2017 AMC amc8 真题 答案 详解

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中英双语真题

2017 AMC8
Problem 1
Which of the following values is the largest?
下面哪个值是最大的？
(A) $2+0+1+7$ (B) $2\times0+1+7$ (C) $2+0\times1+7$ (D) $2+0+1\times7$ (E) $2\times0\times1\times7$

Problem 2
Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?
Alicia, Brenda 和 Colby 是最近的一次竞选学生主席的3个候选人。下面的饼图显示了这3人候选人的投票分布。若 Brenda 得到了36票，那么总共投了多少票？
(A) 70 (B) 84 (C) 100 (D) 106 (E) 120

Problem 3
What is the value of the expression $\sqrt{16\sqrt{8\sqrt{4}}}$?
表达式$\sqrt{16\sqrt{8\sqrt{4}}}$ 的值是多少？
(A) 4 (B) $4\sqrt{2}$ (C) 8 (D) $8\sqrt{2}$ (E) 16

英文真题

Compiled on: January 1, 2021 AMC8 2017 Problems Page 19 of 109 Q1. Which of the following values is largest? A) $2+0+1+7$ B) $2\times0+1+7$ C) $2+0\times1+7$ D) $2+0+1\times7$ E) $2\times0\times1\times7$ Q2. Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together? A) 70 B) 84 C) 100 D) 106 E) 120 Q3. What is the value of the expression $\sqrt{16\sqrt{8\sqrt{4}}}$? A) 4 B) $4\sqrt{2}$ C) 8 D) $8\sqrt{2}$ E) 16 Q4. When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following? A) 210 B) 240 C) 2100 D) 2400 E) 24000 Q5. What is the value of the expression $\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8}{1+2+3+4+5+6+7+8}$? A) 1020 B) 1120 C) 1220 D) 2240 E) 3360 Q6. If the degree measures of the angles of a triangle are in the ratio 3:3:4, what is the degree measure of the largest angle of the triangle? A) 18 B) 36 C) 60 D) 72 E) 90 Q7. Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of Z? A) 11 B) 19 C) 101 D) 111 E) 1111 Q8. Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn’t know her house number. She tells him, “My house number has two digits, and exactly three of the following four statements about it are true.” (1) It is prime. (2) It is even. (3) It is divisible by 7. (4) One of its digits is 9. This information allows Malcolm to determine Isabella’s house number. What is its units digit?

真题文字详解(英文)

Problem 1 Which of the following values is largest?
(A) $2 + 0 + 1 + 7$ (B) $2 \times 0 + 1 + 7$ (C) $2 + 0 \times 1 + 7$ (D) $2 + 0 + 1 \times 7$ (E) $2 \times 0 \times 1 \times 7$

Solution 1 We will compute each expression. a) $2 + 0 + 1 + 7 = 10$ b) $2 \times 0 + 1 + 7 = 8$ c) $2 + 0 \times 1 + 7 = 9$ d) $2 + 0 + 1 \times 7 = 9$ e) $2 \times 0 \times 1 \times 7 = 0$

Ordering these, we get $10, 8, 9, 9, 0$. Out of these, $10$ is the largest number and option (A) adds up to $10$. Therefore, the answer is
(A) $2 + 0 + 1 + 7$.

• SBose

Solution 2 We immediately see that every one of the choices, except for A and D, has a number multiplied by $0$. This will only make the expression's value smaller. We are left with A and D, but in D, $1$ is multiplied by $7$ to get $7$, whereas in answer choice A, we get $8$ out of $7$ and $1$, instead of $7$. Therefore, (A) $2 + 0 + 1 + 7$ is your answer.

https://youtu.be/S1gAyjQWYo

Problem 2 Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received $36$ votes, then how many votes were cast all together?

(A) $70$ (B) $84$ (C) $100$ (D) $106$ (E) $120$

Solution 1 Let $x$ be the total amount of votes cast. From the chart, Brenda received $30\%$ of the votes and had $36$ votes. We can express this relationship as $\frac{30}{100} x = 36$. Solving for $x$, we get $x = (E) 120.

真题文字详解(中英双语)

Problem 1 Which of the following values is largest? 以下哪个值最大?
(A) $2+0+1+7$ (B) $2\times0+1+7$ (C) $2+0\times1+7$ (D) $2+0+1\times7$ (E) $2\times0\times1\times7$

Solution 1 We will compute each expression. 我们将计算每个表达式。
A)$2+0+1+7=10$ B)$2\times0+1+7=8$ C)$2+0\times1+7=9$ D)$2+0+1\times7=9$ E)$2\times0\times1\times7=0$ Ordering these, we get $10, 8, 9, 9, 0$. Out of these, $10$ is the largest number and option $(A)$ adds up to $10$. Therefore, the answer is $\boxed{(A)\ 2+0+1+7}.$

Solution 2 We immediately see that every one of the choices, except for A and D, has a number multiplied by $0$. This will only make the expression's value smaller. We are left with A and D, but in D, $1$ is multiplied by $7$ to get $7$, whereas in answer choice A, we get $8$ out of $7$ and $1$, instead of $7$. Therefore, $\boxed{(A)\ 2+0+1+7}$ is your answer.

Problem 2 Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received $36$ votes, then how many votes were cast all together? Alicia、Brenda 和 Colby 是最近一次学生总统选举的候选人。下面的饼图显示了三位候选人的选票分布情况。如果 Brenda 收到了 36 票，那么一共投出了多少票？