Answer: A
Solution:
We have H=8-7=1 and T=8-2+5=11. Clearly 1-11=-10, so our answer is -10.
中文解析：
Harry的计算结果是：8-7=1；Terry的计算结果是11， H-T=1-11=-10. 答案是A。
Answer: E
Solution:
The fewest amount of coins that can be used is 2 (a quarter and a dime). The greatest amount is 7, if he only uses nickels. Therefore we have 7-2=5.
中文解析:
35分，硬币最多时：只用5分的硬币，需要7个；
35分，硬币最少时：使用1个25分，1个10分，共需要2个硬币。
因此答案是7-2=5. E 。
Answer: B
Solution:
3*36+3*44+10=250.
中文解析：
前3天每天36页，读了3*36=108页。接下来的3天每天44页， 读了44*3=132页。最后一天读10页。共计：108+132+10=250页。答案是B。
Answer: E
Solution:
Since the two prime numbers sum to an odd number, one of them must be even. The only even prime number is 2. The other prime number is 85-2=83, and the product of these two numbers is 83*2=166.
中文解析：
两个Prime number的和是85，和是一个单数，则这两个prime number必须一个是单数，一个是双数。Prime number 里只有唯一的一个2 是双数，因此另外一个prime number是85-2=83. 这两个prime number 分别是2 和83， 其乘积是：2*83=166. 答案是E。
Answer: C
Solution:
Margie can afford 20/4=5 gallons of gas. She can go 32*5=160 miles on this amount of gas.
中文解析：
1gallon汽油的价格是4美元， 20美元可以购买5gallon的汽油， 1gallon 可以行驶32英里，则5 gallon 可以行驶5*32=160英里。答案是C。
Answer: D
Solution:
The sum of the areas is equal to 2*（1+4+9+16+25+36）=2*91=182.
中文解析：
这6个长方形的宽都是2， 长分别是1，4，9， 16， 25， 36， 则面积分别是：2， 8， 18， 32， 50， 72. 面积的和是：2+8+18+32+50+72=182. 答案是D。
Answer: B
Solution:
We can set up an equation with x being the number of girls in the class. The number of boys in the class is equal to x-4. Since the total number of students is equal to 28, we get x+x-4=28. Solving this equation, we get x=16. There are 16-4=12 boys in our class, and our answer is 16:12=4:3.
中文解析：
女孩比男孩多4个， 男孩女孩共28个， 则男孩12个，女孩16个。女孩和男孩的比值是16：12=4：3. 答案是B。
Answer: D
Solution:
The number 1A2 should be divisible by 11. 132/11=12. A=3.
中文解析：
11个人共支付了1A2元，没人支付了同样的钱，因此1A2能够被11整除，我们很熟悉121 是11的平方，121+11=132 也能被11整除，所以A=3. 答案是D。
Answer: D
Solution:
BD=DC, so <DBC=<DCB=70. Then <CDB=180-70-70=40. Since <ADB and <BDC are supplementary, <ADB=180-40=140.
中文解析：
在三角形BDC中， BD=DC，所以角DCB=角DBC=70°。角BDC=180-70-70=40°。角ADB=180-40=140. 答案是D。
Answer: A
Solution:
The seventh AMC 8 would have been given in 1991. If Samantha was 12 then, that means she was born 12 years ago, so she was born in 1991-12= 1979.
中文解析：
第7届AMC是在1991年。Samantha在1991年时是12岁，因此她是1979年出生的。答案是A。
Answer: A
Solution:
We can make a diagram of the roads available to Jack.
Then, we can simply list the possible routes.
There are 4 possible routes.
中文解析：
如下图所示: 按照water pipe标注的方法， 同时要注意避开题中说第一个十字路口，到达目的地有4种路线。 答案是A。
Answer: B
Solution:
There is a 1/3 chance that the reader will choose the correct baby picture for the first person. Next, the second person gives a 1/2 chance, and the last person leaves only 1 choice. Thus, the probability is 1/3 * 1/2 *1=1/6.
中文解析:
第一个人的婴儿照被匹配正确的概率是1/3. 第二个人的婴儿照从剩下的2张婴儿照中选择，匹配正确的概率是1/2. 第三个人的婴儿照只剩一张照片可选了，匹配正确的概率是1. 因此三个人的婴儿照均匹配正确的概率是：1/3 * 1/2 * 1=1/6. 答案是B .
Answer: D
Solution:
Since n*n+m*m is even, either both n*n and m*m are even, or they are both odd. Therefore, n and m are either both even or both odd, since the square of an even number is even and the square of an odd number is odd. As a result, n+m must be even. The answer, then, is D.
