Answer: A
Solution:
In order to have the model cars in complete rows of 6, Danica must have a number of cars that is a multiple of 6. The smallest multiple of 6 which is larger than 23 is 24, so she'll need to buy 1 more model car.
中文解析：
每行6个，汽车模型的数量需要是6的倍数，已经有23个了，因此再增加一个变成24即可。答案是A .
Answer: D
Solution:
The 50% off price of half a pound of fish is $3, so the 100%, or the regular price, of a half pound of fish is $6. Consequently, if half a pound of fish costs $6, then a whole pound of fish is 12 dollars.
中文解析：
每half-pound 的Package是3元，因此full-pound的价格应该是6元，这是在50% off的情况下的价格。正常不打折的情况下， full-pound 的价格应该是12元。答案是D。
Answer: E
Solution:
Notice that we can pair up every two numbers to make a sum of 1:
(-1+2-3+4-…+1000)=（（-1+2）+（-3+4）+…+(-999+1000)）=(1+1+…+1)=500.
4*500=2000.
中文解析：
把-1+2， -3+4， -5+6，。。。。-999+1000 括起来计算， 因此等价于：4*（1+1+1+...+1），共500个1. 所以答案是：4*500=2000. 答案是E。
Answer: C
Solution:
Each of her seven friends paid 2.5 to cover Judi's portion. Therefore, Judi's portion must be 2.5*7=17.5. Since each friend was supposed to pay the same amount, each friend was supposed to pay 1/8 of the total bill; the total bill must be 8*17.5=140.
中文解析：
7个朋友们凑钱支付了Judi应该付的， 因此Judi应该付的钱是: 2.5*7=17.5元。8个人是平均分的餐费，每人都应该是17.5， 因此总账单是: 17.5*8=140元， 答案是C。
Answer: E
Solution:
Lining up the numbers (5, 5, 6, 8, 106), we see that the median weight is 6 pounds.
The average weight of the five kids is (5+5+6+8+106)/5=26.
Therefore, the average weight is bigger, by 26-6=20 pounds.
中文解析：
5个孩子的体重分别是: 5, 5, 6, 8, 106. median是6；mean 是：（5+5+6+8+106）/5=26. mean比median多20， 因此答案是E。
Answer: C
Solution:
600=30*20, so the second number in row two is 20. 20=5*4. Thus, the right number is top row is 4.
中文解析：
600=30*20；因此右下的格内填写20. 20=5*4，因此右上的格内填写4. 答案是C .
Answer: C
Solution:
If Trey saw 6 cars / 10 seconds, then he saw 3 cars/5 seconds. 2 minutes and 45 seconds can also be expressed as 165 seconds. Thus, he saw 165/5 * 3=99 cars. The answer should be C(100).
中文解析：
10秒有6辆车通过，那么2分45秒即165秒有：165*6/10=99辆车通过。因此答案是C。
Answer: C
Solution:
First, there are 2*2*2=8 ways to flip the coins, in order.
The ways to get two consecutive heads are HHT and THH.
The way to get three consecutive heads is HHH.
Therefore, the probability of flipping at least two consecutive heads is 3/8.
中文解析：
一个硬币掷3次，共有2*2*2=8种可能的结果。连续两个正面朝上的结果分别是：+++， ++-， -++。因此题目所求的概率是：3/8. 答案是C。
Answer: C
Solution:
We can solve this problem by listing out how far the Hulk jumps on each jump: we get: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. On the 11th jump, the Hulk jumps 1024 meters > 1000 meters (1 kilometer), so our answer is the 11th jump.
中文解析：
Hulk 跳的距离分别是：1， 2， 4， 8， 16， 32， 64，...... 这是等比数列（Geometric Sequence）。第n项是2的（n-1)次方。第11项是1024，超过了1000m. 因此答案是C。
Answer: C
Solution:
LCM(180, 594)=2*9*10*33;
GCF(180,594)=2*9; the ratio is (2*9*10*33)/(2*9)=10*33=330.
用短除法求得180 和594的最小公倍数和最大公因数。其比值是10*33=330. 答案C。
Answer: D
Solution:
On Monday, He spend 2 miles/5 mph =2/5hours =24 minutes. On Wednesday, he spend 2/3= 2/3 hours =40 minutes. On Friday, he spend 2/4=0.5hours =30minutes. 24+40+30=94 minutes.
