2020 AMC amc8 真题 答案 详解

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中英双语真题

2020 AMC8
Problem 1
Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need?
Luka 正在做柠檬水，准备在学校的募捐会上出售。他的配料表需要的水是糖的四倍，糖是柠檬汁的两倍。他用了 3 杯柠檬汁。他需要多少杯水？
(A) 6 (B) 8 (C) 12 (D) 18 (E) 24

Problem 2
Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $40 give to the others?
四个朋友在周末为他们的邻居打扫院子，收入分别为 $15，$20，$25 和 $40。他们决定平分收入。那么赚了 40 美元的那个朋友总共会给其他人多少钱？
(A) $5 (B) $10 (C) $15 (D) $20 (E) $25

Problem 3
Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest?
Carrie 有一个矩形的花园，尺寸是 6 英尺 x 8 英尺。她在整个花园里都种上了草莓。Carrie 每平方英尺可以种植 4 棵草莓苗，并且每棵草莓苗上她可以收获 10 颗草莓。那么她可以期望总共收获多少颗草莓？
(A) 560 (B) 960 (C) 1120 (D) 1920 (E) 3840

英文真题

Compiled on: January 1, 2021 AMC8 2020 Problems Page 4 of 109 Q1. Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need? A) 6 B) 8 C) 12 D) 18 E) 24 Q2. Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $40 give to the others? A) 5 B) 10 C) 15 D) 20 E) 25 Q3. Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest? A) 560 B) 960 C) 1120 D) 1920 E) 3840 Q4. Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon? A) 35 B) 37 C) 39 D) 43 E) 49 Q5. Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive? A) 5 B) 10 C) 15 D) 20 E) 25 Q6. Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car? A) Aaron B) Darren C) Karen D) Maren E) Sharon Q7. How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.) A) 9 B) 10 C) 15 D) 21 E) 28 Q8. Ricardo has 2020 coins, some of which are pennies (1-cent coins) and the rest of which are nickels (5-cent coins). He has at least one penny and at least one nickel. What is the difference in cents between the greatest possible and least possible amounts of money that Ricardo can have? A) 8062 B) 8068 C) 8072 D) 8076 E) 8082

真题文字详解(英文)

Problem 1 Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need?
(A) 6 (B) 8 (C) 12 (D) 18 (E) 24

Solution 1 (Direct) We have water : sugar : lemon juice = 4 · 2 : 2 : 1 = 8 : 2 : 1, so Luka needs 3 · 8 = (E) 24 cups.

Solution 2 (Stepwise) Since the amount of sugar is twice the amount of lemon juice, Luka uses 3 · 2 = 6 cups of sugar. Since the amount of water is 4 times the amount of sugar, he uses 6 · 4 = (E) 24 cups of water.

Solution 3 (Combination of Solutions 1 and 2) The ratio is Water : Sugar : Lemon Juice, or 8 : 2 : 1. Since we know that Luka used 3 cups of lemon juice, he needs 3 · 2 = 6 cups of sugar. Because the amount of water is 4 times the amount of sugar Luka needs, he will need 6 · 4 = (E) 24 cups of water. Thanks to MRENTHUSIASM for the inspiration! EarthSaver 15:12, 11 June 2021 (EDT)

Problem 2 Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned $40 give to the others?
(A) $5 (B) $10 (C) $15 (D) $20 (E) $25

Solution The friends earn $(15 + 20 + 25 + 40) = $100 in total. Since they decided to split their earnings equally, it follows that each person will get $\left(\frac{100}{4}\right) = $25. Since the friend who earned $40 will need to leave with $25, he will have to give $(40 - 25) = (C) $15 to the others.

Problem 3 Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest?
(A) 560 (B) 960 (C) 1120 (D) 1920 (E) 3840

Solution 1 Note that the unit of the answer is strawberries, which is the product of square feet · plants per square foot · strawberries per plant By conversion factors, we have $(6 ft · 8 ft) · \left(\frac{4 \text{ plants}}{ft^2}\right) · \left(\frac{10 \text{ strawberries}}{\text{plant}}\right) = 6 · 8 · 4 · 10$ strawberries = (D) 1920 strawberries.

Solution 2 The area of the garden is $6 · 8 = 48$ square feet. Since Carrie plants 4 strawberry plants per square foot, there are a total of $48 · 4 = 192$ strawberry plants, each of which produces 10 strawberries on average. Accordingly, she can expect to harvest $192 · 10 = (D) 1920 strawberries.

Problem 4 Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?

真题文字详解(中英双语)

Problem 1 Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need? 卢卡正在制作柠檬水，打算在学校义卖会上出售。他的食谱要求水的用量是糖的4倍，糖的用量是柠檬汁的两倍。他用了3杯柠檬汁。他需要多少杯水？
(A) 6 (B) 8 (C) 12 (D) 18 (E) 24 Solution 1 (Direct) We have water : sugar : lemon juice = 4 · 2 : 2 : 1 = 8 : 2 : 1, so Luka needs 3 · 8 = (E) 24 cups. 我们有水：糖：柠檬汁=4·2:2:1=8:2:1，所以卢卡需要3·8=(E) 24 杯。 Solution 2 (Stepwise) Since the amount of sugar is twice the amount of lemon juice, Luka uses 3 · 2 = 6 cups of sugar. 由于糖的用量是柠檬汁的两倍，卢卡用了3·2=6杯糖。 Since the amount of water is 4 times the amount of sugar, he uses 6 · 4 = (E) 24 cups of water. 由于水的量是糖的4倍，他使用了6·4=(E) 24 杯水。 Solution 3 (Combination of Solutions 1 and 2) 解决方案3（结合解决方案1和2） The ratio is Water : Sugar : Lemon Juice, or 8 : 2 : 1. Since we know that Luka used 3 cups of lemon juice, he needs 3 · 2 = 6 cups of sugar. Because the amount of water is 4 times the amount of sugar Luka needs, he will need 6 · 4 = (E) 24 cups of water. 比率是Water: Sugar: Lemon Juice，或8:2:1。由于我们知道卢卡使用了3杯柠檬汁，他需要3·2=6杯糖。因为水的量是糖的4倍，卢卡将需要6·4=(E) 24 杯水。 Thanks to MRENTHUSIASM for the inspiration! 感谢 MRENTHUSIASM 的灵感！ EarthSaver 15:12, 11 June 2021 (EDT) 地球守护者 15:12, 2021年6月11日 (东部时间) Problem 2 Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned $40 give to the others? 四个朋友周末为邻居做园艺工作，分别赚取了$15、$20、$25和$40。他们决定平均分配他们的收入。总共，赚取$40的朋友会给其他人多少钱？ (A) $5 (B) $10 (C) $15 (D) $20 (E) $25 Solution The friends earn $(15 + 20 + 25 + 40) = $100 in total. Since they decided to split their earnings equally, it follows that each person will get $\left(\frac{100}{4}\right) = $25. Since the friend who earned $40 will need to leave with $25, he will have to give $(40 - 25) = (C) $15 to the others. 朋友们总共赚取了$(15+20+25+40)=$100。由于他们决定平均分配收入，这意味着每个人将得到$\left(\frac{100}{4}\right)=$25。由于赚取$40的朋友需要留下$25，他必须给其他人$(40-25)=(C) $15。 Problem 3 Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest? 卡莉有一个长6英尺、宽8英尺的长方形花园。她用草莓植物种满了整个花园。卡莉每平方英尺能种植4株草莓，每株植物平均收获10颗草莓。她预计可以收获多少草莓？ (A) 560 (B) 960 (C) 1120 (D) 1920 (E) 3840 Solution 1 Note that the unit of