中文解析：
n*n+m*m是个双数，因此n*n 和m*m有相同的奇偶性，同时是奇数或同时是偶数。因此n 和m都是奇数或都是偶数，因此AB都正确。如果n+m是双数，则n和m也拥有相同的奇偶性，C也正确。D选项n+m 是单数，则n和m的奇偶性不同， 不正确。这道题的答案是D。
Answer: B
Solution:
The area of CDE is 1/2 * CE*CD. The area of ABCD is 5*6=30, which also must be equal to the area of CDE. 1/2*CE*CD=30 , Since DC=5, thus CE=12. Then, using the Pythagorean Theorem, you should be able to figure out that CDE is a 5-12-13 triangle. So,DE=13.
中文解析：
直角三角形DCE的底是CE， 高是DC=5. 根据题意，三角形的面积和长方形的面积相等，因此三角形的面积也是30. 根据三角形面积公式代入底和高，得到等式：1/2 * CE*5= 30， 可以求出CE=12. 在直角三角形DCE中， 根据勾股定理， 可得DE=13. 答案是B。
Answer: C
Solution:
For this problem, it is useful to know that the measure of an inscribed angle is half the measure of its corresponding central angle. Since each unit arc is 1/12 of the circle's circumference, each unit central angle measures 360/12=30. Then, we know that the each unit inscribed angle is 15. Thus angle x is 2*15. Angle y is 4*15.so, x+y=2*15+4*15=6*15=90.
中文解析：
同一段圆弧GE，所对应的inscribed angle (角x), 是相对应的Central angle (中心角EOG)的一半。角EOG=60°， 因此x=30°。同样的， 角y是AOI的一半，即60°。所以角x和y的和是90°。答案是C。
Answer: B
Solution:
Within the conference, there are 8 teams, so there are C(8,2)=28 pairings of teams, and each pair must play two games, for a total of 28*2=56 games within the conference.
Each team also plays 4 games outside the conference, and there are 8 teams, so there are a total of 4*8=32 games outside the conference.
Therefore, the total number of games is 56+32=88.
中文解析:
8支队内部，每两个队比赛1场的话是组合C(8, 2)=28. 每两个队比赛两场则需要进行28*2=56场比赛。每个对还需要和协会外的进行4场比赛，共4*8=32场。因此赛季需要进行的比赛场数是: 56+32=88. 答案是B。
Answer: B
Solution:
Note that on a normal day, it takes him 1/3 hour to get to school. However, today it took 1/2 mile /2 mph=1/4 hour to walk the first 1/2 mile. That means that he has 1/3-1/4=1/12 hours left to get to school, and 1/2 mile left to go. Therefore, his speed must be (1/2)/(1/12)=6 mph.
中文解析：
George家离学校的距离是1mile. 他平时需要的时间是1mile/ 3 mph= 1/3 小时=20分钟。今天George的前1/2 mile 花费的时间是: 1/2 mile /2 mph= 1/4 小时=15分钟。他如果还想总共20分钟内到达学校，需要5分钟走1/2 mile， 因此速度需要是：1/2 mile/ 5分钟=1/2 mile/ (1/12 hour)=6 mph. 答案是B。
Answer: D
Solution:
The probability of C occurring is C(4,2)/16=6/(2*2*2*2)=3/8. because we need to choose 2 of the 4 children to be girls. For D, there are two possible cases, 3 girls and 1 boy or 3 boys and 1 girl. The probability of the first case is C(4,1)/16=4/16=1/4 because we need to choose 1 of the 4 children to be a boy. However, the second case has the same probability because we are choosing 1 of the 4 children to be a girl, so the total probability is (1/4)*2=1/2. So the answer is D.
中文解析：
男孩女孩的概率是相等的，因此4个孩子都是男孩，或都是女孩的概率肯定较低，排除A，B， E。这4个孩子的性别情况总共有：2*2*2*2=16种情况。 其中出现2个男孩，2个女孩的情况可以理解为从4个孩子中选出两个男孩的组合， 即C（4，2）=6. 因此选项C的概率是： 6/16=3/8. 选项D 的情况可以理解为从4个孩子中选出1个男孩或者从4个孩子中选出1个女孩。 从4个孩子中选出1个男孩有C（4，1）=4种，同理，选出1个女孩有4种。 因此D选项有8种，其概率是8/16=1/2. 显然D是最有可能的，答案是D。
Answer: A
Solution:
For the least possible surface area that is white, we should have 1 cube in the center, and the other 5 with only 1 face exposed. This gives 5 square inches of white surface area. Since the cube has a surface area of 54 square inches, our answer is 5/54.
中文解析：
由21个红色，6个白色的小正方体组成大正方体， 希望白色的尽量少显露出来，因此尽量把白色的往中间放。大立方体最中间的那个位置放白色的。 每个表面最中间的那块，用白色，大正方体有6个表面，因此每个表面最中间的也放白色小方块，而此时只剩下5个小白方块了，因此能显示在大正方体外表面的只有5个白色小正方体的一面。 大正方体的表面积是： 3*3*6=54，其中5个小正方块是白色的，因此白色占比是: 5/54. 答案是A。
Answer: B
Solution:
The area in the rectangle but outside the circles is the area of the rectangle minus the area of all three of the quarter circles in the rectangle.
