Answer: C

Solution:

Suzanna's speed is 1/5. This means she runs 1/5*30=6.

中文解析：

速度是不变的，从图上看， 1mile用的是5 分钟，即1/12 小时，因此他的速度是：1/（1/12）=12 英里每小时。因此骑行半小时的距离是12/2=6英里，答案是C。

Problem 4

Answer: B

Solution:

The answer is B because the longest piece can't fit in the figure.

中文解析：

选项B中最长的是4个方格，而题目中给出的最长5个方格的没法在B中使用。答案是B。

Problem 5

Answer: D

Solution:

List them out, adding the three previous numbers to get the next number, 1,2,3, 6, 11, 20, 37, 68.

中文解析：

按照题意，这组数分别是: 1,2,3,6,11,20,37,68. 第8个数字是68. 因此答案是D。

Problem 6

Answer: A

Solution:

Each of the four hoses hose fills 24000/4=6000 gallons of water. At the rate it goes at it will take 6000/2.5=2400 minutes, or 40 hours.

中文解析：

4根管子， 每分钟，每根管子供应2.5加仑的水。要充满24000加仑，需要的时间是：24000/(4*2.5)=2400分钟，即40小时。答案是A。

Problem 7

Answer: C

Solution:

The area of a triangle is 1/2*b*h, If we let CD be the base of the triangle, then the height is AB, and the area is 1/2 *3*3=4.5.

中文解析：

三角形ACD的面积等于大三角形ABD的面积减去小三角形ABC的面积。大三角形ABD的面积: 3*6/2=9. 小三角形ABC的面积：3*3/2=4.5. 因此三角形ACD的面积是9-4.5=4.5. 答案是C。

Problem 8

Answer: B

Solution:

In a rectangle with dimensions 10*10, the new rectangle would have dimensions 11*9. The ratio of the new area to the old area is 99/100=99%.

中文解析：

假设长方形原来的长是l, 宽是w, 则新的长是1.1*l, 新的宽是0.9*w. 新的面积是：1.1*0.9*l*w=0.99*l*w. 是原来面积的0.99. 即99%。答案是B。

Problem 9

Answer: B

Solution:

Of the six shapes used to create the polygon, the triangle and octagon are adjacent to the others on one side, and the others are adjacent on two sides. In the triangle and octagon 3+8-2*1=9 sides are on the outside of the final polygon. In the other shapes 4+5+6+7-4*2=14 sides are on the outside. The resulting polygon has 9+14=23 sides.

中文解析：

三角形，4边形，5边形，6边形，7边形，8边形组合在一起。每两个形状组合是，共享的边，由于是在最终形状的内部，不计入边数的统计， 6个图形组合，有5条共同的边。总边数：3+4+5+6+7+8-5*2=23. 答案是B。

Problem 10

Answer: D

Solution:

There are 8*8=64 total squares. There are (8-1)*4=28 unit squares on the perimeter and therefore 64-28=36 NOT on the perimeter. The probability of choosing one of those squares is 36/64=9/16.

中文解析：

在边界的小方格有：8*2+6*2=28个。不在边界的小方格有：64-28=36个。因此随机选择一个小方格，不在边界的概率是：36/64=9/16. 答案是D。

Problem 11

Answer: D

Solution:

Because the pencil costs a whole number of cents, the cost must be a factor of both 143 and 195. They can be factored into 11*13 and 3*5*13. The common factor cannot be 1 or there would have to be more than 30 sixth graders, so the pencil costs 13 cents. The difference in costs that the sixth and seventh graders paid is 195-143=52 cents, which is equal to 52/13=4 sixth graders.

中文解析：

根据题意，铅笔的价格是整数。因此铅笔的价格应该是143分和195分的共同的因子。虽然1分钱是143和195的共同因子， 但如果1分钱1支铅笔，则6年级学生买了195分，即195支铅笔， 有195个学生购买。然而题目告诉我们6年级购买的学生是30人中的一些人购买了，不应该超过30，因此铅笔不能是1分钱1支。求143和195的最大公因数，是13. 则7年级学生购买人数是：143/13=11. 6年级学生购买人数是195/13=15. 15-11=4. 多4人购买。答案是D。

Problem 12

Answer: D

Solution:

The possible sums are 1+2=3; 1+4=5; 1+6=7; 3+2=5；3+4=7；3+6=9；5+2=7；5+4=9；5+6=11. Only 9 is not prime, so there are 7 prime numbers and 9 total numbers for a probability of 7/9.