We now find the amount of time Grandfather would have taken if he walked at 4 mph per day, he spend 2/4*3=90 minutes. Thus, the answer is 94-90=4 minutes.
中文解析：
周一运动的时间是：2 miles/5 =0.4 小时=24分钟。周三运动的时间是：2miles/3=40分钟。周五运动的时间是2miles / 4=30 分钟。这周运动时间共: 24+40+30=94分钟。老人如果是实地走路的话，花费的时间是2miles/4*3=90分钟。比跑步机上运动时间少4分钟。
Answer: B
Solution:
First, find the amount of money one will pay for three sandals without the discount. We have 50*3=150. Then, find the amount of money using the discount: 50+50*0.6+50*0.5=105. Finding the percentage yields 105/150=70%, To find the percent saved, we have 30%.
中文解析：
第一对凉鞋50元，第二对40%off, 则是30元， 第三对50%off, 则是25元，因此三对凉鞋共支付105元。节省了150-105=45元，即45/150=30%。答案是B。
Answer: A
Solution:
Let the two digits be a and b.
The correct score was 10a+b. Clara misinterpreted it as 10b+a. The difference between the two is (10a+b)-(10b+a)=10(a-b)-(a-b)=9(a-b) . Therefore, since the difference is a multiple of 9, the only answer choice that is a multiple of 9 is 45.
中文解析：
假设她正确的分数的十位数是a,个位数是b. 她的成绩应该是 10a+b. 弄反后的分数是10b+a. 其差别是: (10a+b)-(10b+a)=10(a-b)-(a-b)=9(a-b). 因此这个差别一定是9的倍数，答案A。
Answer: C
Solution:
The probability that both show a green bean is 1/2*1/4=1/8. The probability that both show a red bean is 1/2*2/4=1/4. Therefore the probability is 1/4+1/8=3/8.
中文解析：
颜色匹配的情况有两种: 都是红色或都是绿色。
都是绿色的概率: Abe选出绿色的概率是1/2. Bob选出绿色的概率是1/4. 因此都是绿色的概率是1/2 * 1/4=1/8.
都是红色的概率：Abe选出红色的概率是1/2. Bob选出红色的概率是2/4. 因此都是红色的概率是：1/2 * 2/4=2/8.
因此颜色匹配的概率是1/8 + 2/8=3/8. 答案是C。
Answer: B
Solution:
Start with 3^p+3^4=90, =>3^p=9; =>p=2; Now, solve for r. Since 2^r+44=76, => 2^r=32; => r=5. Now, solve for s. 5^3+6^s=1421; =>6^s=1296; =>s=4. P*r*s=2*5*4=40.
中文解析：
第一个式子：因为 3*3*3*3=81， 因此3^p =9. 所以p=2.
第二个式子：2^r=32. 因此r=5.
第三个式子：因为5*5*5=125， 因此6^s=1296. 所以s=4.
P*r*s=2*5*4=40. 答案是B。
Answer: E
Solution:
We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8th graders, in order that we can put the two ratios together: 40:24 , 40:25.
Therefore, the ratio of 8th graders to 7th graders to 6th graders is 40:25:24. Since the ratio is in lowest terms, the smallest number of students participating in the project is 40+25+24=89.
中文解析：
8th 年级和6th年级的比值是5：3， 也可以写成：40：24；
8th年级和7th年级的比值是8：5， 也可以写成：40：25；
因此8年级， 7年级，6年级的可以是：40：25：24. 因此能参加这个项目的学生最少是：40+25+24=89人。答案E。
Answer: B
Solution:
The mean of these numbers is 2013/6=335.5. Therefore the numbers are 333, 334, 335, 336, 337, 338. So the largest is 338.
中文解析：
6个连续的数的和是2013， 则这6个数的平均值是：2013/6=335.5. 这连续6个数的中间两个数分别是335 和336. 因此最大的那个数是：338. 答案是B。
Answer: B
Solution:
There are 12*10=120 cubes on the base of the box. Then, for each of the 4 layers above the bottom (as since each cube is 1 foot by 1 foot by 1 foot and the box is 5 feet tall, there are 4 feet left), there are 9+11+9+11=40 cubes. Hence, the answer is 120+4*40=280.