The area of the rectangle is 3*5=15. The area of all 3 quarter circles is Pi/4+4*PI/4+9Pi/4=7PI/2. Therefore the area in the rectangle but outside the circles is 15-7Pi/2=4.
中文解析：
长方形ABCD的面积是：5*3=15。
圆心为A的圆形，在正方形内部的部分的面积是：1/4* Pi*1=0.25Pi.
圆心为B的圆形，在正方形内部的部分的面积是：1/4* Pi*2*2=Pi.
圆心为C的圆形，在正方形内部的部分的面积是：1/4* Pi*3*3=2.25Pi.
因此题目所求的部分的面积是: 15-0.25Pi-Pi-2.25Pi=15-3.5Pi,约等于4. 答案是B。
Answer: A
Solution:
Since both numbers are divisible by 3, the sum of their digits has to be divisible by 3. 7 + 4 + 5 + 2 + 1 = 19. In order to be a multiple of 3, A + B has to be either 2 or 5 or 8... and so on. We add up the numerical digits in the second number; 3 + 2 + 6 + 4 = 15. We then add two of the selected values, 5 to 15, to get 20. We then see that C = 1, 4 or 7, 10... and so on, otherwise the number will not be divisible by three. So, A is the answer.
中文解析：
74A52B1能被3整除，因此A+B可以是2， 5， 8，.... 326AB4C 也能被3整除，则A+B+C需要是3的倍数， 由于A+B是2，5，8，... 因此C可以是1， 答案是A。
Answer: E
Solution:
We can think of the number as 10a+b, where a and b are digits. Since the number is equal to the product of the digits a*b plus the sum of the digits a+b, we can say that 10a+b=a*b+a+b. We can simplify this to a*(9-b)=0. Thus b=9. The units digit is 9.
中文解析：
假设十位数是a,个位数是b. 这个2位数的数值是10a+b. 根据题意， a*b+a+b=10a+b. 可以推出a*b=9a; 因此b=9. 答案是E。
Answer: A
Solution:
The smallest two digit primes are 11,13,17. The possible sum of two of these numbers are 24, 30, 28. Since Brittany says that the other two people's uniform numbers are earlier, so that means Caitlin and Ashley's numbers must add up to 24. Similarly, Caitlin says that the other two people's uniform numbers is later, so the sum must add up to 30. This leaves 28 as today's date. From this, Caitlin was referring to the uniform wearers 13 and 17, telling us that her number is 11.
中文解析：
由于两个人的号码的和是一个生日的day,因此需要<=31. 由于每个人的号码都是2位的质数。因此他们的号码有可能是11， 13， 17. （不可能是19，因为19+13超过了31）。这3个数中最大的和是: 13+17=30, 是月份中较靠后的，应该是Caitlin 说的， 因此Caitlin 是11. 答案是A。
Answer: C
Solution:
In order to maximize the median, we need to make the first half of the numbers as small as possible. To minimize the first 49, they would each have one can. Subtracting these 49 cans from the 252 cans gives us 203 cans left to divide among 51 people. Taking 203/51=3, gives us 3 and a remainder of 50. Seeing this, the largest number of cans the 50th person could have is 3, which leaves 4 to the rest of the people. The average of 3 and 4 is 3.5.
中文解析：
先假设这100个人买的soda的数量从小到大排列，由于每人至少1个，先假设人都买1个，则剩下252-100=152个。为了让中位数最大化，我们先给从第51个到第100个，每人再买3个，剩下了2个，让第50个人买。因此第50个人买了3瓶soda, 第51人到100人，各买了4瓶，因此中位数是: (3+4)/2=3.5.答案是C。
Answer: B
Solution:
If Robert rides in a straight line, it will take him 1/5 hours. When riding in semicircles, let the radius of the semicircle , then the circumference of a semicircle is Pi*r. The ratio of the circumference of the semicircle to its diameter is Pi/2, so the time Robert takes is 1/5*(Pi/2), which equals to Pi/10 hours.
中文解析：
这条路的长度是1 mile,即5280 feet. 需要沿着半圆形的轨道走，半圆的半径是：40/2=20 feet. 半圆的周长是：Pi*20. 直路40feet 对应的半圆弧是20Pi, 因此直路5280 feet 对应的半圆弧总弧长是: (5280 *20Pi )/ 40 =2640Pi. 由于已知速度是5 mile 每小时，也即5*5280 feet 每小时, 即因此需要的时间是: 2640Pi/（5*5280）=Pi/10. 答案是B。
AMC培训、答疑，请联系微信 / 电话：136 1118 1627
艾蕾特教育 @Elite Edu, 在这里，