2014 AMC amc12a 真题 答案 详解

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中英双语真题

2014 AMC12A 2014 AMC12A Problem 1 What is (10 \cdot \left(\frac{1}{2} + \frac{1}{5} + \frac{1}{10}\right)^{-1})? 下列式子的值是多少 (10 \cdot \left(\frac{1}{2} + \frac{1}{5} + \frac{1}{10}\right)^{-1})? (A) 3 (B) 8 (C) (\frac{25}{2}) (D) (\frac{170}{3}) (E) 170 Problem 2 At the theater children get in for half price. The price for 5 adult tickets and 4 child tickets is $24.50. How much would 8 adult tickets and 6 child tickets cost? 在剧院，儿童票半价，已知5张成人票和4张儿童票的总价是24.5元，问8张成人票和6张儿童票需要多少元？ (A) 35 (B) 38.50 (C) 40 (D) 42 (E) 42.50 Problem 3 Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible? 当 Ralph 走过 Jane 街时，她经过了一排 4 座楼房，每座楼房都涂有不同的颜色。她先经过桔色的房子，再经过红色房子，她先经过蓝色房子，再经过黄色房子，蓝色房子不和黄色房子相邻，这 4 个涂色的房子有多少种可能的排列方法？ (A) 2 (B) 3 (C) 4 (D) 5 (E) 6

英文真题

2014 AMC 12A Problems

Problem 1
What is $10 \cdot (\frac{1}{2} + \frac{1}{5} + \frac{1}{10})^{-1}$?
(A) 3 (B) 8 (C) $\frac{25}{2}$ (D) $\frac{170}{3}$ (E) 170

Problem 2
At the theater children get in for half price. The price for 5 adult tickets and 4 child tickets is $24.50. How much would 8 adult tickets and 6 child tickets cost?
(A) $35 (B) $38.50 (C) $40 (D) $42 (E) $42.50

Problem 3
Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

Problem 4
Suppose that $a$ cows give $b$ gallons of milk in $c$ days. At this rate, how many gallons of milk will $d$ cows give in $e$ days?
(A) $\frac{bde}{ac}$ (B) $\frac{ac}{bde}$ (C) $\frac{abde}{c}$ (D) $\frac{bcde}{a}$ (E) $\frac{abc}{de}$

Problem 5
On an algebra quiz, 10% of the students scored 70 points, 35% scored 80 points, 30% scored 90 points, and the rest scored 100 points. What is the difference between the mean and median score of the students' scores on this quiz?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Problem 6
The difference between a two-digit number and the number obtained by reversing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?
(A) 44 (B) 55 (C) 77 (D) 99 (E) 110

Problem 7
The first three terms of a geometric progression are $\sqrt[3]{3}, \sqrt[3]{3},$ and $\sqrt[6]{3}$. What is the fourth term?
(A) 1 (B) $\sqrt[3]{3}$ (C) $\sqrt[6]{3}$ (D) $\sqrt[9]{3}$ (E) $\sqrt[10]{3}$

Problem 8
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon 1: 10% off the listed price if the listed price is at least $50
Coupon 2: $20 off the listed price if the listed price is at least $100
Coupon 3: 18% off the amount by which the listed price exceeds $100
For which of the following listed prices will coupon 1 offer a greater price reduction than either coupon 2 or coupon 3?
(A) $179.95 (B) $199.95 (C) $219.95 (D) $239.95 (E) $259.95

真题文字详解(英文)

Problem 1 What is $10 \cdot \left(\frac{1}{2} + \frac{1}{5} + \frac{1}{10}\right)^{-1}$?
(A) 3 (B) 8 (C) $\frac{25}{2}$ (D) $\frac{170}{3}$ (E) 170

Solution We have $$10 \cdot \left( \frac{1}{2} + \frac{1}{5} + \frac{1}{10} \right)^{-1}$$ Making the denominators equal gives $$\Rightarrow 10 \cdot \left( \frac{5}{10} + \frac{2}{10} + \frac{1}{10} \right)^{-1}$$ $$\Rightarrow 10 \cdot \left( \frac{5+2+1}{10} \right)^{-1}$$ $$\Rightarrow 10 \cdot \left( \frac{8}{10} \right)^{-1}$$ $$\Rightarrow 10 \cdot \left( \frac{4}{5} \right)^{-1}$$ $$\Rightarrow 10 \cdot \frac{5}{4}$$ $$\Rightarrow \frac{50}{4}$$ Finally, simplifying gives $$\boxed{(C)\frac{25}{2}}$$ Solution 2

真题文字详解(中英双语)

Problem 1 What is $10 \cdot \left(\frac{1}{2} + \frac{1}{5} + \frac{1}{10}\right)^{-1}$?
(A) 3 (B) 8 (C) $\frac{25}{2}$ (D) $\frac{170}{3}$ (E) 170

Solution We have $$10 \cdot \left( \frac{1}{2} + \frac{1}{5} + \frac{1}{10} \right)^{-1}$$ Making the denominators equal gives $$\Rightarrow 10 \cdot \left( \frac{5}{10} + \frac{2}{10} + \frac{1}{10} \right)^{-1}$$ $$\Rightarrow 10 \cdot \left( \frac{5+2+1}{10} \right)^{-1}$$ $$\Rightarrow 10 \cdot \left( \frac{8}{10} \right)^{-1}$$ $$\Rightarrow 10 \cdot \left( \frac{4}{5} \right)^{-1}$$ $$\Rightarrow 10 \cdot \frac{5}{4}$$ $$\Rightarrow \frac{50}{4}$$ Finally, simplifying gives $$\boxed{(C)\frac{25}{2}}$$ Solution 2