2015 Junior Test | Test and Chat

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2015 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. Which o f f the followi n n g numbers i s closest to t t he product of 20 ∙ 15 x 5 1 1 ∙ 02?

3 points

ABCDE

Question 1

Q2. After mu m had hung the t ‐ shirts o o n the wash ing line for d d rying, her s o o n hung a si n n gle sock be t t ween each two t ‐ shirts . Now there are 29 piec e e s of clothin g g on the line . How many of them are t ‐ shirts?

3 points

ABCDE

Question 2

Q3. The grey areas of the square wit h h side length a are boun d d ed by a se m m i ‐ circle and two qu arter ‐ circles respectivel y y . What is th e e ir total are a a ? గ௔ మ ௔ మ గ ௔ మ ௔ ௔ మ గ ௔ మ

3 points

ABCDE

Question 3

Q4. Anna, Be ate and Cin d d y buy a bag of 30 biscui t t s together. T T hey get 10 b b iscuits each. But A nna has pai d d 80 cents, B eate 50 cen t t s and Cindy 20 cents. H o o w many more biscu i i ts should A n n na have got , if they had shared the m m in proport i on with the amoun t t they had e a a ch paid?

3 points

ABCDE

Question 4

Q5. Mr. Hide wants to fin d d a treasure that he buri ed years be f f ore. He can only remem ber that he b b uried the treasure at least 5 m a w w ay from the hedge and n n o more tha n 5 m away f f rom the old d pear tree. W W hich picture sho w w s best the a a rea where M M r. Hide has to look for t t he treasure ? ?

3 points

ABCDE

Question 5

Q6. What is t he unit digit of 2015 ൅ 2015 ൅2 0 0 15 ൅201 5 5 ?

3 points

ABCDE

Question 6

Q7. There ar e e 33 teenag e e rs in a class. Their favou r rite subjects are either c o o mputing, P E or both. T h h ree of them like b o o th subjects . There are t w ice as man n y teenagers who only li k k e computin g g as teenage rs who like PE only. Ho w w many of t h h em like co m m puting?

3 points

ABCDE

Question 7

Q8. Which o f f the followi n n g numbers i s neither a s s quare nor a cubic numb e r? ଵଷ ଵଶ ଵ ଵ ଵ ଵ଴ ଽ

3 points

ABCDE

Question 8

Q9. Herr Wa x x i buys 100 c andles. Eac h h day he bur n n s down on e e candle. Fro m the left o v v ers of seve n n burned down candl es, he can a l l ways make a a new candl e e . After how many days d d oes he hav e e to buy ne w w candles?

3 points

ABCDE

Question 9

Q10. A penta gon is calle d d convex if al l its internal angles are l e e ss than 180 ° ° . The numb b er of right a n n gles in a convex pen t t agon is n . W W hich of the following lis t t s is a compl ete listing o f f all possible values of n ? ?

3 points

ABCDE

Question 10

Q11. In the d iagram one c c an see my d d ecision ‐ die i in three diff e e rent positions. W W hat is the p p robability I g g et a „YES“, w w hen rolling t his die once. ଵ ଵ ହ ଶ ହ

4 points

ABCDE

Question 11

Q12. The sid e e lengths of e e ach of the s s mall square s s in the diag ram are 1. H ow long is t h h e shortest pa t t h from „Sta rt“ to „Ziel“, if you are o n n ly allowed t t o move alo n n g the sides and the dia g g onals of th e e squares?

4 points

ABCDE

Question 12

Q13. Each in h h abitant of a distant pla n n et has at le a a st two ears. Three inha b b itants calle d d Imi, Dimi a n n d Trimi meet in a t r r endy crater. Imi says: „I c c an see 8 ea rs.“ Dimi th e e n replies: „I can see 7 ea a rs.“ Finally T T rimi says: „Strange, I c c an only see 5 ears.” No n n e of them c a a n see their own ears. H o w many ea rs does Trim i have?

4 points

ABCDE

Question 13

Q14. A cuboi d d shaped co n n tainer has a a square bas e e with side l e e ngth 10 cm . It is filled u u p to a heigh t h with water. Now a metal cu b b e with side l ength 2 cm i i s put inside . . It sinks to t h h e bottom o f f the contai n n er. The water now reaches to t h h e top corn e e r of the me t t al cube. Det ermine h !

4 points

ABCDE

Question 14

Q15. The squ are ABCD h a a s area 80. T h e points E, F, G and H a r r e on the si d es of the square a a nd AE = BF = CG = DH. How big is t t he area of t h h e grey part , , if AE ൌ 3 ൈ ൈ EB ?

