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1919 Whatisevt l uviaofa2s0ia 1s6stsev ?(What is the value of 20 W16? (A) 320 (B) 140 (\b) 2016 (D) 32 (E) 800 A( In the figure, the shaded region is what fraction of the circle? (A) W ha (B) W Wa (\b) W h (D) W ta (E) W ia W h W i W s )(The cycling road race through the Adelaide Hills started at 11:15 am and the winner finished at 2:09 pm the same day. The winner’s time in minutes was (A) 135 (B) 174 (\b) 164 (D) 294 (E) 186 3( The fraction ehaWtv haWt is (A) between 0 and 1 (B) between 1 and 10 (\b) between 10 and 100 (D) between 100 and 1000 (E) greater than 1000 B( What is the value of (1 h2) h(3 h4) ? (A) h v (B) v h (\b) v l (D) W t (E) W hi 4( 0.75% of a number is 6. The number is (A) 800 (B) 300 (\b) 1200 (D) 400 (E) 100 \b( In the expression below, the letters Whahthiandsrepresent the numbers 1 h2 h3 h4 and 5 in some order. WW a +t W i +s What is the largest possible value of the expression? (A) 24 (B) 27(\b) 26 (D) 51 (E) 25 What ise v luof20f16?of (Af)o63u) Wh 2016 AMC – Intermediate Questions

20 WhWh atis ev lsaua uoft2au0 lsa 1t26a? (ahAls )u 3 fh)lB 4s)is ev lsa uoft2au \bef(? stDa lsa A2atlaul Ea2)1ala28 IB 3 nB 3 fiB 3 gB 3 r,d I rwd n rcd fi rTd g ryd t(( t2a lsa ut1a ah Hh t i(ei6 vtia0 t ()ha )u ?2t\bh :al\baah 5 th? m th? thelsa2 :al\baah 39 th? pB 4stl )u lsa tifla thA(a :al\baah lsaua ()hau8 r,d .’ W rwd 7b W rcd ’b W rTd mb W ryd 99W ’ W W h a t i s e v l Wu WW Wh tih%sa2a t2a m :(fa Eahu0 . 2a? Eahu th? ’ xa((e\b Eahu )h t :e+B 4)lsefl (ee6)hA0 W lt6a Eahu v2e1 lsa :e+ eha :x ehaB Že\b 1thx Eahu ?e W haa? le lt6a v2e1 lsa :e+ le :a ia2lt)h lstl W stDa tl (atul eha Eah ev atis ie(ef28 r,d p rwd 5rcd 3b rTd 33 ryd 39 tth Wh lsa ?)tA2t10 lsa Dt(fa ev h)u r,d 39b rwd 3bprcd 3b’ rTd 3m’ ryd 339W’ hW hW hW hW tsh Že\b vt2 )u )l v2e1 ale t1atuf2a? )h t ul2t)Asl ()ha8 r,d 9b rwd 9p rcd 3b ‘ 5 W 9 rTd p ‘ 5 W 9 ryd 37 . m . . ’ ’ m a t Wh What ise v luof20f16?of (Af)o63u) 2016 AMC – Intermediate Questions

