2013 AMC amc10b 真题 答案 详解

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中英双语真题

2013 AMC 10B

Problem 1
[ \frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} ] What is ( \frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} )?

(\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}) 的值是多少？

(A) -1 (B) (\frac{5}{36}) (C) (\frac{7}{12}) (D) (\frac{49}{20}) (E) (\frac{43}{3})

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Problem 2
Mr. Green measures his rectangular garden by walking two of the sides and finding that it is 15 steps by 20 steps. Each of Mr. Green's steps is 2 feet long. Mr. Green expects a half a pound of potatoes per square foot from his garden. How many pounds of potatoes does Mr. Green expect from his garden?

格林先生通过自己的步长来测量他的矩形花园，发现大小是 15 步 x 20 步。格林先生的每一步是 2 英尺长。他期望他的花园每平方英尺的土地可以产出半磅的土豆。那么格林先生期望他的花园总共可以产出多少磅的土豆？

(A) 600 (B) 800 (C) 1000 (D) 1200 (E) 1400

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Problem 3
On a particular January day, the high temperature in Lincoln, Nebraska, was 16 degrees higher than the low temperature, and the average of the high and the low temperatures was 3°. In degrees, what was the low temperature in Lincoln that day?

内布拉斯加州林肯市在一月份的某天，高温比低温高 16 度，且高温和低温的平均值是 3 度，那么林肯市那天的低温是多少度？

(A) -13 (B) -8 (C) -5 (D) -3 (E) 11

英文真题

2013 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{49}{20} (E) \frac{43}{3} Problem 2 Mr. Green measures his rectangular garden by walking two of the sides and finding that it is 15 steps by 20 steps. Each of Mr. Green's steps is 2 feet long. Mr. Green expects a half pound of potatoes per square foot from his garden. How many pounds of potatoes does Mr. Green expect from his garden? (A) 600 (B) 800 (C) 1000 (D) 1200 (E) 1400 Problem 3 On a particular January day, the high temperature in Lincoln, Nebraska, was 16 degrees higher than the low temperature, and the average of the high and the low temperatures was 3°. In degrees, what was the low temperature in Lincoln that day? (A) -13 (B) -8 (C) -5 (D) -3 (E) 11 Problem 4 When counting from 3 to 201, 53 is the 51st number counted. When counting backwards from 201 to 3, 53 is the nth number counted. What is n? (A) 146 (B) 147 (C) 148 (D) 149 (E) 150 Problem 5 Positive integers a and b are each less than 6. What is the smallest possible value for 2 · a − a · b? (A) -20 (B) -15 (C) -10 (D) 0 (E) 2 Problem 6 The average age of 33 fifth-graders is 11. The average age of 55 of their parents is 33. What is the average age of all of these parents and fifth-graders? (A) 22 (B) 23.25 (C) 24.75 (D) 26.25 (E) 28 Problem 7 Six points are equally spaced around a circle of radius 1. Three of these points are the vertices of a triangle that is neither equilateral nor isosceles. What is the area of this triangle? (A) \frac{\sqrt{3}}{3} (B) \frac{\sqrt{3}}{2} (C) 1 (D) \sqrt{2} (E) 2 Problem 8 Ray's car averages 40 miles per gallon of gasoline, and Tom's car averages 10 miles per gallon of gasoline. Ray and Tom each drive the same number of miles. What is the cars' combined rate of miles per gallon of gasoline? (A) 10 (B) 16 (C) 25 (D) 30 (E) 40

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{49}{20} (E) \frac{43}{3}

Solution This expression is equivalent to \frac{12}{9} - \frac{9}{12} = \frac{16}{12} - \frac{9}{12} = \boxed{(C)\frac{7}{12}} For the exact same problem but with answer choice D unsimplified, see http://artofproblemsolving.com/wiki/index.php/2011_AMC_10B_Problems/Problem_1 Problem 2 The following problem is from both the 2013 AMC 12B #2 and 2013 AMC 10B #2, so both problems redirect to this page. Mr. Green measures his rectangular garden by walking two of the sides and finds that it is 15 steps by 20 steps. Each of Mr. Green's steps is 2 feet long. Mr. Green expects a half a pound of potatoes per square foot from his garden. How many pounds of potatoes does Mr. Green expect from his garden? (A) 600 (B) 800 (C) 1000 (D) 1200 (E) 1400 Solution Since each step is 2 feet, his garden is 30 by 40 feet. Thus, the area of 30(40) = 1200 square feet. Since he is expecting \frac{1}{2} of a pound per square foot, the total amount of potatoes expected is 1200 × \frac{1}{2} = \boxed{(A) 600} See also Problem 3 The following problem is from both the 2013 AMC 12B #1 and 2013 AMC 10B #3, so both problems redirect to this page. On a particular January day, the high temperature in Lincoln, Nebraska, was 16 degrees higher than the low temperature, and the average of the high and low temperatures was 3. In degrees, what was the low temperature in Lincoln that day? (A) -13 (B) -8 (C) -5 (D) -3 (E) 11 Solution Let L be the low temperature. The high temperature is L + 16. The average is \frac{L+(L+16)}{2}=3. Solving for L, we get L=\boxed{(C)-5} Problem 4 The following problem is from both the 2013 AMC 12B #3 and 2013 AMC 10B #4, so both problems redirect to this page. When counting from 3 to 201, 53 is the 51st number counted. When counting backwards from 201 to 3, 53 is the nth number counted. What is n?

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{49}{20} ) (E) ( \frac{43}{3} )

Solution
This expression is equivalent to ( \frac{12}{9} - \frac{9}{12} = \frac{16}{12} - \frac{9}{12} = \boxed{\text{(C)}\ \frac{7}{12}} ).
这个表达式等同于 ( \frac{12}{9} - \frac{9}{12} = \frac{16}{12} - \frac{9}{12} = \boxed{\text{(C)}\ \frac{7}{12}} ).

For the exact same problem but with answer choice D unsimplified, see http://artofproblemsolving.com/wiki/index.php/2011_AMC_10B_Problems/Problem_1
对于完全相同但选项D未简化的题目，请见http://artofproblemsolving.com/wiki/index.php/2011_AMC_10B_Problems/Problem_1

Problem 2
The following problem is from both the 2013 AMC 12B #2 and 2013 AMC 10B #2, so both problems redirect to this page.
Mr. Green measures his rectangular garden by walking two of the sides and finds that it is 15 steps by 20 steps. Each of Mr. Green's steps is 2 feet long. Mr. Green expects a half a pound of potatoes per square foot from his garden. How many pounds of potatoes does Mr. Green expect from his garden?
(A) 600 (B) 800 (C) 1000 (D) 1200 (E) 1400

Solution
Since each step is 2 feet, his garden is 30 by 40 feet. Thus, the area of ( 30(40) = 1200 ) square feet. Since he is expecting ( \frac{1}{2} ) of a pound per square foot, the total amount of potatoes expected is ( 1200 \times \frac{1}{2} = \boxed{\text{(A)}\ 600} ).

See also
Problem 3
The following problem is from both the 2013 AMC 12B #1 and 2013 AMC 10B #3, so both problems redirect to this page.
On a particular January day, the high temperature in Lincoln, Nebraska, was 16 degrees higher than the low temperature, and the average of the high and low temperatures was 3. In degrees, what was the low temperature in Lincoln that day?
(A) -13 (B) -8 (C) -5 (D) -3 (E) 11

Solution
Let L be the low temperature. The high temperature is ( L + 16 ). The average is ( \frac{L + (L + 16)}{2} = 3 ). Solving for L, we get ( L = \boxed{\text{(C)}\ -5} ).

Problem 4