2013 AMC amc8 真题 答案 详解

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中英双语真题

2013 AMC8
Problem 1
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
Danica 想把她的模型汽车排成每行 6 辆的若干行，她现在有 23 辆模型汽车，那么她还至少需要买多少辆模型汽车才能完成上述安排？
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Problem 2
A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars? (Assume that there are no deals for bulk)
鱼市上的一则标语写着：“降价 50%，仅限今天：半磅重的一包鱼仅需 3 美元。”那么一磅重的鱼原价是多少美元？
(A) 6 (B) 9 (C) 10 (D) 12 (E) 15

Problem 3
What is the value of (4 \cdot (-1 + 2 - 3 + 4 - 5 + 6 - 7 + \cdots + 1000))?
表达式 (4 \cdot (-1 + 2 - 3 + 4 - 5 + 6 - 7 + \cdots + 1000)) 的值是多少？
(A) -10 (B) 0 (C) 1 (D) 500 (E) 2000

Problem 4
Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
8 个朋友在餐馆吃饭，并且商定均摊费用。因为 Judi 忘记带钱了，她的其他 7 个朋友帮她垫付了费用，因此 7 个人每人额外多付了 2.5 美元。那么餐费总共是多少美元？
(A) $120 (B) $128 (C) $140 (D) $144 (E) $160

英文真题

Compiled on: January 1, 2021 AMC8 2013 Problems Page 35 of 109 Q1. Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way? A) 1 B) 2 C) 3 D) 4 E) 5 Q2. A sign at the fish market says, “50% off, today only: half-pound packages for just $3 per package.” What is the regular price for a full pound of fish, in dollars? A) 6 B) 9 C) 10 D) 12 E) 15 Q3. What is the value of 4 · (-1 + 2 - 3 + 4 - 5 + 6 - 7 + ... + 1000)? A) -10 B) 0 C) 1 D) 500 E) 2000 Q4. Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill? A) $120 B) $128 C) $140 D) $144 E) $160 Q5. Hammie is in the 6th grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds? A) median, by 60 B) median, by 20 C) average, by 5 D) average, by 15 E) average, by 20 Q6. The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, 30 = 6 × 5. What is the missing number in the top row? A) 2 B) 3 C) 4 D) 5 E) 6 Q7. Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train? A) 60 B) 80 C) 100 D) 120 E) 140

真题文字详解(英文)

Problem 1 Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Solution 1 The least multiple of 6 greater than 23 is 24. So she will need to add (24 - 23 = \boxed{\textbf{(A)}\ 1}) more model car.
~avamarora
Solution 2 (6 \times 4 = 24), which is 1 more than 23. So, the answer is (\boxed{\textbf{(A)}\ 1}).

Problem 2 A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars?
(A) 6 (B) 9 (C) 10 (D) 12 (E) 15

Solution 50% off the price of half a pound of fish is $3, so 100%, the regular price, of a half pound of fish is $6. If half a pound of fish costs $6, then a whole pound of fish is (\boxed{\textbf{(D)}\ 12}) dollars.
Solution 2 Suppose a full pound at normal price costs (x) dollars. Then, with the 50% off deal, the full pound would cost (x/2) dollars. A half pound of this would cost (x/4) dollars (including the 50% off). 50% off half a pound is $3, so we form the equation (x/4 = 3 \Rightarrow x = \boxed{\textbf{(D)}\ 12}).

Problem 3 What is the value of (4 \cdot (-1 + 2 - 3 + 4 - 5 + 6 - 7 + \cdots + 1000))?
(A) -10 (B) 0 (C) 1 (D) 500 (E) 2000

Solution We group the addends inside the parentheses two at a time:
[ -1 + 2 - 3 + 4 - 5 + 6 - 7 + \ldots + 1000 = (-1 + 2) + (-3 + 4) + (-5 + 6) + \ldots + (-999 + 1000) ]
[ = 1 + 1 + 1 + \ldots + 1 \quad \text{(500 1's)} ]
[ = 500. ]
Then the desired answer is (4 \times 500 = \boxed{\textbf{(E)}\ 2000}).

Problem 4 Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
(A) $120 (B) $128 (C) $140 (D) $144 (E) $160

Solution 1 Since Judi's 7 friends had to pay $2.50 extra each to cover the total amount that Judi should have paid, we multiply (2.50 \cdot 7 = 17.50) is the bill Judi would have paid if she had money. Hence, to calculate the total amount, we multiply (17.50 \cdot 8 = \boxed{\textbf{(C)}\ 140}) to find the total the 8 friends paid.

真题文字详解(中英双语)

Problem 1 Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Solution 1 The least multiple of 6 greater than 23 is 24. So she will need to add 24 - 23 = (A) 1 more model car.
6 的倍数中大于 23 的最小值是 24。所以她不需要再买任何汽车。(A) 1

Solution 2 6 x 4 = 24, which is 1 more than 23. So the answer is (A) 1.
6 乘以 4 等于 24，比 23 多 1。所以答案是 (A) 1。

Problem 2 A sign at the fish market says, "50% off today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars?
(A) 6 (B) 9 (C) 10 (D) 12 (E) 15

Solution 50% off the price of half a pound of fish is $3, so 100%, the regular price, of a half pound of fish is $6. If half a pound of fish costs $6, then a whole pound of fish is (D) 12 dollars.
打八折的半磅鱼的价格是 3 美元，所以 100%，即原价，半磅鱼的价格是 6 美元。如果半磅鱼的价格是 6 美元，那么一磅鱼的价格是 (D) 12 美元。

Solution 2 Suppose a full pound at normal price costs x dollars. Then, with the 50% off deal, the full pound would cost x/2 dollars. A half pound of this would cost x/4 dollars (including the 50% off). 50% off half a pound is 3, so we form the equation x/4 = 3 => x = (D) 12.
假设一磅鱼的正常价格是 x 美元。那么，在打八折的促销下，一磅鱼的价格将是 x/2 美元。半磅鱼的价格将是 x/4 美元（包括八折优惠）。半磅鱼的八折优惠是 3 美元，所以我们列出方程 x/4 = 3 => x = (D) 12.

Problem 3 What is the value of 4 · (-1 + 2 - 3 + 4 - 5 + 6 - 7 + ... + 1000)?
4 · (-1 + 2 - 3 + 4 - 5 + 6 - 7 + ... + 1000) 的值是多少？
(A) -10 (B) 0 (C) 1 (D) 500 (E) 2000