AMATYC Studenl Mathemalics League
st,#2
J a n u a r y - F e b r u a r y2 0 0 2
Which of thefollowing linearequalionssharesa solutionwith thequadraticequatton
x2-t5x-54=o?
A . 6 x + 1 5 = 3 x- 3 B . 6 x - 1 5 = 3 x+ 3 C . 6 x + 1 5 = 5 x- 3 D . 6 x - 1 5 = 4 x + 3 E . 6 x + l 5 = 2 x + 3
The supplementof a nonzeroang)eis k timestheangle'scomplement.lf k is a positiveinteger,whal is its
smallestpossiblevalue?
C.4
8.3
A.2
E.6
D.5
ln quaddlaleralPQRS,PS = PQ = l, ZS = ZQ = 90', andPR = 2. Find SQ
.E
A.+
B.
.6
,t,
c.
+
D. .E
2
E.
wrriJl ortle forlowingis closeslrologl60.002I
A. -0.5
c. -1.5
B. -1.0
D. -2.0
E. -2.5
oDe50 ft wide,theoth€r60 fi wide,meetata 6Ooangle.Whichof thefollowingis closestto
Two highways,
theyform?
theareain sqfl of theintersection
c. 3000
B. 2800
A. 2600
D. 3200
E. 3400
totalof12lb. Tbepuppyandlargerkittenweighexactlylwicethesmaller
A puppyandrwokinenswei8ha
kinen. The puppyand smallerkiltenweighexacllythesameasthelarSerkitlen. Whatis the Puppy'sweight?
2lb
A.
3lb
B.
c.
4lb
5lb
D.
E.
6lb
from the second,multiPliedby $e thid
Four nlmbers havea sumof 45. lf 2 is added1o$e first, subtracted
anddividedinto the fourth,the resullsareequal. Find theproductofthe four numbers.
C. 10000
B. 9600
A. 92AJ
E 1ul40o
D. 12000
as RADAR, A, 5,
A palindromeis a word or numemlwhich readsthe samefotwardsandbackwards,_suci
palindromes?
itself
are
88, or the currenlyear2002. How manyof 2002'spositiveintegerfactotsbesides
A
.
4
8
.
5
C
.
6
D
.
'
7
E
.
8
A smallcjrcleof radiusa ljescompletelyinsidea largercircleof radiusb withoutlouching. The distance
betweentbecenreNis d. Whatis tbelengthofthe shonestline segmenljoiningaPolnton tbe smaller
circleto a pointon thelargercircle?
(b: a)
(a1b)
E.
c.
b-d-2a
D.
B. b-d-a
A. b-a
22mo'71000,
2tom, 3:oj, 5zooo11
. Wharis the smalleslelem€ntof the set{230m31000,
A. 2300q10m
B.22cn071tJf,o
C. 25000
D.33000
E. 9000
. Whatis the smaljestpositiveinteeern for which n I terminalesin exactly88 zeros?
A. 350
B. 354
C. 360
D. 370
E. 440
nuary.February2002
AMATYC Student Malhematics League
page 2
' one daya-sloreb]ou.ghr
in $4400by selling60 ilemsof clorhingconsisring
of panrsfor $30,JackeB
for $g0,
a n o s u l l lso r $ l l U . w n a l l s l n e l a r p e s l n u l ' b e rsoull l sl h es t o t ec o u l dh a v eS O l d ?
4.25
B. 28
C. 29
D. 30
E. 36
. How many solulionsdoesthe equalioncos3x cosx = sin 3x sin x havein the interval [_&r,&r] ?
A. 0
B. 16
C. U
D. 2S
E. an infinire number
. A right trianglehasperimeterK unirs,areaK squareuDitsandoneleg of lengthVK unirs,wirh K * O. The
valueofK in simpleslradicaiformcanbe wrinenasa + b16,with a, b, c positiveinte8ers.Finda+b+c.
A.2n
B.
22
C.
24
D.
25
E. 30
;. what is.thelargeslprimefactorof the smallestnumberwhichis divisibleby 7 and yieldsa remainderof I
whendividedby 2, 3,4,5, and6'!
A. 1l
B.
19
C.
3.7
D.
43
E.
6l
;.For how manysequences
of rhreedecjmaldjgitsis eachdigit at leastaslargeaslhe precedingdigit?
A. 120
B. 130
C. 200
D. 210
E.220
. L,e_l
eachlenerIn theequalionAMA -,TYC = B represenl
a digitfromOto 9, wilh differenllenersrepresenling
differenldigits.so tharlhelefrsideof lheequation
represents-the
difference
of lwo lhree-digir
numtrs. ln'
how manywayscanthe lettersbereplacedto producea trueequatjon?
A.5
B. 10
C. 12
D. 13
E. 15
i. In rectangle
CDEF, CD = 32 andDE = 24, andin recrangleDFGH, Fc = 12. The areaof the regioninside
bothrectanSles
at onceis
A. 150
B.
330
c.
438
D.
480
E.
630
'. Two-2Gfootlengrhs-offencecrossatrhejr midpojntsal a 90'angle to form anx. A goatis tiedro one
endof
-onefenceu'ith a 2Gft rope. Whatis the areato thenearesrl0 sqiare feetthatrhe goaicanreachif it cango
aroundthefencesbul not overor underthern?
A. 1020
B.
1120
C.
ll50
D.
1200
E.
1220
r,A boxhoids9 idenricalballslab€ledI rhrough9. A ball is drawnat randomfrom the box, retumedto the
box,andthena secondball is dra$,nal random. For what vajueof k will the even8 "thesumof thetwo
numbersjs k" and "thetrvonumbersaredifferenf'be independent?
'7
,4'.6
B.
C.
8
D.
9
E.
tO