18th AMC 8 2002 2 1. A circ and tw distinct ins ar drawn n a sht f papr. What is th argst pssib nbr f pints f intrsctin f ths figrs? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 2. Hw any diffrnt cbinatins f $5 bis and $2 bis can b sd t ak a tta f $17? Ordr ds nt attr in this prb. (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 3. What is th sast pssib avrag f fr distinct psitiv vn intgrs? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 4. Th yar 2002 is a paindr (a nbr that rads th sa fr ft t right as it ds fr right t ft). What is th prdct f th digits f th nxt yar aftr 2002 that is a paindr? (A) 0 (B) 4 (C) 9 (D) 16 (E) 25 5. Cars Mntad was brn n Satrday, Nvbr 9, 2002. On what day f th wk wi Cars b 706 days d? (A) Mnday (B) Wdnsday (C) Friday (D) Satrday (E) Snday 6. A birdbath is dsignd t vrfw s that it wi b sf-caning. Watr fws in at th rat f 20 iiitrs pr int and drains at th rat f 18 iiitrs pr int. On f ths graphs shws th v f watr in th birdbath dring th fiing ti and cntining int th vrfw ti. Which n is it? Ti Ti Ti Ti Ti A B C D E (A) A (B) B (C) C (D) D (E) E
18th AMC 8 2002 3 7. Th stdnts in Mrs. Sawyr s cass wr askd t d a tast tst f fiv kinds f candy. Each stdnt chs n kind f candy. A bar graph f thir prfrncs is shwn. What prcnt f hr cass chs candy E? S W E E T T O O T H 7 6 5 4 3 2 1 0 A B C D E Kinds f candy (A) 5 (B) 12 (C) 15 (D) 16 (E) 20 Nbr f Stdnts 8 Prbs 8,9 and 10 s th data fnd in th accpanying paragraph and tab: Jan s Od Staping Grnds Jan rganizs th staps in his cctin by cntry and by th dcad in which thy wr issd. Th prics h paid fr th at a stap shp wr: Brazi and Franc, 6c ach, Pr 4c ach, and Spain 5c ach. (Brazi and Pr ar Sth Arican cntris and Franc and Spain ar in Erp.) Nbr f Staps by Dcad Cntry 50s 60s 70s 80s Brazi 4 7 12 8 Franc 8 4 12 15 Pr 6 4 6 10 Spain 3 9 13 9 Jan s Stap Cctin 8. Hw any f his Erpan staps wr issd in th 80s? (A) 9 (B) 15 (C) 18 (D) 24 (E) 42 9. His Sth Arican staps issd bfr th 70s cst hi (A) $0.40 (B) $1.06 (C) $1.80 (D) $2.38 (E) $2.64 10. Th avrag pric f his 70s staps is csst t (A) 3.5c (B) 4c (C) 4.5c (D) 5c (E) 5.5c
18th AMC 8 2002 4 11. A sqnc f sqars is ad f idntica sqar tis. Th dg f ach sqar is n ti ngth ngr than th dg f th prvis sqar. Th first thr sqars ar shwn. Hw any r tis ds th svnth sqar rqir than th sixth? (A) 11 (B) 12 (C) 13 (D) 14 (E) 15 12. A bard ga spinnr is dividd int thr rgins abd A, B and C. Th prbabiity f th arrw stpping n rgin A is 1 3 and n rgin B is 1 2. Th prbabiity f th arrw stpping n rgin C is B A C (A) 1 12 (B) 1 6 (C) 1 5 (D) 1 3 (E) 2 5 13. Fr his birthday, Brt gts a bx that hds 125 jybans whn fid t capacity. A fw wks atr, Carri gts a argr bx f f jybans. Hr bx is twic as high, twic as wid and twic as ng as Brt s. Apprxiaty, hw any jybans did Carri gt? (A) 250 (B) 500 (C) 625 (D) 750 (E) 1000 14. A rchant ffrs a arg grp f its at 30% ff. Latr, th rchant taks 20% ff ths sa prics and cais that th fina pric f ths its is 50% ff th rigina pric. Th tta discnt is (A) 35% (B) 44% (C) 50% (D) 56% (E) 60% 15. Which f th fwing pygns has th argst ara? (A) A (B) B (C) C (D) D (E) E
18th AMC 8 2002 5 16. Right isscs triangs ar cnstrctd n th sids f a 3-4-5 right triang, as shwn. A capita ttr rprsnts th ara f ach triang. Which n f th fwing is tr? Z 5 W 4 Y X 3 (A) X + Z = W + Y (B) W + X = Z (C) 3X + 4Y = 5Z (D) X + W = 1 2 (Y + Z) (E) X + Y = Z 17. In a athatics cntst with tn prbs, a stdnt gains 5 pints fr a crrct answr and ss 2 pints fr an incrrct answr. If Oivia answrd vry prb and hr scr was 29, hw any crrct answrs did sh hav? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 18. Gag skatd 1 hr 15 in ach day fr 5 days and 1 hr 30 in ach day fr 3 days. Hw ng wd h hav t skat th ninth day in rdr t avrag 85 ints f skating ach day fr th ntir ti? (A) 1 hr (B) 1 hr 10 in (C) 1 hr 20 in (D) 1 hr 40 in (E) 2 hr 19. Hw any wh nbrs btwn 99 and 999 cntain xacty n 0? (A) 72 (B) 90 (C) 144 (D) 162 (E) 180 20. Th ara f triang XY Z is 8 sqar inchs. Pints A and B ar idpints f cngrnt sgnts XY and XZ. Atitd XC biscts Y Z. Th ara (in sqar inchs) f th shadd rgin is X A B Y C Z (A) 1 1 2 (B) 2 (C) 2 1 2 (D) 3 (E) 3 1 2
18th AMC 8 2002 6 21. Hard tsss a nick fr tis. Th prbabiity that h gts at ast as any hads as tais is (A) 5 16 (B) 3 8 (C) 1 2 (D) 5 8 (E) 11 16 22. Six cbs, ach an inch n an dg, ar fastnd tgthr, as shwn. Find th tta srfac ara in sqar inchs. Incd th tp, btt and sids. (A) 18 (B) 24 (C) 26 (D) 30 (E) 36 23. A crnr f a tid fr is shwn. If th ntir fr is tid in this way and ach f th fr crnrs ks ik this n, thn what fractin f th tid fr is ad f darkr tis? (A) 1 3 (B) 4 9 (C) 1 2 (D) 5 9 (E) 5 8 24. Miki has a dzn rangs f th sa siz and a dzn pars f th sa siz. Miki ss hr jicr t xtract 8 ncs f par jic fr 3 pars and 8 ncs f rang jic fr 2 rangs. Sh aks a par-rang jic bnd fr an qa nbr f pars and rangs. What prcnt f th bnd is par jic? (A) 30 (B) 40 (C) 50 (D) 60 (E) 70 25. Lki, M, Nick and Ott ar gd frinds. Ott had n ny, bt th thrs did. M gav Ott n-fifth f his ny, Lki gav Ott n-frth f his ny and Nick gav Ott n-third f his ny. Each gav Ott th sa ant f ny. What fractina part f th grp s ny ds Ott nw hav? (A) 1 10 (B) 1 4 (C) 1 3 (D) 2 5 (E) 1 2