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全部分类AlgebraGeometryNumber TheoryCounting, Probability & Statistics
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1996 AMC8 #1 · Number Theory · ★
How many positive factors of 36 are also multiples of 4?
36 的正因数中有多少个也是 4 的倍数？

正确答案：B · 分值：1

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1996 AMC8 #2 · Algebra · ★
Jose, Thuy, and Kareem each start with the number 10 . Jose subtracts 1 from the number 10 , doubles his answer, and then adds 2 . Thuy doubles the number 10 , subtracts 1 from her answer, and then adds 2 . Kareem subtracts 1 from the number 10 , adds 2 to his number, and then doubles the result. Who gets the largest final answer?
Jose、Thuy 和 Kareem 各从数字 10 开始。Jose 从 10 中减去 1，将结果加倍，然后加上 2。Thuy 将 10 加倍，从中减去 1，然后加上 2。Kareem 从 10 中减去 1，加上 2，然后将结果加倍。谁得到最大的最终答案？

正确答案：C · 分值：1

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1996 AMC8 #3 · Algebra · ★
The 64 whole numbers from 1 through 64 are written, one per square, on a checkerboard (an 8 by 8 array of 64 squares). The first 8 numbers are written in order across the first row, the next 8 across the second row, and so on. After all 64 numbers are written, the sum of the numbers in the four corners will be
1 到 64 的 64 个正整数被写在一个棋盘（8行8列共 64 格）上，每格一个数。前 8 个数按顺序写在第一行，接下来 8 个写在第二行，以此类推。所有 64 个数写完后，四个角落方格中的数之和是

正确答案：A · 分值：1

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1996 AMC8 #5 · Algebra · ★★
The letters PP , QQ , RR , SS , and TT represent numbers located on the number line as shown.
Which of the following expressions represents a negative number?
字母 PP、QQ、RR、SS 和 TT 表示数轴上的数，如图所示。
以下哪个表达式表示一个负数？

正确答案：A · 分值：1

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1996 AMC8 #6 · Algebra · ★★
What is the smallest result that can be obtained from the following process? Choose three different numbers from the set {3,5,7,11,13,17}\{3,5,7,11,13,17\} . Add two of these numbers. Multiply their sum by the third number.
以下过程可以得到的最小结果是多少？
从集合 {3,5,7,11,13,17}\{3,5,7,11,13,17\} 中选择三个不同的数。 将其中两个数相加。 将它们的和乘以第三个数。

正确答案：C · 分值：1

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1996 AMC8 #7 · Algebra · ★★
Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish?
Brent 的金鱼数量每个月翻四倍，Gretel 的金鱼数量每个月翻一倍。如果在 Brent 有 4 条金鱼的同时 Gretel 有 128 条金鱼，那么从那时起多少个月后他们的金鱼数量将相等？

正确答案：B · 分值：1

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1996 AMC8 #8 · Geometry · ★★
Points AA and BB are 10 units apart. Points BB and CC are 4 units apart. Points CC and DD are 3 units apart. If AA and DD are as close as possible, then the number of units between them is
点 AA 和 BB 相距 10 个单位。点 BB 和 CC 相距 4 个单位。点 CC 和 DD 相距 3 个单位。如果 AA 和 DD 尽可能接近，则它们之间的距离是多少个单位？

正确答案：B · 分值：1

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1996 AMC8 #9 · Algebra · ★★
If 5 times a number is 2, then 100 times the reciprocal of the number is
如果 5 乘某个数等于 2，则 100 乘该数的倒数等于

正确答案：D · 分值：1

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1996 AMC8 #10 · Algebra · ★★
When Walter drove up to the gasoline pump, he noticed that his gasoline tank was 1/8 full. He purchased 7.5 gallons of gasoline for 10 dollars. With this additional gasoline, his gasoline tank was then 5/8 full. The number of gallons of gasoline his tank holds when it is full is
当 Walter 开车到加油站时，他注意到他的油箱只有 1/8 满。他以 10 美元的价格买了 7.5 加仑汽油。加了这些额外的汽油后，他的油箱变为 5/8 满。油箱装满时的容量是多少加仑？

正确答案：D · 分值：1

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1996 AMC8 #11 · Algebra · ★★★
Let xx be the number
0.0000...0000⏟1996 zeros1,0.\underbrace{0000...0000}_{1996\text{ zeros}}1,
where there are 1996 zeros after the decimal point. Which of the following expressions represents the largest number?
设 xx 为上面所示的数（小数点后有 1996 个零）。以下哪个表达式表示最大的数？

正确答案：D · 分值：1

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1996 AMC8 #12 · Counting, Probability & Statistics · ★★★
What number should be removed from the list
1,2,3,4,5,6,7,8,9,10,111,2,3,4,5,6,7,8,9,10,11
so that the average of the remaining numbers is 6.1 ?
应该从列表 1,2,3,4,5,6,7,8,9,10,11 中移除哪个数，使剩余数的平均数为 6.1？

正确答案：B · 分值：1

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1996 AMC8 #13 · Algebra · ★★★
In the fall of 1996, a total of 800 students participated in an annual school clean-up day. The organizers of the event expect that in each of the years 1997, 1998, and 1999, participation will increase by 50% over the previous year. The number of participants the organizers will expect in the fall of 1999 is
1996 年秋季，共有 800 名学生参加了一年一度的学校清洁日。活动组织者预计在 1997、1998 和 1999 年每年，参与人数将在前一年的基础上增加 50%。组织者预计 1999 年秋季的参与人数是

