Then thi s s folded p iece of strin g g is cut so tha t several pie c c es emerge. A A mongst the resulting pi e e ces there ar e e some with length 4 m a n n d some wit h h length 9 m. Which of th e e following lengths c c annot be th e e total lengt h h of the origi n n al piece of s t t ring?

5 points

ABCDE

Question 29

Q30. Thre e lines disec t t a big triangl e into four tr r iangles and t t hree quadrila t t erals. The s u u m of the pe r r imeters of t h h e three qua d d rialterals is 2 2 5 cm. The sum m of the peri m m eters of the four triangle s s is 20 cm. T h h e perimeter of the big trian gle is 19 cm. How big is t h h e sum of th e e lengths of t h h e three diss e cting lines?

5 points

ABCDE

Question 30

2012 Kadett Test | Test and Chat