中文解析：
底部block的数量是：12*10=120 块。边长为12的那个侧面的block的数量是：12*4 (因为底层已经计算过了，因此剩下的高度按4计算）。两个边长为12的侧面的Blockde 数量是：2*12*4=96. 2个边长为10的侧面的block的数量是：2*8*4=64. 因此总共的block数量是：120+96+64=280. 答案是B。
Answer: D
Solution:
If Hannah did better than Cassie, there would be no way she could know for sure that she didn't get the lowest score in the class. Therefore, Hannah did worse than Cassie. Similarly, if Hannah did worse than Bridget, there is no way Bridget could have known that she didn't get the highest in the class. Therefore, Hannah did better than Bridget, so our order is Cassie, Hannah, Bridget.
中文解析：
Cassie说Cassie不是最低分，说明Cassie的分数比Hannah高。Bridget说Bridget不是最高分，说明Hannah的分数比Bridge高。因此Cassie的分数最高， 其次是Hannah, 最低的是Bridget。答案是D。
Answer: C
Solution:
A semicircle has symmetry, so the center is exactly at the midpoint of the 2 side on the rectangle, making the radius, by the Pythagorean Theorem,sqrt(1*1+1*1)=sqrt(2). The area is (Pi*2)/2=Pi.
中文解析:
如下图所示: 根据股沟定理，可以计算该圆的半径为sqrt(2). (2的平方根). 因此这个半圆的面积是: 1/2 * Pi * 2=Pi. 答案是C。
Answer: E
Solution:
The number of ways from Samantha's house to City Park is 3. and the number of ways from City Park to school is 6. Since there's one way to go through City Park (just walking straight through), the number of different ways to go from Samantha's house to City Park to school3*6=18.
中文解析：
如下图所示，根据water pipe方法， 从Samantha的家到公园的西南角有3条路径。从公园的东北角到学校有6条路径。因此从Samantha的家到学校共有：3*6=18种方法。答案是E。
Answer: E
Solution:
There are 61 vertical columns with a length of 32 toothpicks, and there are 33 horizontal rows with a length of 60 toothpicks. Thus, our answer is 61*32+60*33=3932.
中文解析：
横着的每行有32根牙签，共有60+1行。因此横着摆放的牙签共有：32*61=1952根。
竖着的每列有60根牙签，共有32+1列，因此竖着摆放的牙签共有：60*33=1980根。
因此该题的答案是：1952+1980=3932根。答案是E。
Answer: B
Solution:
If the semicircle on AB were a full circle, the area would be 16Pi. Therefore the diameter of the first circle is 8. The arc of the largest semicircle would normally have a complete diameter of 17. The Pythagorean theorem says that the other side has length 15, so the radius is 7.5.
中文解析：
半圆AB的面积是8Pi, 因此该圆的直径是8，即线段AB=8. 半圆弧AC的长度是8.5Pi,因此该圆的直径是17， 即线段AC=17. 在直角三角形ABC中，根据勾股定理， BC=15. 因此BC所在的圆的半径是7.5. 答案是B。
Answer: C
Solution:
First let s=2 (where s is the side length of the squares) for simplicity. We can extend IJ until it hits the extension of AB. Call this point X. The area of triangle AXJ then is 3*4/2=6. The area of rectangle BXIC is 2*1=2. Thus, our desired area is 6-2=4. Now, the ratio of the shaded area to the combined area of the three squares is 4/(3*2*2)=4/12=1/3.
中文解析：
延长AB， IJ至X点，如下图所示：
假设每个小正方形的边长是2， 即AB=2, 由于点C是HI的中点，因此CI=1， 所以AX=AB+BX=3. XJ =2+2=4. 三角形AXJ的面积是: 1/2 * 3*4=6. 长方形BCIX的面积是：2*1=2. 因此图中阴影部分的面积三角形AXJ的面积减去长方形BCXI 的面积，即6-2=4. 三个小正方形的面积总和是：3*2*2=12. 因此答案是 4/12=1/3. （C）
Answer: A
Solution:
The radius of the ball is 2 inches. If you think about the ball rolling, you see that in the first semi circle, it loses 2Pi inches. It gains 2Pi inches in the second semi circle. It loses 2 Pi inches in the third circle. So, the departure from the length of the track means that the answer is 200Pi+60Pi+80Pi-2Pi +2Pi-2Pi=238Pi.
中文解析：
如红色圆弧所示是小球球心的路径轨迹。因小球的直径是4，半径是2， 因此其路径上的半径分别是100-2=98， 60+2=62， 80-2=78. 因此题目所求的距离是：98Pi+62Pi+78Pi=238Pi. 答案是A。
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