4 points

ABCDE

Question 15

Q16. If the w hole numbe r age of a fa t t her is multi p p lied by the w w hole num b b er th age of his s o o n, one obt a a ins 2015. B o o th are born in the 20 c entury. Ho w big is the age g a a p between father and s on?

4 points

ABCDE

Question 16

Q17. Four ob j j ects a, b, c, d are place d d on a doubl e e balance as s s hown. The n n two of the o o bjects are exchanged, which resul t t s in the cha nge of posit i i on of the bala n n ce as show n n . Which tw o o objects we re exchanged ? ?

4 points

ABCDE

Question 17

Q18. It is kno wn that the solutions of the quadrat t ic equation ݔ ݔ െ85ݔ൅ ܿൌ0 are p p rime numb e e rs. What is the digit sum o f f c ?

4 points

ABCDE

Question 18

Q19. How m a a ny three ‐ di g g it positive w w hole numb e e rs are ther e e , where the digits when placed side by side always diff e e r by 3?

4 points

ABCDE

Question 19

Q20. Which v v alue of the v v ariable n is a counterex a a mple to th e e statement „ „ If n is a pri m m e number, t t hen exactly one of the t t wo number s s n – 2 and n n + 2 is a pri m m e number.“ ? ?

4 points

ABCDE

Question 20

Q21. In the d iagram we c a a n see seve n n sections w h h ich are bor d d ered by thr e e e circles. O n ne number is w w ritten into e e ach section . It is known that each n u u mber is eq u u al to the su m m of all the n u u mbers in th e adjacent z o o nes. (Two z ones are cal led adjacen t if they have e more than o o ne corner p p oint in com m m on.) Whic h h number is w w ritten into t t he inner ar e e a?

5 points

ABCDE

Question 21

Q22. How m a a ny two ‐ digi t t numbers c a a n be writte n n as sum of e e xactly six di f f ferent pow e e rs of two? ( Hint: 0 1 1 2 Powers of t w w o are 2 , 2 , 2 , …)

5 points

ABCDE

Question 22

Q23. Petra h a a s three diff e e rent diction aries and t w w o different n n ovels on he r bookshelf. In how man y y different ways can s h h e arrange t h h e books, if a a ll the dictio n n aries shoul d d stay toget h h er and like w w ise the nov e e ls as well?

5 points

ABCDE

Question 23

Q24. Lines p a a rallel to the base AC of t t riangle ABC are drawn through X a nd Y . In eac h h case, the a reas of the g g rey parts ar e e equal in siz . . The ratio ܤ ܺ ܺ :ܺܣൌ4: 1 1 is known. W W hat is the ratio ܤܻ:ܻܣ ?

5 points

ABCDE

Question 24

Q25. In a rig h h t ‐ angled tri a a ngle the an g g le bisector o o f an acute a a ngle splits t he opposite side into se g g ments of length 1 an d d 2 respecti v v ely. How lo n n g is this an g g le bisector?

5 points

ABCDE

Question 25

Q26. A two ‐ d d igit number with the di g g its ݔ , ݕ , can be written i n n the form ത ݔ ത ത ݕ ത . Let ܽ , ܾ , ܿ ܿ be differe n t digits. In how many w w ay can the digits ܽ , ܾ , ܿ ܿ be chosen, so that ܾܽ ത ത ത ൏ ൏ ܾܿ ത ത ത ൏ܿ ത ത ܽ ത ?

5 points

ABCDE

Question 26

Q27. If one o f f the numb e e rs 1 , 2 , 3 , ... , ݊െ1 , ݊ , i i s crossed o u u t, the avera g g e of the re m m aining nu m m bers is

5 points

ABCDE

Question 27

Q28. The ant Tanti starts a a n adventur e at a verte x x of a cube w w ith side len g g th 1. She wants t t o walk alon g g each edge o o f the cube a a t least onc e e and return to the starti n ng point at t he end. What is the minimum p ossible leng t t h of her wa l l k?

5 points

ABCDE

Question 28

Q29. Ten diff e e rent numb e e rs are writt e e n down. Ea c c h number w w hich is equ a a l to the pro d d uct of the o o ther nine numbers c a a n then be u n n derlined. W W hat is the m m aximum am ount of nu m m bers that ca n be underli ned?

5 points

ABCDE

Question 29

Q30. Several points are m m arked on a s s traight line. Then all po s s sible conne c c ting lines b e e tween eac h h two points are drawn. O One such p o o int lies with i i n exactly 8 0 0 of those co n necting lin e e s, and anot h h er one lies w w ithin exactly 90 o o f those. Ho w w many poin ts were mar r ked on the s s traight line?

5 points

ABCDE

Question 30

2015 Junior Test | Test and Chat