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AMC8 2005

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AMC8 · 2005

Q1
Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?
Connie 将一个数乘以 2，得到 60。但是，她本应该将这个数除以 2 才能得到正确答案。正确答案是什么？
Q2
Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day?
Karl 在 Pay-A-Lot 买了五个文件夹，每个 2.50 美元。第二天 Pay-A-Lot 举行 20% 折扣促销。如果 Karl 等一天再买，他能节省多少钱？
Q3
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal BD of square ABCD?
要使正方形 ABCD 的对角线 BD 成为对称轴，需要将多少个小正方形涂成黑色？
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Q4
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?
一个正方形和一个三角形的周长相等。三角形的边长分别是 6.1 cm、8.2 cm 和 9.7 cm。正方形的面积是多少平方厘米？
Q5
Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?
苏打水有 6 罐、12 罐和 24 罐的包装。要买正好 90 罐苏打水，需要的最少包装数量是多少？
Q6
Suppose d is a digit. For how many values of d is 2.00d5 > 2.005?
假设 d 是一个数字。有多少个 d 的值使 2.00d5 > 2.005？
Q7
Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. How many miles is he, in a direct line, from his starting point?
比尔向南走 1/2 英里，然后向东走 3/4 英里，最后向南走 1/2 英里。他与起点直线距离有多少英里？
Q8
Suppose m and n are positive odd integers. Which of the following must also be an odd integer?
假设 m 和 n 是正奇整数。以下哪一项一定是奇整数？
Q9
In quadrilateral ABCD, sides AB and BC both have length 10, sides CD and DA both have length 17, and the measure of angle ADC is 60°. What is the length of diagonal AC?
在四边形 ABCD 中，边 AB 和 BC 长度均为 10，边 CD 和 DA 长度均为 17，角 ADC 的度量为 60°。对角线 AC 的长度是多少？
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Q10
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?
乔走完回家到学校的半途时意识到自己迟到了。他跑完了剩下的路程。他的跑速是他走速的 3 倍。乔走半途到学校用了 6 分钟。乔从家到学校总共用了多少分钟？
Q11
The sales tax rate in Bergville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up $90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up $90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total?
Bergville 的销售税率为 6%。在 Bergville Coat Closet 的促销活动中，一件外套的价格从 $90.00 折扣 20%。两位店员 Jack 和 Jill 独立计算账单。Jack 输入 $90.00 并加上 6% 的销售税，然后从这个总额中减去 20%。Jill 输入 $90.00，减去价格的 20%，然后在折扣价格上加上 6% 的销售税。Jack 的总额减去 Jill 的总额是多少？
Q12
Big Al, the ape, ate 100 bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May 5?
大猩猩 Big Al 从 5 月 1 日到 5 月 5 日吃了 100 根香蕉。每天他比前一天多吃 6 根香蕉。Big Al 在 5 月 5 日吃了多少根香蕉？
Q13
The area of polygon ABCDEF is 52 with AB = 8, BC = 9 and FA = 5. What is DE + EF?
多边形 ABCDEF 的面积为 52，AB = 8，BC = 9，FA = 5。DE + EF 是多少？
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Q14
The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?
Little Twelve 篮球联盟有两个分区的每个分区有 6 个队。每队与其本分区的其他队各打两次，与另一分区的每队打一次。联盟总共安排了多少场比赛？
Q15
How many different isosceles triangles have integer side lengths and perimeter 23?
有多少不同等腰三角形具有整数边长且周长为 23？
Q16
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?
一个五脚火星人有一个抽屉，里面装满了红、白、蓝色的袜子，每种颜色至少有五只袜子。火星人闭眼一次抽出一只袜子。要保证有5只相同颜色的袜子，火星人需要取出多少只袜子？
Q17
The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?
越野队的训练跑结果如下图所示。哪位学生平均速度最快？
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Q18
How many three-digit numbers are divisible by 13?
多少个三位数能被13整除？
Q19
What is the perimeter of trapezoid ABCD?
梯形ABCD的周长是多少？
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Q20
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
爱丽丝和鲍勃玩一个游戏，圆周上均匀分布12个点，从1到12顺时针编号。两人从点12开始。爱丽丝顺时针移动，鲍勃逆时针移动。每回合，爱丽丝顺时针移动5点，鲍勃逆时针移动9点。游戏在他们停在同一点时结束。需要多少回合？
Q21
How many distinct triangles can be drawn using three of the dots below as vertices?
使用以下点中的三个作为顶点，可以画出多少个不同的三角形？
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Q22
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy:
一家公司销售三种不同尺寸的洗涤剂盒子：小号(S)、中号(M)和大号(L)。中号的价格是小号的50%更高，包含的洗涤剂比大号少20%。大号包含的洗涤剂是小号的两倍，价格是中号的30%更高。将三种尺寸从最佳购买到最差购买排名：
Q23
Isosceles right triangle ABC encloses a semicircle of area $2\pi$. The circle has its center O on hypotenuse AB and is tangent to sides AC and BC. What is the area of triangle ABC?
等腰直角三角形ABC内有一个面积为$2\pi$的半圆。圆心O在斜边AB上，且该圆与边AC和BC相切。三角形ABC的面积是多少？
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Q24
A certain calculator has only two keys [+1] and [×2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed “9” and you pressed [+1], it would display “10.” If you then pressed [×2], it would display “20.” Starting with the display “1,” what is the fewest number of keystrokes you would need to reach “200”?
某计算器只有两个按键[+1]和[×2]。按下按键时，计算器自动显示结果。例如，如果计算器原显示“9”，按[+1]则显示“10”，再按[×2]则显示“20”。从显示“1”开始，到达“200”需要的最少按键次数是多少？
Q25
A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?
一个边长为2的正方形和一个圆同心。圆内、正方形外的区域总面积等于圆外、正方形内的区域总面积。求圆的半径。
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