中文解析：

题意要求两个数的和是质数。我们先看看有可能的和分别是：1+2=3；1+4=5；1+6=7， 3+2=5， 3+4=7， 3+6=9；5+2=7， 5+4=9， 5+6=11. 这些和中，3,5,7，11 是质数。因此题目所求的概率是：7/9. 答案是D。

Problem 13

Answer: B

Solution:

The number is divisible by 5 if and only if the number ends in 5 (also 0, but that case can be ignored, as none of the digits are 0) If we randomly arrange the three digits, the probability of the last digit being 5 is 1/3.

中文解析：

当个位数是5时，这个三位数可以被5整除。由1,3,5组成的3位数， 个位数可以是1,3,5. 因而5位于个位数的概率是1/3. 答案是B。

Problem 14

Answer: B

Solution:

The way to Temple took 50/60=5/6 hours, and the way back took 50/40=5/4 hours for a total of 5/6+5/4=25/12 hours. The trip is 50*2=100 miles. The average speed is 100/(25/12)=48 miles per hour.

中文解析：

平均速度等于总距离除以总时间。总的距离是50*2=100 英里。去程的时间是：50/60=5/6小时。返程的时间是：50/40=5/4小时。因此平均速度是：100/(5/6+5/4）=48. 答案是B。

Problem 15

Answer: D

Solution:

Limited by the amount of milk, Jordan can make at most 7/4 * 5=35/4 servings.

中文解析：

Jordan所有的食材和配方相比，最少的是milk，不足配方要求的4杯牛奶的2杯，其他的食材都超过2倍了，因此影响成品数量的是牛奶的量。根据比例关系，4杯牛奶可做5份热巧，7杯牛奶能做热巧的份数是：7/4*5=35/4. 答案是D。

Problem 16

Answer: D

Solution:

With the digits listed from least to greatest, the 3-digit integers are 138,146,226,234; 226 can be arranged in 3*2*1/2=3 ways, and the other three can be arranged in 3*2*1=6 ways. There are 3+6*3=21 3-digit positive integers.

中文解析：

三个个位数的乘积是24. 我们从小到大按顺序写出其可能的组合序列：1 3 8；1 4 6；2 2 6；2 3 4。由3个不同的数字组成的三位数排列有3！即6个。 2 2 6 ，由于2重复了2次，因此能组成的3位数排列是3！/2=3种。 共3*6+3=21种。 答案是D。

Problem 17

Answer: B

Solution:

The prime factorization of 360=2*2*2*3*3*5. If a number is a perfect square, all of the exponents in its prime factorization must be even. Thus we need to multiply by a 2 and a 5, for a product of 10, which is the minimum possible value of x. Similarly, y can be found by making all the exponents divisible by 3, so the minimum possible value of y is 3*5*5=75. Thus, our answer is 10+75=85.

中文解析：

360*x 是平方数， 360*y是立方数。写出360的质因数序列：360=2*2*2*3*3*5. 再补上2*5，即可凑成平方数，因此x=2*5即10. 360再补上3*5*5即可凑成立方数，则y=3*5*5,即75. x+y=85. 答案是B。

Problem 18

Answer: C

Solution:

The number of white tiles in the first row of 15-foot-by-15-foot is 8. The 15-foot-by-15-foot floor needs 8 rows which including white tiles. Thus, total 8*8=64 white unit files.

中文解析：

图中的7*7方格中白色小方格的数量情况：第一行4个，第二行0个，第三行4个，第四行0个。。。扩展到15*15 的大方格中， 白色小方格的规律应该是：第一行8个，第二行0个，第三行8个，第四行0个。因此15*15的大方块中，白色方格的数量是：8*8=64个。答案是C。

Problem 19

Answer: D

Solution:

There are 3 cases:

1. X is the base angle with 70 as the other base angle. X=70;

2. X is the base angle with 70 as the vertex angle , x=55;

3. X is the vertex angle with 70 as the base angle. X=40.

The 3 possible values of x are 70, 55, 40. So, 70+55+40=165.

