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AMC8 1991

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AMC8 · 1991

Q1
$1,000,000,000,000 - 777,777,777,777 =$
$1,000,000,000,000 - 777,777,777,777 = $
Q2
$\frac{16 + 8}{4 - 2} =$
$\frac{16 + 8}{4 - 2} = $
Q3
Two hundred thousand times two hundred thousand equals
二十万乘以二十万等于
Q4
If $991 + 993 + 995 + 997 + 999 = 5000 - N$, then $N =$
如果 $991 + 993 + 995 + 997 + 999 = 5000 - N$，则 $N = $
Q5
A "domino" is made up of two small squares: $\square$. Which of the "checkerboards" illustrated below CANNOT be covered exactly and completely by a whole number of non-overlapping dominoes?
一个“多米诺骨牌”由两个小方格组成：$\square\square$。下面所示的哪个“棋盘”无法被整数量目的不重叠的多米诺骨牌完全精确覆盖？
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Q6
Which number in the array below is both the largest in its column and smallest in its row? (columns go up and down, rows go right and left.)
下面数组中，哪个数字既是其列中最大的，又是其行中最小的？（列上下，行左右。）
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Q7
The value of $\frac{(487,000)(12,027,300) + (9,621,001)(487,000)}{(19,367)(.05)}$ is closest to
$ \frac{(487,000)(12,027,300) + (9,621,001)(487,000)}{(19,367)(.05)}$ $的值最接近
Q8
What is the largest quotient that can be formed using two numbers chosen from the set $\{-24, -3, -2, 1, 2, 8\}$?
从集合 $\{-24, -3, -2, 1, 2, 8\}$ 中选择两个数字，能形成的最大商是多少？
Q9
How many whole numbers from 1 through 46 are divisible by either 3 or 5 or both?
从 1 到 46 中，有多少个整数能被 3 或 5（或两者）整除？
Q10
The area in square units of the region enclosed by parallelogram ABCD is
平行四边形 ABCD 所围区域的面积（平方单位）是
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Q11
There are several sets of three different numbers whose sum is 15 which can be chosen from $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. How many of these sets contain a 5?
从集合$\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$中可以选择若干个不同数字之和为15的三元组集合。其中包含5的集合有多少个？
Q12
If $\frac{2 + 3 + 4}{3} = \frac{1990 + 1991 + 1992}{N}$, then $N =$
如果$\frac{2 + 3 + 4}{3} = \frac{1990 + 1991 + 1992}{N}$，则$N=$
Q13
How many zeros are at the end of the product $25 \times 25 \times 25 \times 25 \times 25 \times 25 \times 8 \times 8 \times 8$?
$25 \times 25 \times 25 \times 25 \times 25 \times 25 \times 8 \times 8 \times 8$这个乘积末尾有多少个零？
Q14
Several students are competing in a series of three races. A student earns 5 points for winning a race, 3 points for finishing second and 1 point for finishing third. There are no ties. What is the smallest number of points that a student must earn in the three races to be guaranteed of earning more points than any other student?
几名学生参加三场赛跑的系列赛。学生赢得比赛得5分，第二名得3分，第三名得1分。没有并列名次。一个学生在三场比赛中必须获得的最少积分，以保证比任何其他学生获得的积分都多，是多少？
Q15
All six sides of a rectangular solid were rectangles. A one-foot cube was cut out of the rectangular solid as shown. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?
一个长方体所有六个面都是矩形。从长方体中按图示切出一个一英尺的立方体。新长方体表面的总平方英尺数比原长方体的表面积多多少或少多少？
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Q16
The 16 squares on a piece of paper are numbered as shown in the diagram. While lying on a table, the paper is folded in half four times in the following sequence: (1) fold the top half over the bottom half (2) fold the bottom half over the top half (3) fold the right half over the left half (4) fold the left half over the right half Which number square is on top after step 4?
纸上有一个由16个方格组成的图示编号。当纸平放在桌子上时，按照以下顺序对折四次：(1) 将上半部分折叠到下半部分 (2) 将下半部分折叠到上半部分 (3) 将右半部分折叠到左半部分 (4) 将左半部分折叠到右半部分 第4步后，哪个编号的方格在最上面？
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Q17
An auditorium with 20 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for an exam is
一个有20排座位的礼堂，第一排有10个座位。每后一排比前一排多一个座位。如果考试学生可以坐在任何一排，但同一排不能与另一个学生相邻，那么最多可以容纳的学生数量是
Q18
The vertical axis indicates the number of employees, but the scale was accidentally omitted from this graph. What percent of the employees at the Gauss Company have worked there for 5 years or more?
纵轴表示员工数量，但该图的纵轴刻度意外遗漏了。高斯公司在那里工作5年或更长时间的员工占总员工的百分比是多少？
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Q19
The average (arithmetic mean) of 10 different positive whole numbers is 10. The largest possible value of any of these numbers is
10个不同的正整数的平均数（算术平均）是10。这些数中最大的可能值是
Q20
In the addition problem, each digit has been replaced by a letter. If different letters represent different digits then $C =$
在加法问题中，每个数字都被字母替换。如果不同的字母代表不同的数字，那么$C=$
Q21
For every 3° rise in temperature, the volume of a certain gas expands by 4 cubic centimeters. If the volume of the gas is 24 cubic centimeters when the temperature is 32°, what was the volume of the gas in cubic centimeters when the temperature was 20°?
对于每升高3°的温度，某种气体的体积膨胀4立方厘米。如果温度为32°时气体的体积是24立方厘米，那么温度为20°时气体的体积是多少立方厘米？
Q22
Each spinner is divided into 3 equal parts. The results obtained from spinning the two spinners are multiplied. What is the probability that this product is an even number?
每个转盘分为3等份。旋转两个转盘得到的结果相乘。这个积是偶数的概率是多少？
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Q23
The Pythagoras High School band has 100 female and 80 male members. The Pythagoras High School orchestra has 80 female and 100 male members. There are 60 females who are members in both band and orchestra. Altogether, there are 230 students who are in either band or orchestra or both. The number of males in the band who are NOT in the orchestra is
毕达哥拉斯高中乐队有100名女生和80名男生。毕达哥拉斯高中管弦乐队有80名女生和100名男生。有60名女生同时是乐队和管弦乐队的成员。总共有230名学生至少参加了一个乐队或管弦乐队。不在管弦乐队的乐队男生人数是
Q24
A cube of edge 3 cm is cut into $N$ smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters, then $N =$
一个边长3 cm的立方体被切成$N$个较小的立方体，不全相同大小。如果每个小立方体的边长是整厘米，则$N =$
Q25
An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?
一个等边三角形最初涂成黑色。每次改变时，每个黑色三角形中间四分之一变成白色。经过五次改变后，原始黑色三角形面积的哪一部分仍然是黑色？
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