Answer: A

Solution:

Set up the proportion 12meals/18people=x meals/12people; Solving for x give us 8.

中文解析：

这是一个比例问题， 12份餐够18人吃，点x份餐够12人吃，即：12/18=2/12， 求得x=8. 答案是A。

Problem 4

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Answer: B

Solution:

There are C(4,3) ways to choose three starters. Thus the answer is 4.

中文解析：

从4个人种选择3个人，也可以理解为从4个人种选出1个人不参加比赛。从4个人种选出1个人有4种方法， 答案是B。

Problem 5

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Answer: D

Solution:

The remaining team will be the only undefeated one. The other 15 teams must have lost a game before getting out, thus fifteen games yielding fifteen losers.

中文解析：

从16个人中选出1个冠军，也就是排除15个人。每场比赛产生1名失败者， 排除15人，需要15场比赛。答案是D。

Problem 6

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Answer: C

Solution:

Sally made 20*55%=11 shots originally. Letting x be the number of shots she made, we have (11+x)/（20+5）=56%， Solving for x gives us x=3.

中文解析：

最初的20次中中了20*55%=11次。假设后来的5次中中了x次，则一共中了11+x次 ，其成功率是56%，可得到等式：（11+x)/(20+5)=56%. 从而求得x=3. 答案是C。

Problem 7

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Answer: B

Solution:

The maximum heart rate is 220-26=194 beats per minute. The target heart rate is then 0.8*194=155 beats per minute.

中文解析：

26岁的理论最大心跳是220-26=194. 运动员的目标心跳是：194*80%=155。答案是B。

Problem 8

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Answer: B

Solution:

The numbers are 16, 25, 34, 43, 52, 61, 70, which gives us a total of 7.

中文解析：

两位数，其个位数和十位数的和是7的有：16，25，34，43，52，61，70. 共有7个。答案是B。

Problem 9

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Answer: D

Solution:

Let the 5 numbers be a,b,c,d, and e. Thus, 48*2+c+d+e=54*5. So, c+d+e=174. Dividing by 3 gives the average of 58.

中文解析：

前两个人比总平均54各少了6，共少了12. 后三个数需要比54共大12， 平均分给3个数，则每个数需要比54大4. 即58. 答案是D。

Problem 10

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Answer: E

Solution:

Convert everything to minutes and add them together. 75+50+145+30=300 minutes. It’s 5 hours thus 5*3=15 dollars.

中文解析：

Handy Aaron帮助邻居的时间分别是: 75, 50, 145, 30 分钟。合计300分钟，即5小时，因此收入是5*3=15元。答案是E。

Problem 11

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Answer: C

Solution:

From rule 1, the largest number, 12, can be second or third. From rule 2, because there are five places, the smallest number 2 can either be third or fourth. The median, 6 can be second, third, or fourth. Because we know the middle three numbers, the first and last numbers are 4 and 9, disregarding their order. Their average is (4+9)/2=6.5 .

中文解析：

根据规则1， 12 只可能是第二个数或者第三个数；根据规则2， 2只能是第四或第五个数。根据规则3， 6不是第一个也不是最后一个。因此第一个位置的数不是12，不是2，不是6. 最后一个位置的数不是12， 不是2，不是6. 第一和最后一个位置的数只能是4或9. 其平均值是（4+9）/2=6.5. 答案是C。

Problem 12

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Answer: B

Solution:

When not being used, the cell phone uses up 1/24 of its battery per hour. When being used, the cell phone uses up 1/3 of its battery per hour. Since Niki's phone has been on for 9 hours, of those 8 simply on and 1 being used to talk, 8*(1/24)+1*(1/3) of its battery has been used up. To drain the remaining 1/3 the phone can last for 8 more hours without being used.

中文解析：

手机待机状态能持续24小时，通话状态能持续3小时，可以发现: 通话1小时，相当于待机8小时。这个手机放置了9小时，其中通话占了1小时，待机了8小时。通过1小时相当于待机8小时，因此剩下的电池可以持续24-8-8=8小时。答案是B。

Problem 13

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Answer: E

Solution:

If Bill is the oldest, then Amy is not the oldest, and both statements I and II are true, so statement I is not the true one.

If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements II and III are true, so statement II is not the true one.

Therefore, statement III is the true statement, and both I and II are false. From this, Amy is the oldest, Celine is in the middle, and lastly Bill is the youngest. This order is E.

