(6?3) + 4 - (2 - 1) = 5. To make this statement true, the question mark between the 6 and the 3 should be replaced by (A) ÷ (B)\ × (C) + (D)\ - (E)\ None of these
💡 解题思路
Simplifying the given expression, we get: $(6?3)=2.$
2
第 2 题
几何·角度
What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock? [图]
💡 解题思路
At $10:00$ , the hour hand will be on the $10$ while the minute hand on the $12$ .
3
第 3 题
规律与数列
Which triplet of numbers has a sum NOT equal to 1? (A)\ (1/2,1/3,1/6) (B)\ (2,-2,1) (C)\ (0.1,0.3,0.6) (D)\ (1.1,-2.1,1.0) (E)\ (-3/2,-5/2,5)
💡 解题思路
By adding each triplet, we can see that $\boxed{(D)}$ gives us $0$ , not $1$ , as our sum.
4
第 4 题
行程问题
The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Alberto biked than Bjorn? [图] (A)\ 15 (B)\ 20 (C)\ 25 (D)\ 30 (E)\ 35
💡 解题思路
After 4 hours, we see that Bjorn biked 45 miles, and Alberto biked 60. Thus the answer is $60-45=15$ $\boxed{\text{(A)}}$ .
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第 5 题
几何·面积
A rectangular garden 60 feet long and 20 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden? (A)\ 100 (B)\ 200 (C)\ 300 (D)\ 400 (E)\ 500
💡 解题思路
We need the same perimeter as a $60$ by $20$ rectangle, but the greatest area we can get. right now the perimeter is $160$ . To get the greatest area while keeping a perimeter of $160$ , the sides sho
6
第 6 题
应用题
Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bo has as much money as Flo. Both Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money? (A)\ Bo (B)\ Coe (C)\ Flo (D)\ Jo (E)\ Moe
💡 解题思路
Use logic to solve this problem. You don't actually need to use any equations.
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第 7 题
应用题
The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center? (A)\ 90 (B)\ 100 (C)\ 110 (D)\ 120 (E)\ 130
💡 解题思路
There are $160-40=120$ miles between the third and tenth exits, so the service center is at milepost $40+(3/4)(120) = 40+90=\boxed{\text{(E)}\ 130}$ .
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第 8 题
几何·面积
Six squares are colored, front and back, (R = red, B = blue, O = orange, Y = yellow, G = green, and W = white). They are hinged together as shown, then folded to form a cube. The face opposite the white face is [图] (A)\ B (B)\ G (C)\ O (D)\ R (E)\ Y
💡 解题思路
When G is arranged to be the base, B is the back face and W is the front face. Thus, $\boxed{\text{(A)}\ B}$ is opposite W.
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第 9 题
综合
Three flower beds overlap as shown. Bed A has 500 plants, bed B has 450 plants, and bed C has 350 plants. Beds A and B share 50 plants, while beds A and C share 100. The total number of plants is [图] (A)\ 850 (B)\ 1000 (C)\ 1150 (D)\ 1300 (E)\ 1450
💡 解题思路
Plants shared by two beds have been counted twice, so the total is $500 + 450 + 350 - 50 - 100 = \boxed{\text{(C)}\ 1150}$ .
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第 10 题
概率
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will NOT be green? (A)\ \frac{1}{4} (B)\ \frac{1}{3} (C)\ \frac{5}{12} (D)\ \frac{1}{2} (E)\ \frac{7}{12}
💡 解题思路
\[\frac{\text{time not green}}{\text{total time}} = \frac{R + Y}{R + Y + G} = \frac{35}{60} = \boxed{\text{(E)}\ \frac{7}{12}}\]
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第 11 题
几何·面积
Each of the five numbers 1, 4, 7, 10, and 13 is placed in one of the five squares so that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column. The largest possible value for the horizontal or vertical sum is [图] (A)\ 20 (B)\ 21 (C)\ 22 (D)\ 24 (E)\ 30
💡 解题思路
The largest sum occurs when $13$ is placed in the center. This sum is $13 + 10 + 1 = 13 + 7 + 4 = \boxed{\text{(D)}\ 24}$ . Note: Two other common sums, $18$ and $21$ , are also possible.
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第 12 题
分数与比例
The ratio of the number of games won to the number of games lost (no ties) by the Middle School Middies is 11/4 . To the nearest whole percent, what percent of its games did the team lose? (A)\ 24\% (B)\ 27\% (C)\ 36\% (D)\ 45\% (E)\ 73\%
💡 解题思路
The ratio means that for every $11$ games won, $4$ are lost, so the team has won $11x$ games, lost $4x$ games, and played $15x$ games for some positive integer $x$ . The percentage of games lost is ju
13
第 13 题
统计
The average age of the 40 members of a computer science camp is 17 years. There are 20 girls, 15 boys, and 5 adults. If the average age of the girls is 15 and the average age of the boys is 16, what is the average age of the adults? (A)\ 26 (B)\ 27 (C)\ 28 (D)\ 29 (E)\ 30
💡 解题思路
First, find the total amount of the girl's ages and add it to the total amount of the boy's ages. It equals $(20)(15)+(15)(16)=540$ . The total amount of everyone's ages can be found from the average
14
第 14 题
几何·面积
In trapezoid ABCD , the sides AB and CD are equal. The perimeter of ABCD is [图] (A)\ 27 (B)\ 30 (C)\ 32 (D)\ 34 (E)\ 48
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set {C,H,L,P,R}, the second from {A,I,O}, and the third from {D,M,N,T}. When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of ADDITIONAL license plates that can be made by adding two letters? (A)\ 24 (B)\ 30 (C)\ 36 (D)\ 40 (E)\ 60
💡 解题思路
There are currently $5$ choices for the first letter, $3$ choices for the second letter, and $4$ choices for the third letter, for a total of $5 \cdot 3 \cdot 4 = 60$ license plates.
