2001 AMC amc8 真题 答案 详解

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中英双语真题

2001 AMC8
Problem 1
Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?
Casey 的职业技能实践课是制作一个高尔夫奖杯。他必须在一个人造高尔夫球上画 300 个凹坑。如果他需要 2 秒钟才能画出一个凹坑，他需要多少分钟才能完成他的工作？
(A) 4 (B) 6 (C) 8 (D) 10 (E) 12

Problem 2
I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
我在想两个整数。他们的积是 24，和是 11。较大的那个数是多少？
(A) 3 (B) 4 (C) 6 (D) 8 (E) 12

Problem 3
Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?
Smith 奶奶有 63 美元。Elberta 比 Anjou 多 2 美元，Anjou 的钱是 Smith 奶奶的三分之一。那么 Elberta 有多少美元？
(A) 17 (B) 18 (C) 19 (D) 21 (E) 23

Problem 4
The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is
数字 1, 2, 3, 4 和 9 每个使用一次，形成最小的五位偶数。则这个数的十位数字是？
(A) 1 (B) 2 (C) 3 (D) 4 (E) 9

英文真题

Compiled on: January 1, 2021 AMC8 2001 Problems Page 91 of 109 Q1. Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job? A) 4 B) 6 C) 8 D) 10 E) 12 Q2. I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number? A) 3 B) 4 C) 6 D) 8 E) 12 Q3. Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have? A) 17 B) 18 C) 19 D) 21 E) 23 Q4. The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is A) 1 B) 2 C) 3 D) 4 E) 9 Q5. On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning. A) 1 B) ( \frac{1}{2} ) C) 2 D) ( 2\frac{1}{2} ) E) 3 Q6. Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees? A) 90 B) 100 C) 105 D) 120 E) 140 Q7. To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid. What is the number of square inches in the area of the small kite? A) 21 B) 22 C) 23 D) 24 E) 25

真题文字详解(英文)

Problem 1 Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will it take for him to finish?
(A) 4 (B) 6 (C) 8 (D) 10 (E) 12

Solution It will take him $300 \cdot 2 = 600$ seconds to paint all the dimples. This is equivalent to $\frac{600}{60} = 10$ minutes $\Rightarrow \boxed{D}$.

Problem 2 I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
(A) 3 (B) 4 (C) 6 (D) 8 (E) 12

Solution 1 Let the numbers be $x$ and $y$. Then we have $x + y = 11$ and $xy = 24$. Solving for $x$ in the first equation yields $x = 11 - y$, and substituting this into the second equation gives $(11-y)(y)=24$. Simplifying this gives $-y^2+11y=24$, or $y^2-11y+24=0$. This factors as $(y-3)(y-8)=0$, so $y=3$ or $y=8$, and the corresponding $x$ values are $x=8$ and $x=3$. These are essentially the same answer: one number is 3 and one number is 8, so the largest number is $\boxed{D}$.

Solution 2 Use the answers to attempt to "reverse engineer" an appropriate pair of numbers. Looking at option A, guess that one of the numbers is 3. If the sum of two numbers is 11 and one is 3, then other must be $11-3=8$. The product of those numbers is $3\cdot8=24$, which is the second condition of the problem, so our numbers are 3 and 8. However, 3 is the smaller of the two numbers, so the answer is 8 or $\boxed{D}$.

Solution 3 We go through the divisor pairs of 24 to see which two numbers sum to 11. The numbers clearly cannot be negative. If one was negative, then the other must also be negative in order to multiply to a positive product, but it would be impossible for the numbers to add up to a positive sum. So we look at the positive divisor pairs of 24, namely 1 and 24, 2 and 12, 3 and 8, and 4 and 6. The only pair of numbers that sums to 11 is 3 and 8. The larger number is 8, so the answer is $\boxed{D}$.

Problem 3 Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?
(A) 17 (B) 18 (C) 19 (D) 21 (E) 23

Solution Since Anjou has $\frac13$ the amount of money as Granny Smith and Granny Smith has $63, Anjou has $\frac13\times63=21$ dollars. Elberta has $2 more than this, so she has $23, or $\boxed{E}$.

Problem 4 The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is

真题文字详解(中英双语)

Problem 1 Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will it take for him to finish? 凯西的商业课程正在制作一个高尔夫奖杯。他必须在高尔夫球上画300个凹痕。如果他每画一个凹痕需要2秒钟，那么他需要多少分钟才能完成？ (A) 4 (B) 6 (C) 8 (D) 10 (E) 12 Solution It will take him $300 \cdot 2 = 600$ seconds to paint all the dimples. 他将需要 $300 \cdot 2 = 600$ 秒钟来画所有的凹痕。 This is equivalent to $\frac{600}{60} = 10$ minutes $\Rightarrow \boxed{D}$ 这相当于 $\frac{600}{60} = 10$ 分钟 $\Rightarrow \boxed{D}$ Problem 2 I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number? 我在考虑两个整数。它们的积是24，和是11。较大的数是多少？ (A) 3 (B) 4 (C) 6 (D) 8 (E) 12 Solution 1 Let the numbers be $x$ and $y$. Then we have $x + y = 11$ and $xy = 24$. Solving for $x$ in the first equation yields $x = 11 - y$, and substituting this into the second equation gives $(11-y)(y)=24$. Simplifying this gives $-y^2+11y=24$, or $y^2-11y+24=0$. This factors as $(y-3)(y-8)=0$, so $y=3$ or $y=8$, and the corresponding $x$ values are $x=8$ and $x=3$. These are essentially the same answer: one number is 3 and one number is 8, so the largest number is $\boxed{D}$. 设这两个数分别为$x$和$y$。那么我们有$x+y=11$和$xy=24$。在第一个方程中求解$x$得到$x=11-y$，将其代入第二个方程中得到$(11-y)(y)=24$。简化后得到$-y^2+11y=24$，即$y^2-11y+24=0$。它可以分解为$(y-3)(y-8)=0$，所以$y=3$或$y=8$，相应的$x$值为$x=8$和$x=3$。这两个答案基本上是一样的：一个数是3，另一个数是8，所以最大的数是$\boxed{D}$。 Solution 2 Use the answers to attempt to "reverse engineer" an appropriate pair of numbers. Looking at option A, guess that one of the numbers is 3. If the sum of two numbers is 11 and one is 3, then other must be $11-3=8$. The product of those numbers is $3\cdot8=24$, which is the second condition of the problem, so our numbers are 3 and 8. 使用答案尝试“逆向工程”一个合适的数字对。看看选项A，猜测其中一个数是3。如果两个数的和是11，一个是3，那么另一个必须是$11-3=8$。这些数的乘积是$3\cdot8=24$，这是问题的第二个条件，所以我们有3和8。 However, 3 is the smaller of the two numbers, so the answer is 8 or $\boxed{D}$. 然而，3是这两个数中较小的一个，所以答案是8或$\boxed{D}$。 Solution 3