2005 AMC amc8 真题 答案 详解

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中英双语真题

2005 AMC8
Problem 1
Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?
Connie 把一个数字乘以 2，得到答案为 60。然而，她本应该把数字除以 2 才能得到正确的答案。那么正确答案是：
(A) 7.5 (B) 15 (C) 30 (D) 120 (E) 240

Problem 2
Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day?
Karl 从 Pay-A-Lot 买了五个文件夹，每个价格为 2.5 美元。Pay-A-Lot 第二天降价 20%。那么 Karl 如果等一天他本可以省下多少钱？
(A) $1.00 (B) $2.00 (C) $2.50 (D) $2.75 (E) $5.00

Problem 3
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal BD of square ABCD?
要使得正方形 ABCD 的一条对称轴位于对角线 BD 上，则至少需要将多少个小正方形涂成黑色？
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

英文真题

Compiled on: January 1, 2021 AMC8 2005 Problems Page 72 of 109 Q1. Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer? A) 7.5 B) 15 C) 30 D) 120 E) 240 Q2. Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day? A) $1.00 B) $2.00 C) $2.50 D) $2.75 E) $5.00 Q3. What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal BD of square ABCD? A) 1 B) 2 C) 3 D) 4 E) 5 Q4. A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters? A) 24 B) 25 C) 36 D) 48 E) 64 Q5. Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda? A) 4 B) 5 C) 6 D) 8 E) 15 Q6. Suppose d is a digit. For how many values of d is 2.00d5 > 2.005? A) 0 B) 4 C) 5 D) 6 E) 10 Q7. Bill walks (\frac{1}{2}) mile south, then (\frac{3}{4}) mile east, and finally (\frac{1}{2}) mile south. How many miles is he, in a direct line, from his starting point? A) 1 B) (1\frac{1}{4}) C) (1\frac{1}{2}) D) (1\frac{3}{4}) E) 2 Q8. Suppose m and n are positive odd integers. Which of the following must also be an odd integer? A) (m + 3n) B) (3m - n) C) (3m^2 + 3n^2) D) ((nm + 3)^2) E) (3mn)

真题文字详解(英文)

Problem 1

Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?
(A) 7.5 (B) 15 (C) 30 (D) 120 (E) 240

Solution

If ( x ) is the number, then ( 2x = 60 ) and ( x = 30 ). Dividing the number by 2 yields ( \frac{30}{2} = \boxed{\text{(B)}\ 15} ).

A second way to do it is to divide the number by 4, as you multiplied by 2 when you were supposed to divide by 2. So, ( \frac{60}{4} = \boxed{\text{(B)}\ 15} ).

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Problem 2

Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day?

(A) $1.00 (B) $2.00 (C) $2.50 (D) $2.75 (E) $5.00

Solution

Karl paid ( 5 \cdot 2.50 = \$12.50 ). 20% of this cost that he saved is ( 12.50 \cdot .2 = \boxed{\text{(C)}\ $2.50} ).

Solution 2

Each folder can also be ( \frac{5}{2} ) dollars, and 20% can be shown as ( \left(\frac{1}{5}\right) ). We can multiply ( \left(\frac{5}{2}\right) \cdot \left(\frac{1}{5}\right) = \left(\frac{1}{2}\right) ). ( \left(\frac{1}{2}\right) ) is also 50 cents or the amount of money that is saved after the 20% discount. So each folder is ( 2.50 - 0.5 = \$2 ). Since Karl bought 5 folders all of the folders after the discount is ( (5)(2) = 10 ), and the money bought before the discount is ( (5)(2.50) = \$12.50 ). To find the money Karl saves all we have to do is subtract ( 12.50 - 10 = 2.50 ). Thus the answer is ( \boxed{\text{(C)}\ $2.50} ).

Solution 3

Having a 20% off sale is equivalent to a "Buy 4 get 1 free" sale. Thus, he would have saved the price of 1 folder, which is ( \boxed{\text{(C)}\ $2.50} ).

-JeffersonJ

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Problem 3

What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal ( \overline{BD} ) of square ( ABCD )?

真题文字详解(中英双语)

Problem 1 Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer? 康妮将一个数乘以2，得到了60。然而，她应该将这个数除以2才能得到正确答案。正确答案是什麽？
(A) 7.5 (B) 15 (C) 30 (D) 120 (E) 240

Solution If x is the number, then 2x = 60 and x = 30. Dividing the number by 2 yields 30/2 = (B) 15. 如果x是这个数，那么2x=60和x=30。将这个数除以2得到30/2=(B) 15。
A second way to do it is to divide the number by 4, as you multiplied by 2 when you were supposed to divide by 2. So, 60/4 = (B) 15. 另一种方法是除以4，因为你本应除以2却乘了2。所以，60/4=(B) 15。

Problem 2 Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day? 卡尔在Pay-A-Lot花$2.50元买了五个文件夹。第二天Pay-A-Lot打八折促销。卡尔如果等一天的话，能在购买上节省多少钱？
(A) $1.00 (B) $2.00 (C) $2.50 (D) $2.75 (E) $5.00

Solution Karl paid 5 · 2.50 = $12.50. 20% of this cost that he saved is 12.50 · .2 = (C) $2.50.
Solution 2 Each folder can also be 5/2 dollars, and 20% can be shown as (1/5). We can multiply (5/2) · (1/5) = (1/2). (1/2) is also 50 cents or the amount of money that is saved after the 20% discount. So each folder is 2.50 - 0.5 = $2. Since Karl bought 5 folders all of the folders after the discount is (5)(2) = 10, and the money bought before the discount is (5)(2.50) = $12.50. To find the money Karl saves all we have to do is subtract 12.50 - 10 = 2.50. Thus the answer is (C) $2.50.
Solution 3 Having a 20% off sale is equivalent to a "Buy 4 get 1 free" sale. Thus, he would have saved the price of 1 folder, which is (C) $2.50. -JeffersonJ

Problem 3 What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal BD of square ABCD?