2121 WhaW hathis ev tluaof 2 0s1ts af a6fhta?su a6faus l fs0ahathis ev tluaof ( 0s1tsfA )3l1 af 13s ltsl a6 fBolts 0s1tsf ev 13s fs0ahathis Whahe4stsu ?\b 13s hathisD EW8 ( W EI8WW 2 En8 ( Efi8 (W W2 Eg8W Wta r3s 4lios ev hvet ,3ah3 d WWh w( ha af EW8 c EI8 TEn8 d Efi8 2y Eg8 ( Wia Wutas66sH Is11\b l6u nl13\b ,sts 13s e6i\b 13tss he0:s1a1etf :lt1aha:l1a65 a6 l fstasf ev l13is1ah s4s61fA m6 slh3 s4s61H 13s ,a66st 5s1f 9 :ea61fH fshe6u 5s1f ( :ea61f l6u 13atu 5s1f 2 :ea61A Wv1st 13s s4s61fH Wutas66s 3lf T :ea61fH Is11\b 3lf 22 :ea61f l6u nl13\b 3lf p :ea61fA m6 3e, 0l6\b s4s61f uau Wutas66s he0s fshe6uD EW8 y EI8 2En8 ( Efi8 9 Eg8 d Wsa )3l1 af 13s f0liisf1 6o0?st avet ,3ah3 What W af l :stvsh1 fBoltsD EW8 2d EI8 (En8 p. Efi8 2( Eg8 ’ Wea 7a4s :se:is lts fa11a65 lteo6u l hathisA be0s li,l\bf 1sii 13s 1to13H ,3aif1 13s e13stf li,l\bf iasA glh3 :stfe6 hila0f 1e ?s fa11a65 ?s1,ss6 1,e ialtfA %e, 0l6\b ev 13s0 lts 1siia65 13s 1to13D EW8 y EI8 2En8 ( Efi8 9 Eg8 d Wva W h\bia6utahli 5ilff ev Ea6faus8 ual0s1st . h0 l6u 3sa531 22 h0 af xiisu l6u 13s6 1ai1su 1e l dp W l65is fe 13l1 fe0s ,l1st e4st+e,fA %e, 0oh3 ,l1st af isv1 a6 a1D EW8 dTW 0Ž EI8 dpW0Ž En8 ..W0Ž Efi8 ’(W 0Ž Eg8 .9W0Ž Wlars6 f1ous61f fa1 l 1sf1 he6faf1a65 ev (y Bosf1ae6fA r,e f1ous61f 5s1 T Bosf1ae6f hettsh1 l6u e6s f1ous61 5s1f c Bosf1ae6f hettsh1A r3s ts0la6a65 fs4s6 f1ous61f lii 5s1 l1 islf1 2y Bosf1ae6f hettsh1 l6u 13s l4stl5s 6o0?st ev Bosf1ae6f l6f,stsu hettsh1i\b ?\b 13sfs fs4s6 f1ous61f af l6 a61s5stA mv 13s l4stl5s 6o0?st ev Bosf1ae6f l6f,stsu hettsh1i\b ?\b lii 1s6 f1ous61f af life l6 a61s5stH 13s6 13l1 a61s5st af EW8 2y EI8 22En8 2( Efi8 29 Eg8 2d What ise v luof20f16?of (Af)o63u) Wh 2016 AMC – Intermediate Questions

22 WhaWhat isevluiofs2se fv0s2 i16i at 6ves ?2o6 (aA)Als iv20t3 B 4\bu0oo0h Dsv2 oE 0hs isevlt hvt v AhvaE 0o v 8Iu0oo0h Dsv23 nE 0hs tv6s vfils vt 0hs 8Iu0oo0h Dsv2 at v 4gu0oo0h Dsv2 0hv0 e2arst v AhvaE 0o v ,\bu0oo0h Dsv2 oE 0hs i16i3 do2 srs2) 8\b\b Ao6ils0s 2srol10aoEt o? 0hs isevltw hof 6vE) 0a6st eost 0hs Dsv2 oE 0hs i16i 012Ec TBy 8H\b T:y gI\b T5y 8\bm T9y p4 T.y 4m Wh WhaW Wh Wa ti sh WtaB Dv2esEs2 fathst 0o i10 v Aa2A1lv2 fv0s2 ?sv012s Tiooly aE v 2aDh0uvEDlse 02avED1lv2 ilo0 0hv0 hvt taest o? H 6 vEe ’ 6 oE a0t 0fo t6vllst0 taest3 7hv0 at 0hs 2vea1t aE 6s02st o? 0hs lv2Dst0 iool 0hv0 fall b0c TBy g W g h 8 T:y g T5y , T9y 4 T.y g W g WWa B ts%1sEAs o? 8\b ls00s2t at 6ves vAAo2eaED 0o 0hs ?ollofaED 21lst3 a Whs ls00s2 x AvE oEl) (s ?ollofse () + o2 Ž3 a Whs ls00s2 + AvE oEl) (s ?ollofse () Ž o2 ‘3 a Whs ls00s2 Ž AvE oEl) (s ?ollofse () ‘ o2 W3 a Whs ls00s2 ‘ AvE oEl) (s ?ollofse () W o2 x3 a Whs ls00s2 W AvE oEl) (s ?ollofse () x o2 +3 ’of 6vE) iotta(ls ts%1sEAst v2s 0hs2s fhs2s 0hs b2t0w ?o120hw vEe 0sE0h ls00s2t v2s vll +c TBy H4 T:y 4pT5y 4g T9y ,I T.y 4H Wia 5)E0hav“t v?0s2EooE 02vaE Eo26vll) v22arst v0 hs2 t0v0aoE v0 I”4\b i6 svAh ev)w fhs2s ths at iaA•se 1i () BlvE vEe e2arsE ho6s3 nEs ev) ths fvt oE vE sv2las2 02vaE fhaAh v22arse v0 I i6w vEe ths esAaese 0o fvl• aE 0hs ea2sA0aoE BlvE fvt Ao6aED ?2o6 ho6s3 BlvE hve ls?0 aE 0a6s 0o 6ss0 0hs I”4\b i6 02vaEw (10 0hat 0a6s hs iaA•se 1i 5)E0hav vEe 0hs) v22arse ho6s 8\b 6aE10st sv2las2 0hvE 1t1vl3 do2 hof 6vE) 6aE10st hve 5)E0hav fvl•se (s?o2s BlvE iaA•se hs2 1ic TBy g\b T:y 4\bT5y gI T9y 8\b T.y 8I tt What ise v luof20f16?of (Af)o63u) 2016 AMC – Intermediate Questions

