2011 AMC amc10b 真题 答案 详解

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中英双语真题

2011 AMC 10B
Problem 1
[ \frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} ]
What is the value?
[ \frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} ]
(A) -1 (B) (\frac{5}{36}) (C) (\frac{7}{12}) (D) (\frac{147}{60}) (E) (\frac{43}{3})

Problem 2
Josanna's test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise her test average at least 3 points with her next test. What is the minimum test score she would need to accomplish this goal?

Josanna 目前的考试成绩是 90、80、70、60 和 85。她的目标是靠下次考试将她的考试平均分提高至少 3 分，那么她下次至少需要考多少分才能完成这个目标？

(A) 80 (B) 82 (C) 85 (D) 90 (E) 95

Problem 3
At a store, when a length is reported as (x) inches that means the length is at least (x-0.5) inches and at most (x+0.5) inches. Suppose the dimensions of a rectangular tile are reported as 2 inches by 3 inches. In square inches, what is the minimum area for the rectangle?

在某家商店，长度标为 (x) 英寸表示实际长度至少为 (x-0.5) 英寸，至多为 (x+0.5) 英寸。假设一块长方形瓷砖的尺寸标为 2 x 3 英寸。则在这个长方形瓷砖的最小面积是多少平方英寸？

(A) 3.75 (B) 4.5 (C) 5 (D) 6 (E) 8.75

英文真题

2011 AMC 10B Problems Problem 1 What is \frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6} (A) -1 (B) \frac{5}{36} (C) \frac{7}{12} (D) \frac{147}{60} (E) \frac{43}{3} Problem 2 Josanna's test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise her test average at least 3 points with her next test. What is the minimum test score she would need to accomplish this goal? (A) 80 (B) 82 (C) 85 (D) 90 (E) 95 Problem 3 At a store, when a length is reported as x inches that means the length is at least x-0.5 inches and at most x+0.5 inches. Suppose the dimensions of a rectangular tile are reported as 2 inches by 3 inches. In square inches, what is the minimum area for the rectangle? (A) 3.75 (B) 4.5 (C) 5 (D) 6 (E) 8.75 Problem 4 LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip, it turned out that LeRoy had paid A dollars and Bernardo had paid B dollars, where A < B. How many dollars must LeRoy give to Bernardo so that they share the costs equally? (A) \frac{A+B}{2} (B) \frac{A-B}{2} (C) \frac{B-A}{2} (D) B-A (E) A+B Problem 5 In multiplying two positive integers a and b, Ron reversed the digits of the two-digit number a. His erroneous product was 161. What is the correct value of the product of a and b? (A) 116 (B) 161 (C) 204 (D) 214 (E) 224 Problem 6 On Halloween Casper ate \frac{1}{3} of his candies and then gave 2 candies to his brother. The next day he ate \frac{1}{3} of his remaining candies and then gave 4 candies to his sister. On the third day he ate his final 8 candies. How many candies did Casper have at the beginning? (A) 30 (B) 39 (C) 48 (D) 57 (E) 66 Problem 7 The sum of two angles of a triangle is \frac{6}{5} of a right angle, and one of these two angles is 30° larger than the other. What is the degree measure of the largest angle in the triangle? (A) 69 (B) 72 (C) 90 (D) 102 (E) 108 Problem 8 At a certain beach if it is at least 80°F and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded about the weather conditions on June 10? (A) The temperature was cooler than 80°F and it was not sunny. (B) The temperature was cooler than 80°F or it was not sunny.

真题文字详解(英文)

Problem 1 What is \frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6}?
(A) -1 (B) \frac{5}{36} (C) \frac{7}{12} (D) \frac{147}{60} (E) \frac{43}{3}

Solution
\frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6}=\frac{12}{9}-\frac{9}{12}=\frac{4}{3}-\frac{3}{4}=\boxed{\frac{7}{12}}(C)

Note: This exact problem was reused in 2013 AMC 10B: https://artofproblemsolving.com/wiki/index.php/2013_AMC_10B_Problems/Problem_1

Problem 2
Josanna's test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise her test average at least 3 points with her next test. What is the minimum test score she would need to accomplish this goal?
(A) 80 (B) 82 (C) 85 (D) 90 (E) 95

Solution
The average of her current scores is 77. To raise it 3 points, she needs an average of 80, and so after her 6 tests, a sum of 480. Her current sum is 385, so she needs a 480-385=\boxed{(E) 95}

Problem 3
At a store, when a length is reported as x inches that means the length is at least x-0.5 inches and at most x+0.5 inches. Suppose the dimensions of a rectangular tile are reported as 2 inches by 3 inches. In square inches, what is the minimum area for the rectangle?
(A) 3.75 (B) 4.5 (C) 5 (D) 6 (E) 8.75

Solution
The minimum dimensions of the rectangle are 1.5 inches by 2.5 inches. The minimum area is 1.5 × 2.5 = \boxed{(A) 3.75} square inches.

Problem 4
LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip it turned out that LeRoy had paid A dollars and Bernardo had paid B dollars, where A < B. How many dollars must LeRoy give to Bernardo so that they share the costs equally?
(A) \frac{A+B}{2} (B) \frac{A-B}{2} (C) \frac{B-A}{2} (D) B-A (E) A+B

真题文字详解(中英双语)

Problem 1 What is \frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}?
(A) -1 (B) \frac{5}{36} (C) \frac{7}{12} (D) \frac{147}{60} (E) \frac{43}{3}

Solution
\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} = \frac{12}{9} - \frac{9}{12} = \frac{4}{3} - \frac{3}{4} = \boxed{\frac{7}{12}} (C)

Note: This exact problem was reused in 2013 AMC 10B:
注意：这个精确的问题在2013年AMC 10B中再次使用：
https://artofproblemsolving.com/wiki/index.php/2013_AMC_10B_Problems/Problem_1

Problem 2
Josanna's test scores to date are 90, 80, 70, 60, and 85. Her goal is to raise her test average at least 3 points with her next test. What is the minimum test score she would need to accomplish this goal?
乔斯安娜到目前为止的考试成绩是90、80、70、60和85。她的目标是下一次考试将她的平均分至少提高3分。她需要至少得到多少分才能实现这个目标？
(A) 80 (B) 82 (C) 85 (D) 90 (E) 95

Solution
The average of her current scores is 77. To raise it 3 points, she needs an average of 80, and so after her 6 tests, a sum of 480. Her current sum is 385, so she needs a 480-385=\boxed{(E) 95}.
她目前的平均分是77。为了提高3分，她需要的平均分是80，所以在她6次考试后，总分要达到480。她目前总分是385，所以她需要480-385=\boxed{(E) 95}。

Problem 3
At a store, when a length is reported as ( x ) inches that means the length is at least ( x - 0.5 ) inches and at most ( x + 0.5 ) inches. Suppose the dimensions of a rectangular tile are reported as 2 inches by 3 inches. In square inches, what is the minimum area for the rectangle?
在一家商店，当长度报告为( x )英寸时，这意味着长度至少是( x - 0.5 )英寸，最多是( x + 0.5 )英寸。假设一个矩形瓷砖的尺寸报告为2英寸乘以3英寸。以平方英寸为单位，这个矩形的最大面积是多少？
(A) 3.75 (B) 4.5 (C) 5 (D) 6 (E) 8.75

Solution
The minimum dimensions of the rectangle are 1.5 inches by 2.5 inches. The minimum area is 1.5 × 2.5 = \boxed{(A) 3.75} square inches.
矩形的最小尺寸是1.5英寸乘以2.5英寸。最小面积是1.5 × 2.5 = \boxed{(A) 3.75} 平方英寸。