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1987 AMC8 #4 · Algebra · ★★
Martians measure angles in clerts. There are 500 clerts in a full circle. How many clerts are there in a right angle?
火星人以 clert 为单位度量角度。一整个圆周有 500 clert。一个直角有多少 clert？

正确答案：C · 分值：1

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1987 AMC8 #6 · Algebra · ★★
The smallest product one could obtain by multiplying two numbers in the set {−7,−5,−1,1,3}\{ -7,-5,-1,1,3 \} is
将集合 {−7,−5,−1,1,3}\{-7,-5,-1,1,3\} 中的两个数相乘，能得到的最小乘积是

正确答案：B · 分值：1

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1987 AMC8 #7 · Geometry · ★★
The large cube shown is made up of 27 identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is
所示大正方体由 27 个相同大小的小正方体组成。大正方体的每个面，其相对面的着色方式相同。至少有一个面被着色的小正方体总数是

正确答案：C · 分值：1

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1987 AMC8 #8 · Algebra · ★★
If the letters are replaced by digits so that the given addition problem is correct, then the number of digits (not necessarily different) in the sum of the three whole numbers is
若字母被数字替换使得给定的加法算式正确，则三个整数的和的位数（数字不必不同）为

正确答案：B · 分值：1

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1987 AMC8 #9 · Number Theory · ★★
When finding the sum 12+13+14+15+16+17\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7} , the least common denominator used is
求 12+13+14+15+16+17\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7} 的和时，使用的最小公分母是

正确答案：C · 分值：1

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1987 AMC8 #11 · Algebra · ★★★
The sum 217+312+5119\displaystyle 2\frac17+3\frac12+5\frac{1}{19} is between
和 217+312+5119\displaystyle 2\frac17+3\frac12+5\frac{1}{19} 在以下哪两个数之间？

正确答案：B · 分值：1

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1987 AMC8 #12 · Geometry · ★★★
What fraction of the large 12 by 18 rectangular region is shaded?
着色部分占 12 × 18 大矩形区域的几分之几？

正确答案：C · 分值：1

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1987 AMC8 #13 · Algebra · ★★★
Which of the following fractions has the largest value?
以下哪个分数值最大？

正确答案：E · 分值：1

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1987 AMC8 #14 · Algebra · ★★★
A computer can do 10,000 additions per second. How many additions can it do in one hour?
一台计算机每秒可以做 10,000 次加法。它在一小时内能做多少次加法？

正确答案：B · 分值：1

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1987 AMC8 #15 · Algebra · ★★★
The sale ad read: "Buy three tires at the regular price and get the fourth tire for $3. " Sam paid $240 for a set of four tires at the sale. What was the regular price of one tire?
促销广告写道："以原价购买三个轮胎，第四个轮胎仅需 $3。" Sam 在促销中以 $240 买了一套四个轮胎。一个轮胎的原价是多少？

正确答案：D · 分值：1

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1987 AMC8 #16 · Algebra · ★★★
Joyce made 12 of her first 30 shots in the first three games of this basketball season, so her seasonal shooting average was 40% . In her next game, she took 10 shots and raised her seasonal shooting average to 50% . How many of these 10 shots did she make?
Joyce 在本篮球赛季的前三场比赛中前 30 次出手命中 12 次，因此她的赛季命中率为 40%。在下一场比赛中，她出手 10 次并将赛季命中率提高到 50%。这 10 次出手她命中了多少次？

正确答案：E · 分值：1

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1987 AMC8 #17 · Counting, Probability & Statistics · ★★★
Abby, Bret, Carl, and Dana are seated in a row of four seats numbered #1 to #4 . Joe looks at them and says: \hspace{2em} "Bret is next to Carl." \hspace{2em} "Abby is between Bret and Carl." However each one of Joe's statements is false. Bret is actually sitting in seat #3 . Who is sitting in seat #2 ?
Abby、Bret、Carl 和 Dana 坐在编号为 #1 到 #4 的四个座位上。Joe 看着他们说：
\hspace{2em} "Bret 挨着 Carl。"
\hspace{2em} "Abby 在 Bret 和 Carl 之间。"
然而 Joe 的每句话都是假的。实际上 Bret 坐在 #3 号座位。谁坐在 #2 号座位？

正确答案：D · 分值：1

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1987 AMC8 #18 · Algebra · ★★★
Half the people in a room left. One third of those remaining started to dance. There were then 12 people who were not dancing. The original number of people in the room was
房间中一半的人离开了。剩下的人中有三分之一开始跳舞。此时有 12 人没有跳舞。房间里原来的人数是