2323 WhaWha tise iv avluoufe2 0a11l6 h? (se 2uAe)evf 3hlha)e2 1h1B0fu340\b iv2 Divf fh oi4e i0 oiv6 2uAe)evf 3hlha)e2 eEaulife)il f)uiv8le0 i0 1h00uIle\b a0uv8 ft)ee 0fu340n five egio1le u0 0thDv te)en rDh f)uiv8le0 i)e vhf 3hv0u2e)e2 2uAe)evf u? fte6 i)e )hfifuhv0 h) )e,e3fuhv0 h? ei3t hfte)n dhD oiv6 2uAe)evf f)uiv8le0 i)e 1h00uIlew cTy H: c5y : cmy 9p c.y :’ c7y bp Ilae )e2 )e2 WtaTWhatisevluof22v 0eEaev3e u0 i lu0f h? Dthle vaoIe)0 Duft fte 1)h1e)f6 ftif\b ?)ho fte ftu)2 fe)o hvDi)20\b ese)6 fe)o u0 fte 0ao h? ill h? fte 1)esuha0 fe)o0n %h) egio1le\b bW xW :W bpW hhh dhD oiv6 0a1e)B%uIhvi33u 0eEaev3e0 0fi)fuv8 Duft b uvshlse fte vaoIe) 9pb’w cTy b c5y Hcmy : c.y + c7y Ž Wia rte )u8tfBiv8le2 f)uiv8le at iti0 i)ei 9pb’ 3o Wn ‘uve0 as\bse \bsv \bvl \blu \buo 2usu2e fte li)8e f)uiv8le uvfh 0esev 0oille) f)uiv8le0 h? eEail i)ein ’? Wtsv u0 iv u0h03ele0 f)uiv8le\b (v2 fte lev8ft h? to uv 3evfuoef)e0n 5 m T ’ % 7 d . “ Wsa T 06ooef)u3il 3)h00 Duft eEail i)o0 ti0 iv i)ei h? 9pb’ 3o Wiv2 ill 0u2e0 h? uvB fe8e) lev8ft uv 3evfuoef)e0n ”tif u0 fte 0oille0f 1e)uoefe) fte 3)h00 3iv tise\b uv 3evfuoef)e0w What ise v luof20f16?of (Af)o63u) Wh 2016 AMC – Intermediate Questions

24 WhaWha tai stevaits li uof20f16s 1oths 2foss off t00? o tast( Wha s20Aas 0) tha 0thaA ilia stevaits 3aAa B4\b BD\b BE\b B8\b 8I\b 84\b 8E\b 8n\b oiv 8B\b oiv uof20f16s s20Aa 3os o 3h0fa ie1fiaA( Wha tao2haA hov 1ova o 1lsto?a li 2of2efotlig uof20f16s s20Aa( r)taA sha 20AAa2tav haA 1lsto?a\b fi0th tha 1aoi oiv tha 1avloi 0) off tha s20Aas li2Aaosav fi, I(E( WhaAa oAa t30 d0sslfifa 20AAa2t s20Aas thot uof20f1 20efv howa hov( chot ls tha se1 0) thasa t30 s20AasT Wta r hlgh s2h00f 1oA2hlig fioiv 2oi fia oAAoigav li o Aa2toigefoA )0A1otl0i 3lth ayo2tf, thAaa fi0,s li ao2h A03 oiv ayo2tf, Hwa glAfs li ao2h 20fe1i( WhaAa oAa sawaAof sl:as 0) 1oA2hlig fioiv )0A 3hl2h thls ls d0sslfifa( chot ls tha se1 0) off se2h d0sslfifa sl:asT isa rA0eiv o 2lA2fa\b 5 dfo2a m9 apeoff, sdo2av d0lits\b s0 thot thaAa oAa m9WmD h4 . 4I’m d0sslfifa 2h0Avs fiat3aai thasa d0lits( 5 vAo3 s01a 0) thasa 2h0Avs\b fiet ao2h 2h0Av 2oii0t 2et o2A0ss 10Aa thoi 0ia 0thaA 2h0Av( chot ls tha 1oyl1e1 ie1fiaA 0) 2h0Avs 5 2oi vAo3T Wh What ise v luof20f16?of (Af)o63u) 2016 AMC – Intermediate Questions