正确答案：E · 分值：1

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1996 AMC8 #14 · Number Theory · ★★★
Six different digits from the set
{1,2,3,4,5,6,7,8,9}\{ 1,2,3,4,5,6,7,8,9\}
are placed in the squares in the figure shown so that the sum of the entries in the vertical column is 23 and the sum of the entries in the horizontal row is 12. The sum of the six digits used is
从集合 {1,2,3,4,5,6,7,8,9}\{1,2,3,4,5,6,7,8,9\} 中选取六个不同的数字填入图中所示的方格，使得竖列各项之和为 23，横行各项之和为 12。所用六个数字之和为

正确答案：B · 分值：1

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1996 AMC8 #15 · Number Theory · ★★★
The remainder when the product 1492⋅1776⋅1812⋅19961492\cdot 1776\cdot 1812\cdot 1996 is divided by 5 is
乘积 1492⋅1776⋅1812⋅19961492\cdot 1776\cdot 1812\cdot 1996 除以 5 的余数是

正确答案：E · 分值：1

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1996 AMC8 #16 · Algebra · ★★★
1−2−3+4+5−6−7+8+9−10−11+⋯+1992+1993−1994−1995+1996=1-2-3+4+5-6-7+8+9-10-11+\cdots + 1992+1993-1994-1995+1996=

正确答案：C · 分值：1

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1996 AMC8 #17 · Geometry · ★★★
Figure OPQROPQR is a square. Point OO is the origin, and point QQ has coordinates (2,2). What are the coordinates for TT so that the area of triangle PQTPQT equals the area of square OPQROPQR ?
NOT TO SCALE
图形 OPQROPQR 是一个正方形。点 OO 是原点，点 QQ 的坐标为 (2,2)。点 TT 的坐标应为何值，才能使三角形 PQTPQT 的面积等于正方形 OPQROPQR 的面积？
（图形未按比例绘制）

正确答案：C · 分值：1

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1996 AMC8 #18 · Algebra · ★★★
Ana's monthly salary was $2000 in May. In June she received a 20% raise. In July she received a 20% pay cut. After the two changes in June and July, Ana's monthly salary was
Ana 五月份的月薪是 $2000。六月份她获得了 20% 的加薪。七月份她的薪水被削减了 20%。经过六月和七月的两次变动后，Ana 的月薪是

正确答案：A · 分值：1

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1996 AMC8 #19 · Counting, Probability & Statistics · ★★★
The pie charts below indicate the percent of students who prefer golf, bowling, or tennis at East Junior High School and West Middle School. The total number of students at East is 2000 and at West, 2500. In the two schools combined, the percent of students who prefer tennis is
以下饼图显示了 East 初中和 West 中学喜欢高尔夫、保龄球或网球的学生百分比。East 共有 2000 名学生，West 共有 2500 名。两所学校合计，喜欢网球的学生的百分比是

正确答案：C · 分值：1

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1996 AMC8 #20 · Algebra · ★★★
Suppose there is a special key on a calculator that replaces the number xx currently displayed with the number given by the formula 1/(1-x) . For example, if the calculator is displaying 2 and the special key is pressed, then the calculator will display -1 since 1/(1-2)=-1 . Now suppose that the calculator is displaying 5. After the special key is pressed 100 times in a row, the calculator will display
假设计算器上有一个特殊键，将当前显示的数 xx 替换为公式 1/(1-x) 给出的数。例如，如果计算器显示 2 并按下特殊键，计算器将显示 -1，因为 1/(1-2)=-1。现在假设计算器显示 5。连续按下特殊键 100 次后，计算器将显示

正确答案：A · 分值：1

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1996 AMC8 #21 · Counting, Probability & Statistics · ★★★★
How many subsets containing three different numbers can be selected from the set {89,95,99,132,166,173}\{ 89,95,99,132,166,173 \} so that the sum of the three numbers is even?
从集合 {89,95,99,132,166,173}\{ 89,95,99,132,166,173 \} 中选取包含三个不同数的子集，使得三数之和为偶数，共有多少种选法？

正确答案：D · 分值：1

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1996 AMC8 #22 · Geometry · ★★★
The horizontal and vertical distances between adjacent points equal 1 unit. What is the area of triangle ABCABC ?
相邻点之间的水平和垂直距离均为 1 个单位。三角形 ABCABC 的面积是多少？

正确答案：B · 分值：1

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1996 AMC8 #23 · Algebra · ★★★★
The manager of a company planned to distribute a $50 bonus to each employee from the company fund, but the fund contained $5 less than what was needed. Instead the manager gave each employee a $45 bonus and kept the remaining $95 in the company fund. The amount of money in the company fund before any bonuses were paid was
某公司经理计划从公司基金中给每位员工发放 $50 的奖金，但基金比所需金额少 $5。于是经理改为给每位员工发放 $45 的奖金，并将剩余的 $95 保留在公司基金中。在发放任何奖金之前，公司基金中的金额是

正确答案：E · 分值：1

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1996 AMC8 #24 · Geometry · ★★★★
The measure of angle ABCABC is 50∘50^\circ , AD‾\overline{AD} bisects angle BACBAC , and DC‾\overline{DC} bisects angle BCABCA . The measure of angle ADCADC is
∠ABC\angle ABC 的度数为 50∘50^\circ，AD‾\overline{AD} 平分 ∠BAC\angle BAC，DC‾\overline{DC} 平分 ∠BCA\angle BCA。∠ADC\angle ADC 的度数是

正确答案：C · 分值：1

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1996 AMC8 #25 · Counting, Probability & Statistics · ★★★★
A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region?
在一个圆形区域内随机选取一个点。该点离圆心比离边界更近的概率是多少？

正确答案：A · 分值：1

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