中文解析：

第一句和第二句没有矛盾是一致的，或者都正确，或者都不正确。由于三句话中只有1句是正确的，因此第一句和第二句只能是都不正确，则第三局是正确的，即Celine 不是年龄最小的。因为第一句和第二句都不正确，那么他们的相反的内容是正确的，即Bill 不是最年长的, Amy 是最年长的。综合起来， Amy是最年长的， 其次是Celine；最年幼的是Bill。答案是E。

Problem 14

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Answer: C

Solution:

The total area of the square is 10*10=100, compute the area which is not in the quadrilateral. Separate these area with trapezoid and triangles. 100-1/2*(5+6)*3-1/2*3*7-1/2*5*4-1/2*6*10=22.5.

中文解析：

根据Ficks定律：=B/2+I-1; 边界上的点有5个，内部的点有21个。因此面积是：5/2+21-1=22.5. 答案是C。

Problem 15

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Answer: C

Solution:

The first ring around the middle tile has 6 tiles, and the second has 12. From this pattern, the third ring has 18 tiles. Of these, 6+18=24 are white and 1+12=13 are black, with a difference of 24-13=11.

中文解析：

外围再增加一圈白色的，18个。因此白色的共18+6=24个。黑色的有13个。其差值是24-13=11个。答案是C。

Problem 16

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Answer: C

Solution:

The first pitcher contains 600*1/3=200 mL of orange juice. The second pitcher contains 600*2/5=240 mL of orange juice. In the large pitcher, there is a total of 200+240=440 mL mL of orange juice and 600+600 mL of fluids, giving a fraction of 440/1200=11/30.

中文解析：

第一个有600*1/3=200ml的橙汁，第二个有600*2/5=240ml. 共440ml的橙汁。混合后的液体共600+600=1200ml. 因此混合后橙汁的比例是：440/1200=11/30. 答案是C。

Problem 17

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Answer: D

Solution:

For each person to have at least one pencil, assign one of the pencil to each of the three friends so that you have 3 left. In partitioning the remaining 3 pencils into 3 distinct groups, use “sticks and stones” to find the number of possibilities is C(5,2)=10.

中文解析：

先给每个人分一支笔，剩下的3支笔分给3个人，根据stick and stone方法， 是C（5，2） 。套用组合的公式，结果是10. 答案是D。

Problem 18

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Answer: A

Solution:

The only way to get Ben's score is with 1+3=4. Cindy's score can be made of 1+6, 2+5, 3+4, but since Ben already hit the 1,3. Cindy hit 2+5=7. Similarly, Dave's darts were in the region 4+7=11. Lastly, because there is no 7 left, Alice must have hit the regions 6+10=16, and Ellen 8+9=17.

中文解析：

5个人掷了10个飞镖，10个飞镖的分数在1-10之间，各不相同。每个人的分数和分别是：16， 4， 7， 11， 17. 从4入手，4必须分成1+3（ 不能是2+2， 因为每个飞镖的分数都不相同）。下一个从较小的7入手。7不能分成1+6，因为1已被占用，7也不能分成3+4，因为3已被占用，7只能分成2+5. 下一个从11入手， 同样的道理，11只能分成4+7. 下一个数字16只能分成6+10. 因此6是Alice。答案是A。

Problem 19

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Answer: B

Solution:

The smallest number divisible by 3,4,5,and 6, or their least common multiple, can be found to be 60. The number we are looking for is therefore 60+2=62.

中文解析：

能被3，4，5，6 都乘除的最小的数，即3，4，5，6的最小公倍数是60. 那么62除以3，4，5，6的余数都是2. 符合题意。答案是B。

Problem 20

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Answer: D

Solution:

Working backwards, if 3/4 of the chairs are taken and 6 are empty, then there are three times as many taken chairs as empty chairs, or 3*6=18. If x is the number of people in the room and 2/3 are seated, then 2/3*x=18, and x=27.

中文解析：

3/4的椅子座的有人， 1/4的椅子是空的。题目告知空的椅子是6把，则椅子共有24个。其中座人的椅子有18个。说明18个人做在椅子上。题目告知2/3的人座在椅子上，因此可以得到总人数是27人。答案是D。

Problem 21

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Answer: D

Solution:

An even number comes from multiplying an even and even, even and odd, or odd and even. Since an odd number only comes from multiplying an odd and odd, there are less cases and it would be easier to find the probability of spinning two odd numbers from 1. Multiply the independent probabilities of each spinner getting an odd number together and subtract it from 1. 1-(2/4*2/3)=1-1/3=2/3.

