2011 AMC amc12a 真题 答案 详解

---

中英双语真题

2011 AMC12A

Problem 1
A cell phone plan costs $20 dollars each month, plus 5 cents per text message sent, plus 10 cents for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
一种手机套餐每个月有 20 美元的固定费用。此外，每条短信收取 5 美分，语音通话超过 30 小时的部分，每分钟收取 10 美分。Michelle 在 1 月份共发送了 100 条短信，拨打了 30.5 小时语音通话，问她需要支付多少美元？
(A) 24.00 (B) 24.50 (C) 25.50 (D) 28.00 (E) 30.00

Problem 2
There are 5 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
下图显示了平放在桌子上的 5 枚硬币。那么硬币从上到下的顺序分别为什么？
(A) (C, A, E, D, B) (B) (C, A, D, E, B) (C) (C, D, E, A, B) (D) (C, E, A, D, B) (E) (C, E, D, A, B)

Problem 3
A small bottle of shampoo can hold 35 milliliters of shampoo, whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
一个小瓶洗发水可以装 35 毫升洗发水，而一个大瓶洗发水可以装 500 毫升洗发水。Jasmine 想买最少数量的小瓶洗发水来装满一大瓶，她必须买多少小瓶？
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15

英文真题

2011 AMC 12A Problems

Problem 1

A cell phone plan costs $20 dollars each month, plus 5 cents per text message sent, plus 10 cents for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?

(A) 24.00 (B) 24.50 (C) 25.50 (D) 28.00 (E) 30.00

Problem 2

There are 5 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

(A) (C, A, E, D, B)

(B) (C, A, D, E, B)

(C) (C, D, E, A, B)

(D) (C, E, A, D, B)

(E) (C, E, D, A, B)

Problem 3

A small bottle of shampoo can hold 35 milliliters of shampoo, whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?

(A) 11 (B) 12 (C) 13 (D) 14 (E) 15

Problem 4

At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

(A) 12 (B) ( \frac{37}{3} ) (C) ( \frac{88}{7} ) (D) 13 (E) 14

Problem 5

Last summer 30% of the birds living on Town Lake were geese, 25% were swans, 10% were herons, and 35% were ducks. What percent of the birds that were not swans were geese?

(A) 20 (B) 30 (C) 40 (D) 50 (E) 60

Problem 6

The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?

(A) 13 (B) 14 (C) 15 (D) 16 (E) 17

Problem 7

A majority of the 30 students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than 1. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was 17.71. What was the cost of a pencil in cents?

(A) 7 (B) 11 (C) 17 (D) 23 (E) 77

真题文字详解(英文)

Problem 1
A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay?
(A) $24.00$ (B) $24.50$ (C) $25.50$ (D) $28.00$ (E) $30.00$

Solution
The base price of Michelle's cell phone plan is $20$ dollars. If she sent $100$ text messages and it costs $5$ cents per text, then she must have spent $500$ cents for texting, or $5$ dollars. She talked for $30.5$ hours, but $30.5 - 30$ will give us the amount of time exceeded past $30$ hours. $30.5 - 30 = .5$ hours $= 30$ minutes. Since the price for phone calls is $10$ cents per minute, the additional amount Michelle has to pay for phone calls is $30 * 10 = 300$ cents, or $3$ dollars. Adding $20 + 5 + 3$ dollars $[28 \text{ (D)}]$

Problem 2
There are $5$ coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
(A) $(C,A,E,D,B)$ (B) $(C,A,D,E,B)$ (C) $(C,D,E,A,B)$ (D) $(C,E,A,D,B)$ (E) $(C,E,D,A,B)$

Solution
By careful inspection and common sense, the answer is (E).
Solution
Note that this image is quite similar to a topological map. This means that the coin that appears closest to us is at the top and the coin that appears farthest from us is at the bottom.

See also
Problem 3
A small bottle of shampoo can hold $35$ milliliters of shampoo, whereas a large bottle can hold $500$ milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
(A) $11$ (B) $12$ (C) $13$ (D) $14$ (E) $15$

Solution 1
To find how many small bottles we need, we can simply divide $500$ by $35$. This simplifies to $\frac{100}{7} = 14\frac{2}{7}$. Since the answer must be an integer greater than $14$, we have to round up to $15$ bottles, or [E]

Solution 2
We double $35$ to get $70$. We see that $70 \cdot 7 = 490$, which is very close to $500$. Thus, $2 \cdot 7 + 1 = [(E)15]$ bottles are enough. ~Technodoggo

Problem 4
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12$, $15$, and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?
(A) $12$ (B) $\frac{37}{3}$ (C) $\frac{88}{7}$ (D) $13$ (E) $14$

真题文字详解(中英双语)

Problem 1

A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay?

一个月的手机套餐费用为每月$20$美元，每发送一条短信需支付$5$分钱，超过$30$小时的使用时间还需支付每分钟$10$分钱。一月份，Michelle发了$100$条短信，通话时长为$30.5$小时。她需要支付多少钱？

(A) $24.00$

(B) $24.50$

(C) $25.50$

(D) $28.00$

(E) $30.00$

Solution

The base price of Michelle's cell phone plan is $20$ dollars. If she sent $100$ text messages and it costs $5$ cents per text, then she must have spent $500$ cents for texting, or $5$ dollars. She talked for $30.5$ hours, but $30.5 - 30$ will give us the amount of time exceeded past $30$ hours. $30.5 - 30 = .5$ hours $= 30$ minutes. Since the price for phone calls is $10$ cents per minute, the additional amount Michelle has to pay for phone calls is $30 * 10 = 300$ cents, or $3$ dollars. Adding $20 + 5 + 3$ dollars $[28 \text{ (D)}]$

Michelle的手机套餐基础价格为$20$美元。如果她发送了$100$条短信，每条短信费用为$5$分钱，那么她必须花费$500$分钱用于短信，或$5$美元。她的通话时长为$30.5$小时，但$30.5-30$将告诉我们超出$30$小时的使用时长。$30.5-30=.5$小时=$30$分钟。由于电话费是每分钟$10$分钱，Michelle需要额外支付的通话费用为$30*10=300$分钱，或$3$美元。加上$20+5+3$美元$[28\text{(D)}]$。

Problem 2

There are $5$ coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

根据图示，有$5$枚硬币平放在桌子上。从上到下的硬币顺序是什么？

(A) $(C,A,E,D,B)$

(B) $(C,A,D,E,B)$

(C) $(C,D,E,A,B)$

(D) $(C,E,A,D,B)$

(E) $(C,E,D,A,B)$

Solution

By careful inspection and common sense, the answer is $(E)$.

通过仔细观察和常识，答案是$(E)$。

Solution

Note that this image is quite similar to a topological map. This means that the coin that appears closest to us is at the top and the coin that appears farthest from us is at the bottom.

注意，这张图片与拓扑地图非常相似。这意味着离我们最近的硬币在最上面，而离我们最远的硬币在下面。

See also

Problem 3

A small bottle of shampoo can hold $35$ milliliters of shampoo, whereas a large bottle can hold $500$ milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?

一小瓶洗发水可以容纳$35$毫升洗发水，而一大瓶可以容纳$500$毫升洗发水。Jasmine想要购买刚好能装满一大瓶的最少数量的小瓶。她需要购买多少瓶？

(A) $11$

(B) $12$

(C) $13$

(D) $14$

(E) $15$

Solution 1