中文解析：

在这个等腰三角形中，如果70和x都是底角，则x=70°。如果x是顶角，则x=180-70-70=40°。如果70°角是顶角，则x=(180-70)/2=55°。x的可能值是：70， 40, 55. 合计70+40+55=165°。答案是D。

Problem 20

Answer: D

Solution:

Assume the base of the triangle is on the bottom four points because a congruent triangle can be made by reflecting the base on the top four points. For a triangle with a base of length 1, there are 3 triangles. For a triangle with a base of length 2, there are 3 triangles. For length 3, there are 2. In total, the number of non-congruent triangles is 3+3+2=8.

中文解析：

以第二行的点为底，第一行的点为顶点，构造三角形。底的长度为1的不同的三角形有3个，底的长度为2的不同的三角形有3个。底的长度为3的三角形有2个。因此共有3+3+2=8个。答案是D。

Problem 21

Answer: D

Solution:

Note that 40A=75B=sum of the numbers in the array. This means that A/B=15/8 using basic algebraic manipulation.

中文解析：

40行的平均值是A， 则总数是40*A。75列的平均是B， 则总数是75*B。因此A/B=75/40=15/8 . 答案是D。

Problem 22

Answer: D

Solution:

Note that this is the same as finding how many numbers with up to three digits do not contain 1. Since there are 10 total possible digits, and only one of them is not allowed (1), each digit has its choice of 9 digits, for a total of 9*9*9=729 such numbers. However, we over counted by one; 0 is not between 1 and 1000, so there are 728 numbers.

中文解析：

个位数中不含1的数字有：2,3,4，......9,共8个。十位数中不含1的数字：个位数不含1的有：0,2,3,4,......9. 共9个。十位数上不含1的共有：2,3,4，.....9, 共8个。即：8*9=72个。百位数中不含1的数字：个位数不含1的有9个；十位数不含1的数字有9个，百位数不含1的有8个，合计：8*9*9=648个。合计：648+72+8=728. 答案是D。

Problem 23

Answer: B

Solution:

If there are x girls, then there are x+2 boys. She gave each girl x jellybeans and each boy x+2 jellybeans, for a total of x*x+(x+2)*(x+2) jellybeans. She gave away 400-6=394 jellybeans. x*x+(x+2)*(x+2) =394 =>x=13. There are 13 girls, 15 boys, and 28 students.

中文解析：

假设有x个女孩，男孩的个数是x+2个。给女孩的beans的总数是x*x个，给男孩的beans的总数是（x+2）(x+2)个。发给男孩和女孩的beans的总数是400-6=394个。即x*x +(x+2)(x+2)=394. 两个数的平方和小于400， 假设测试，求得x=13. 即女孩个数是13， 男孩是15个，共28个。答案是B。

Problem 24

Answer: E

Solution:

Because B+A=A， B must be 0. Next, because B-A=A, => 0-A=A, we get A=5. (A-1)-C=0, =>C=4; A+C=D=>5+4=9,thus D=9.

中文解析：

看个位数：B+A=A， B-A=A；则B=0， A=5. 看十位数：A+C =D ; (A-1)-C =0. 由（A-1）-C=0， A=5， 推出C=4. 由A+C=D， A=5,C=4,求得D=9. 答案是E。

Problem 25

Answer: E

Solution:

The tops of A, B, C, and D in the figure formed has sum 1+1+1+1=4 as do the bottoms. Thus, the total so far is 8. Now, one of the sides has area one, since it combines all of the heights of A,B,C,and D, which is 1. The other side also satisfies this. Thus the total area now is 10. From the front, the surface area is half, because if you looked at it straight from the front it would look exactly like A, with surface area half. From the back it is the same thing. Thus, the total is 10+1/2+1/2=11.

中文解析：

表面积分6个面，我们分别计算。上面的面积和是：1+1+1+1=4. 同理，下面的面积也是4. 前面的4个面：1/2， 1/3， 1/17， 及另外一个，合起来是1. 后面的面积也是1. 左侧面的4个侧面加起来是1/2. 同理右侧面的4个侧面加起来也是1/2. 总表面积是：4+4+1+1+1/2+1/2=11. 答案是E。

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