2014 AMC amc8 真题 答案 详解

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中英双语真题

2014 AMC8
Problem 1
Harry and Terry are each told to calculate (8 - (2 + 5)). Harry gets the correct answer. Terry ignores the parentheses and calculates (8 - 2 + 5). If Harry's answer is (H) and Terry's answer is (T), what is (H - T)?

Harry 和 Terry 都要求去计算 (8 - (2 + 5))，Harry 得到了正确答案，Terry 忽略了括号，计算成了 (8 - 2 + 5)，假设 Harry 的答案是 (H)，Terry 的答案是 (T)，则 (H - T) 是多少？

(A) (-10) (B) (-6) (C) (0) (D) (6) (E) (10)

Problem 2
Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?

Paul 欠 Paula 35 美分。Paula 目前口袋里有一堆 5 美分、10 美分和 25 美分的硬币可以用来还钱，他可用于还钱的最多硬币数目和最少硬币数目的差是多少？

(A) (1) (B) (2) (C) (3) (D) (4) (E) (5)

Problem 3
Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three days and an average of 44 pages per day for the next three days. She then finished the book by reading 10 pages on the last day. How many pages were in the book?

Isabella 的学校作业是花一周的时间读一本书。她前三天每天平均读 36 页，后三天平均每天读 44 页，之后在最后一天读了 10 页把整本书读完了。问这本书总共有多少页？

(A) (240) (B) (250) (C) (260) (D) (270) (E) (280)

Problem 4
The sum of two prime numbers is 85. What is the product of these two prime numbers?

两个质数之和为 85，问这两个质数的乘积是多少？

(A) (85) (B) (91) (C) (115) (D) (133) (E) (166)

英文真题

Compiled on: January 1, 2021 AMC8 2014 Problems Page 31 of 109 Q1. Harry and Terry are each told to calculate (8 - (2 + 5)). Harry gets the correct answer. Terry ignores the parentheses and calculates (8 - 2 + 5). If Harry's answer is (H) and Terry's answer is (T), what is (H - T)? A) (-10) B) (-6) C) (0) D) (6) E) (10) Q2. Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her? A) (1) B) (2) C) (3) D) (4) E) (5) Q3. Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three days and an average of 44 pages per day for the next three days. She then finished the book by reading 10 pages on the last day. How many pages were in the book? A) (240) B) (250) C) (260) D) (270) E) (280) Q4. The sum of two prime numbers is 85. What is the product of these two prime numbers? A) (85) B) (91) C) (115) D) (133) E) (166) Q5. Margie's car can go 32 miles on a gallon of gas, and gas currently costs $4 per gallon. How many miles can Margie drive on $20 worth of gas? A) (64) B) (128) C) (160) D) (320) E) (640) Q6. Six rectangles each with a common base width of 2 have lengths of 1, 4, 9, 16, 25, and 36. What is the sum of the areas of the six rectangles? A) (91) B) (93) C) (162) D) (182) E) (202) Q7. There are four more girls than boys in Ms. Raub’s class of 28 students. What is the ratio of number of girls to the number of boys in her class? A) (3:4) B) (4:3) C) (3:2) D) (7:4) E) (2:1) Q8. Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $1A2. What is the missing digit (A) of this 3-digit number? A) (0) B) (1) C) (2) D) (3) E) (4) Q9. In (\triangle ABC), (D) is a point on side (\overline{AC}) such that (BD = DC) and (\angle BCD) measures (70^\circ). What is the degree measure of (\angle ADB)? A) (100) B) (120) C) (135) D) (140) E) (150) Q10. The first AMC 8 was given in 1985 and it has been given annually since that time. Samantha turned 12 years old the year that she took the seventh AMC 8. In what year was Samantha born?

真题文字详解(英文)

Problem 1 Harry and Terry are each told to calculate $8 - (2 + 5)$. Harry gets the correct answer. Terry ignores the parentheses and calculates $8 - 2 + 5$. If Harry's answer is $H$ and Terry's answer is $T$, what is $H - T$?
$\textbf{(A)}\ -10 \qquad \textbf{(B)}\ -6 \qquad \textbf{(C)}\ 0 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 10$

Solution We have $H = 8 - 7 = 1$ and $T = 8 - 2 + 5 = 11$. Clearly $1 - 11 = -10$, so our answer is $\textbf{(A)\ -10}$.

