2005
A 1Two is 10%of x and 20%of y .What is x −y ?
A.1
B.2
C.5
D.10
E.202The equations 2x +7=3and bx −10=−2have the same solution.What is the value of b ?
A.-8
B.-4
C.-2
D.4
E.83A rectangle with a diagonal length of x is twice as long as it is wide.What is the area of the rectangle?
A.14x 2
B.25x 2
C.12x 2
D.x 2
E.32
x 24A store normally lls windows at $100each.This week the store is offering one free window for each purcha of four.Dave needs ven windows and Doug needs eight windows.How much will they save if they purcha the windows together than rather parately?
A.100
后市B.200
C.300
D.400
E.5005The average (mean)of 20numbers is 30,and the average of 30other numbers is 20.What is the average of all 50numbers?
A.23
B.24
C.25
D.26
E.276Josh and Mike live 13miles apart.Yesterday,Josh started to ride his bicycle toward Mike’s hou.A little later Mike started to ride his bicycle toward Josh’s hou.When they met,Josh had ridden for twice the length of time as Mike and at four-fifths of Mike’s rate.How many miles had Mike ridden when they met?
A.4
B.5
C.6
D.7
E.87Square EF GH is inside the square ABCD so that each side of EF GH can be extended to pass through a vertex of ABCD .Square ABCD has side length √50and BE =1.What is the area of the inner square EF GH ?
托福阅读算分A.25
B.32
C.36
D.40
E.428Let A,M ,and C be digits with
(100A +10M +C )(A +M +C )=2005
What is A ?
A.1
B.2
C.3
D.4
E.5This file was downloaded from the AoPS −MathLinks Math Olympiad Resources Page Page 1/
20059There are two values of a for which the equation 4x 2+ax +8x +9=0has only one solution for x .What is the sum of the values of a ?
A.-16
B.-8
C.0
D.8
E.2010A wooden cube n units on a side is painted red on all six faces and then cut into n 3unit
cubes.Exactly one-fourth of the total number of faces of the unit cubes are red.What is n ?
A.3
B.4
C.5
D.6
E.711How many three-digit numbers satisfy the property that the middle digit is the average of
认为英文the first and the last digits?
A.41
八下英语作业本答案浙教版B.42
C.43
D.44
E.4512A line pass through A(1,1)and B(100,1000).How many other points with integer coordi-
nates are on the line and strictly between A and B?
A.0B.2C.3D.8E.913The regular 5-point star ABCDE is drawn and in each vertex,there is a number.Each
A,B,C,D,and E are chon such that all 5of them came from t 3,5,6,7,9.Each letter is a different number (so one possible ways is A=3,B=5,C=6,D=7,E=9).Let AB be the sum of the numbers in A an
d B.If AB,BC,CD,DE,and EA form an arithmetic quence (not necessarily this order),find the value of CD.
A.9
B.10
C.11
D.12
E.1314On a standard die one of the dots is removed at random with each dot equally likely to be
chon.The die is then rolled.What is the probability that the top face has an odd number of dots?
(A)5
11(B)10
21(C)1
2(D)11
21(E)6
1115Let AB be a diameter of a circle and C be a point on AB with 2·AC =BC .Let D and E
be points on the circle such that DC ⊥AB and DE is a cond diameter.What is the ratio of the area of DCE to the area of ABD ?
(A)16(B)14(C)13(D)12(E)2316Three circles of radius s are drawn in the first quadrant of the xy -plane.The first circle is
tangent to both axes,the cond is tangent to the first circle and the x -axis,and the third is tangent to the first circle and the y -axis.A circle of radius r >s is tangent to both axes and to the cond and third circles.What is r/s ?
200517A unit cube is cut twice to form three triangular prisms,two of which are congruent,as shown
in Figure 1.The cube is then cut in the same manner along the dashed lines shown in Figure
2.This creates nine pieces.What is the volume of the piece that contains vertex W ?
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A)112B)19C)18D)16E)1418Call a number ”prime-looking”if it is composite but not divisible by 2,3,or 5.The three smallest
prime-looking numbers are 49,77,and 91.There are 168prime numbers less than 1000.How many prime-looking numbers are there less than 1000?
(A)100(B)102(C)104(D)106(E)10819A faulty car odometer proceeds from digit 3to digit 5,always skipping the digit 4,regardless of
position.If the odometer now reads 002005,how many miles has the car actually traveled?
(A)1404
(B)1462(C)1604(D)1605(E)180420For each x in [0,1],define
f (x )=2x,
if 0≤x ≤12;
f (x )=2−2x,if 12<x ≤1.Let f [2](x )=f (f (x )),and f [n +1](x )=f [n ](f (x ))for each integer n ≥2.For how many values of x in [0,1]is f [2005](x )=12
?(A)0(B)2005(C)4010(D)20052(E)2200521How many ordered triples of integers (a,b,c ),with a ≥2,b ≥1,and c ≥0,satisfy both log a b =c 2005
and a +b +c =2005?
(A)0(B)1(C)2(D)3(E)422A rectangular box P is inscribed in a sphere of radius r .The surface area of P is 384,and the sum
of the lengths of its 12edges is 112.What is r ?
(A)8(B)10(C)12(D)14(E)16
200523Two distinct numbers a and b are chon randomly from the t {2,22,23,...,225}.What is the
probability that log a b is an integer?
(A)2
25(B)31
300(C)13
100(D)7
50(E)1
224Let P (x )=(x −1)(x −2)(x −3).For how many polynomials Q (x )does there exist a polynomial
R (x )of degree 3such that P (Q (x ))=P (x )·R (x )?
(A)19(B)22(C)24(D)27(E)3225Let S be the t of all points with coordinates (x,y,z ),where x,y,and z are each chon from the
t {0,1,2}.How many equilateral triangles have all their vertices in S ?
(A)72(B)76(C)80(D)84(E)88
2005cyndi lauper
B 1A scout troop buys 1000candy bars at a price of five for $2.They ll all the candy bars at a price of two for $1.What was their profit,in dollars?
A.100
B.200on the tip of my tongue
C.300
wickedsick
D.400
E.5002A positive number x has the property that x %of x is 4.What is x ?
A.2
B.4
C.10
D.20
宝贝用德语怎么说
kiss me good byeE.403Brianna is using part of the money she earned on her weekend job to buy veral equally-priced CDs.She ud one fifth of her money to buy one third of the CDs.What fraction of her money will she left after she buys all the CDs?
A.15
B.13
C.25
D.23
E.454At the beginning of the school year,Lisa’s goal was to earn an A on at least 80%of her 50quizzes for the year.She earned an A on 22of the first 30quizzes.If she is to achieve her goal,on at most how many of the remaining quizzes can she earn a grade lower than an A?
A.1
B.2
globalenglishC.3
D.4
E.55An 8-foot by 10-foot floor is tiled with square tiles of size 1foot by 1foot.Each tile has a pattern consisting of four white quarter circles of radius 1/2foot centered at each corner of the tile.The remaining portion of the tile is shaded.How many square feet of the floor are shaded?
A.80−20π
B.60−10π
C.80−10π
D.60+10π
E.80+10π6In ABC ,we have AC =BC =7and AB =2.Suppo that D is a point on line AB such that B lies between A and D and CD =8.What is BD ?A.3B.2√3C.4D.5E.4√2