正确答案：C · 分值：1

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1987 AMC8 #19 · Algebra · ★★★
A calculator has a squaring key x2\boxed{x^2} which replaces the current number displayed with its square. For example, if the display is          3\boxed{\ \ \ \ \ \ \ \ \ 3} and the x2\boxed{x^2} key is depressed, then the display becomes          9\boxed{\ \ \ \ \ \ \ \ \ 9} . If the display reads          2\boxed{\ \ \ \ \ \ \ \ \ 2} , how many times must you depress the x2\boxed{x^2} key to produce a displayed number greater than 500 ?
一个计算器有一个平方键 x2\boxed{x^2}，将当前显示的数替换为其平方。例如，如果显示为 3\boxed{3} 并按下 x2\boxed{x^2} 键，则显示变为 9\boxed{9}。如果显示 2\boxed{2}，需要按多少次 x2\boxed{x^2} 键才能产生一个大于 500 的显示数？

正确答案：A · 分值：1

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1987 AMC8 #20 · Number Theory · ★★★
"If a whole number nn is not prime, then the whole number n-2 is not prime." A value of nn which shows this statement to be false is
"如果一个正整数 nn 不是质数，则正整数 n-2 也不是质数。" 以下哪个 nn 的值能证明该陈述为假？

正确答案：A · 分值：1

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1987 AMC8 #21 · Algebra · ★★★
Suppose n∗n^{*} means 1n\displaystyle \frac{1}{n} , the reciprocal of nn . For example, 5∗=15\displaystyle 5^{*}=\frac{1}{5} . How many of the following statements are true? \hspace{2em} i) 3∗+6∗=9∗3^*+6^*=9^* \hspace{2em} ii) 6∗−4∗=2∗6^*-4^*=2^* \hspace{2em} iii) 2∗⋅6∗=12∗2^*\cdot 6^*=12^* \hspace{2em} iv) 10∗÷2∗=5∗10^*\div 2^* =5^*
设 n∗n^{*} 表示 1n\displaystyle \frac{1}{n}，即 nn 的倒数。例如 5∗=15\displaystyle 5^{*}=\frac{1}{5}。以下陈述中有多少条为真？
\hspace{2em} i) 3∗+6∗=9∗3^*+6^*=9^*
\hspace{2em} ii) 6∗−4∗=2∗6^*-4^*=2^*
\hspace{2em} iii) 2∗⋅6∗=12∗2^*\cdot 6^*=12^*
\hspace{2em} iv) 10∗÷2∗=5∗10^*\div 2^* =5^*

正确答案：C · 分值：1

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1987 AMC8 #22 · Geometry · ★★★★
ABCDABCD is a rectangle, DD is the center of the circle, and BB is on the circle. If AD=4 and CD=3 , then the area of the shaded region is between
ABCDABCD 是一个矩形，DD 是圆的圆心，BB 在圆上。如果 AD=4 且 CD=3，则着色区域的面积在以下哪两个数之间？

正确答案：D · 分值：1

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1987 AMC8 #23 · Counting, Probability & Statistics · ★★★
The table below gives the 1980 U.S. population for each of the four geographic regions and for each of two ethnic groups. To the nearest percent, what percent of the U.S. Black population lived in the South?
下表给出了 1980 年美国四个地理区域和两个族裔的人口。取整到最近的百分比，美国黑人人口中有百分之多少居住在南方？

正确答案：D · 分值：1

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1987 AMC8 #24 · Number Theory · ★★★★
A multiple choice examination consists of 20 questions. The scoring is +5 for each correct answer, -2 for each incorrect answer, and 0 for each unanswered question. John's score on the examination is 48 . What is the maximum number of questions he could have answered correctly?
一项选择题考试包含 20 道题。评分规则为：每答对一题 +5 分，每答错一题 -2 分，未答题 0 分。John 的考试分数为 48。他最多可能答对了多少道题？

正确答案：D · 分值：1

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1987 AMC8 #25 · Counting, Probability & Statistics · ★★★★
Ten balls numbered 1 to 10 are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is even is
一个罐子中有编号 1 到 10 的十个球。Jack 从罐中随机取出一个球。然后 Jill 从罐中随机取一个不同的球。取出的两个球上的数字之和为偶数的概率是

正确答案：A · 分值：1

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