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第 16 题
综合
Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more problems would she have needed to answer correctly to earn a 60% passing grade? (A)\ 1 (B)\ 5 (C)\ 7 (D)\ 9 (E)\ 11
💡 解题思路
First, calculate how many of each type of problem she got right:
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第 17 题
统计
At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists this items: 1\frac{1}{2} cups of flour, 2 eggs, 3 tablespoons butter, \frac{3}{4} cups sugar, and 1 package of chocolate drops. They will make only full recipes, not partial recipes. Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.) (A)\ 1 (B)\ 2 (C)\ 5 (D)\ 7 (E)\ 15
💡 解题思路
If $108$ students eat $2$ cookies on average, there will need to be $108\cdot 2 = 216$ cookies. There are $15$ cookies per pan, meaning there needs to be $\frac{216}{15} = 14.4$ pans. However, since h
18
第 18 题
统计
At Central Middle School the 108 students who take the AMC8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists this items: 1\frac{1}{2} cups flour, 2 eggs, 3 tablespoons butter, \frac{3}{4} cups sugar, and 1 package of chocolate drops. They will make only full recipes, not partial recipes. They learn that a big concert is scheduled for the same night and attendance will be down 25\% . How many recipes of cookies should they make for their smaller party? (A)\ 6 (B)\ 8 (C)\ 9 (D)\ 10 (E)\ 11
💡 解题思路
If $108$ students eat $2$ cookies on average, there will need to be $108\cdot 2 = 216$ cookies. But with the smaller attendance, you will only need $100\% - 25\% = 75\%$ of these cookies, or $75\% \cd
19
第 19 题
统计
At Central Middle School, the 108 students who take the AMC 8 meet in the evening to talk about food and eat an average of two cookies apiece. Hansel and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: 1\frac{1}{2} cups flour, 2 eggs, 3 tablespoons butter, \frac{3}{4} cups sugar, and 1 package of chocolate drops. They will make full recipes, not partial recipes. Hansel and Gretel must make enough pans of cookies to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be leftover, of course.) (A)\ 5 (B)\ 6 (C)\ 7 (D)\ 8 (E)\ 9
💡 解题思路
For $216$ cookies, you need to make $\frac{216}{15} = 14.4$ pans. Since fractional pans are forbidden, round up to make $\lceil \frac{216}{15} \rceil = 15$ pans.
20
第 20 题
立体几何
Figure 1 is called a "stack map." The numbers tell how many cubes are stacked in each position. Fig. 2 shows these cubes, and Fig. 3 shows the view of the stacked cubes as seen from the front. Which of the following is the front view for the stack map in Fig. 4? [图] [图]
💡 解题思路
The third view is a direct, head-on view of the cubes. Thus, you will only see the highest (or, in these cases, higher) tower in each up-down column. For figure $4$ :
21
第 21 题
几何·角度
The degree measure of angle A is [图] (A)\ 20 (B)\ 30 (C)\ 35 (D)\ 40 (E)\ 45
💡 解题思路
Angle-chasing using the small triangles:
22
第 22 题
综合
In a far-off land three fish can be traded for two loaves of bread and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth? (A)\ \frac{3}{8} (B)\ \frac{1}{2} (C)\ \frac{3}{4} (D)\ 2\frac{2}{3} (E)\ 3\frac{1}{3}
💡 解题思路
Let $f$ represent one fish, $l$ a loaf of bread, and $r$ a bag of rice. Then: $3f=2l$ , $l=4r$
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第 23 题
几何·面积
Square ABCD has sides of length 3. Segments CM and CN divide the square's area into three equal parts. How long is segment CM ? [图] (A)\ √(10) (B)\ √(12) (C)\ √(13) (D)\ √(14) (E)\ √(15)
💡 解题思路
Since the square has side length $3$ , the area of the entire square is $9$ .
24
第 24 题
数论
When 1999^{2000} is divided by 5 , the remainder is (A)\ 0 (B)\ 1 (C)\ 2 (D)\ 3 (E)\ 4
💡 解题思路
Note that the units digits of the powers of 9 have a pattern: $9^1 = {\bf 9}$ , $9^2 = 8{\bf 1}$ , $9^3 = 72{\bf 9}$ , $9^4 = 656{\bf 1}$ , and so on. Since all natural numbers with the same last digi
25
第 25 题
几何·面积
Points B , D , and J are midpoints of the sides of right triangle ACG . Points K , E , I are midpoints of the sides of triangle JDG , etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6 , then the total area of the shaded triangles is nearest [图] (A)\ 6 (B)\ 7 (C)\ 8 (D)\ 9 (E)\ 10
💡 解题思路
Since $\triangle FGH$ is fairly small relative to the rest of the diagram, we can make an underestimate by using the current diagram. All triangles are right-isosceles triangles.