Solution 2 We use PEMDAS, $8-(2+5)$ is the same as $8-7$ which is $1$, $8-2+5$ is the same as $6+5$ because $8-2$ comes first, and the sum is $11$. H-T is $1-11$ which is $\textbf{(A)\ -10}$.

Problem 2 Paul owes Paula $35$ cents and has a pocket full of $5$-cent coins, $10$-cent coins, and $25$-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?
$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Solution The fewest amount of coins that can be used is $2$ (a quarter and a dime). The greatest amount is $7$, if he only uses nickels. Therefore we have $7 - 2 = \textbf{(E)}\ 5$.

Problem 3 Isabella had a week to read a book for a school assignment. She read an average of $36$ pages per day for the first three days and an average of $44$ pages per day for the next three days. She then finished the book by reading $10$ pages on the last day. How many pages were in the book?
$\textbf{(A)}\ 240 \qquad \textbf{(B)}\ 250 \qquad \textbf{(C)}\ 260 \qquad \textbf{(D)}\ 270 \qquad \textbf{(E)}\ 280$

Solution Isabella read $3 \cdot 36 + 3 \cdot 44$ pages in the first $6$ days. Although this can be calculated directly, it is simpler to calculate it as $3 \cdot (36 + 44) = 3 \cdot 80$, which gives that she read $240$ pages. On her last day, she read $10$ more pages for a total of $240 + 10 = \textbf{(B)}\ 250$.

Problem 4 The sum of two prime numbers is $85$. What is the product of these two prime numbers?
$\textbf{(A)}\ 85 \qquad \textbf{(B)}\ 91 \qquad \textbf{(C)}\ 115 \qquad \textbf{(D)}\ 133 \qquad \textbf{(E)}\ 166$

真题文字详解(中英双语)

Problem 1 Harry and Terry are each told to calculate $8 - (2 + 5)$. Harry gets the correct answer. Terry ignores the parentheses and calculates $8 - 2 + 5$. If Harry's answer is $H$ and Terry's answer is $T$, what is $H - T$? 哈利和特里各自被告知要计算 $8 - (2 + 5)$。哈利得到了正确答案。特里忽略了括号，计算了 $8 - 2 + 5$。如果哈利的答案是 $H$ ，特里的答案是 $T$ ，那么 $H - T$ 是多少？
(A) −10 (B) −6 (C) 0 (D) 6 (E) 10 Solution We have $H = 8 - 7 = 1$ and $T = 8 - 2 + 5 = 11$. Clearly $1 - 11 = -10$, so our answer is (A) −10 我们有 $H = 8 - 7 = 1$ 和 $T = 8 - 2 + 5 = 11$。显然 $1 - 11 = -10$，所以我们的答案是 (A) −10 Solution 2 We use PEMDAS, $8-(2+5)$ is the same as $8-7$ which is $1$, $8-2+5$ is the same as $6+5$ because $8-2$ comes first, and the sum is $11$. H-T is $1-11$ which is (A) −10 我们使用运算优先级规则，$8-(2+5)$ 等同于 $8-7$，结果是 $1$；$8-2+5$ 等同于 $6+5$，因为 $8-2$ 先计算，总和是 $11$。H-T 是 $1-11$，结果是 (A) −10 Problem 2 Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her? 保罗欠保拉35美分，他口袋里装满了5分的硬币、10分的硬币和25分的硬币，可以用这些硬币来还她。他用这些硬币来还钱时最多和最少硬币数量的差值是多少？ (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Solution The fewest amount of coins that can be used is 2 (a quarter and a dime). The greatest amount is 7, if he only uses nickels. Therefore we have $7 - 2 = \textbf{(E)}\ 5$ 可以使用的最少硬币数量是 2（一个二十五分硬币和一个十分分硬币）。最大数量是 7，如果他只使用五分硬币的话。因此我们有 $7 - 2 = \textbf{(E)}\ 5$ Problem 3