中文解析：

如果两个数的乘积是双数，则必须有1个数是双数。如果第一个数是双数，其概率是2/4. 第二个数是单数，双数都可，其概率是1. 这种情况下的概率是2/4 * 1，即1/2. 如果第一个数是单数，其概率是2/4，则第二个数必须是双数，概率是1/3. 这种情况下的概率是2/4*1/3，即1/6. 这两种情况下，乘积都是双数，其概率相加，是2/3. 答案是D。

Problem 22

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Answer: B

Solution:

Assume here are 5 women in the room, of which 5*2/5=2 are single , 5-2=3 are married. Each married woman came with her husband, so there are 3 married men in the room as well for a total of 5+3=8 people. The fraction of the people that are married men is 3/8.

中文解析：

参加活动的人有3种，单身女性， 已婚男性及其妻子。注意：已婚男性和已婚女性（已婚男性的妻子）的人数比值是1：1. 在女性中，单身女性的比值是2/5， 则说明单身女性和已婚女性的比值是2：3。由于已婚女性和已婚男性的人数相同，则单身女性：已婚女性：已婚男性的比值是: 2:3:3. 因此已婚男性占的比值是3/8. 答案是B。

Problem 23

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Answer: D

Solution:

For her distance to be represented as a constant horizontal line, Tess would have to be running in a circular shape with her home as the center. Since she is running around a rectangle, this is not possible, ruling out B and E with straight lines. Because J is the diagonal of the rectangle, and L is at the middle distance around the perimeter, her maximum distance should be in the middle of her journey. The maximum in A is at the end, and C has two maximums, ruling both out. Thus the answer is D.

中文解析 :

从J到K的过程中，距离J的距离是越来越大， 从K到L的过程中， 距离J的距离也是越来越大，从L到M的过程中， 距离J的距离越来越小。从M到J的过程中， 距离J的距离也是越来越小，直到0. 答案是D。

Problem 24

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Answer: C

Solution:

The area of the parallelogram can be found in two ways. The first is by taking rectangle ABCD and subtracting the areas of the triangles cut out to create parallelogram EFGH. This is (4+6)*(5+3)-2*1/2*6*5-2*1/2*3*4=80-30-12=38. The second way is by multiplying the base of the parallelogram such as FG with its altitude d, which is perpendicular to both bases. Triangle FGC is a 3-4-5 triangle so FG=5. Set these two representations of the area together. 5*d=38, so d=7.6

中文解析：

在直角三角形AHE中， 两条直角边分别是3和4， 根据勾股定理，斜边是5. HE是平行四边形HEFG的底。平行四边形的高是d. 根据平行四边形的面积公式，底*高，即5*d. 下面，我们从长方形ABCD的面积减去4个小三角形AHE， DHG，GFC，EBF的方法去求。三角形AHE的面积是6；三角形HDG的面积是15；三角形GFC的面积是6， 三角形EBF的面积是15. 长方形ABCD的面积是80. 因此平行四边形HEFG的面积是：80-6-15-6-15=38. 因此：5*d=38, 求得d=7.6 答案是C。

Problem 25

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Answer: D

Solution:

If the circle was shaded in, the intersection of the two squares would be a smaller square with half the side length, 2. The area of this region would be the two larger squares minus the area of the intersection, the smaller square. This is 4*4+4*4-2*2=28.

The diagonal of this smaller square created by connecting the two points of intersection of the squares is the diameter of the circle. This value can be found with Pythagorean or a 45°-45°-90° circle to be 2*sqrt(2). The radius is half the diameter, sqrt(2). The area of the circle is Pi*r*r=2*Pi. The area of the shaded region is the area of the two squares minus the area of the circle which is 28-2*Pi.

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中文解析：

如上图所示，， AD是4*4正方形边长的一半，即2. 在正方形ABCD中，边长是2， 则对角线是2*sqrt(2). 因此中间的圆形的半径是sqrt（2），则圆的面积是：Pi*2. 一个大正方形的面积是4*4=16，两个大正方形的面积是16*2=32. 这两个大正方形相交后，行成的小正方形的面积是2*2=4. 因此这两个大正方形相交后形成的图形的面积是：32-4=28. 阴影部分的面积是28减去圆形的面积2Pi，即28-2Pi. 答案是D。

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