Answer: B

Solution:

The problem wants us to find the time of sunset and gives us the length of daylight and time of sunrise. Adding, we find that the time of sunset is 6:57am+10:24=17:21. =5：21 pm.

中文解析：

日出时间是6：57am, 白天是10小时24分钟， 因此日落的时间是： 6：57加10小时24分钟，即：5：21pm。 答案是B。

Problem 4

Answer: C

Solution:

Peter ate 1+1/2=3/2 slices. The pizza has 12 slices total. Taking the ratio of the amount of slices Peter ate to the amount of slices in the pizza, we find that Peter ate (3/2)/12=3/24=1/8 of the pizza.

中文解析：

Peter吃了1块，是1/12. 他和别人合吃了一块，因此是1/24. 总共： 3/24， 即1/8. 答案是C。

Problem 5

Answer: E

Solution:

The figure is the same height on both sides, so the sum of the lengths contributing to the height on the left side will equal the sum of the lengths contributing to the height on the left side. 1+1+1+2+x=1+2+1+6 ; =>x=5.

中文解析：

这个图形从左边看和从右边看高度是一致的。右边的高度是： 1+2+1+6=10； 左边的高度是： 1+1+1+2+X. 即5+X. 因此X=10. 答案是E。

Problem 6

Answer: E

Solution:

The area of the photograph is 8*10=80 square inches. The height of the whole frame (including the photograph) would be 8+2+2=12, the width of the whole frame would be 10+2+2=14. Therefore, the area of the whole figure would be 12*14=168 square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80=88.

中文解析：

如上图所示： 题目所求的border部分即为图中所示的阴影部分的面积。 大长方形的长是2+10+2=14； 宽是2+8+2=12. 小长方形的长是10，宽是8. 阴影部分的面积即为大长方形的面积减去小长方形的面积。 即： 14*12-10*8=88. 答案是E。

Problem 7

Answer: B

Solution:

Isabella wants an average grade of 95 on her 4 tests; this also means that she wants the sum of her test scores to be at least 95*4=380. She's already taken two tests, which sum to 97+91=188, which means she needs 192 more points to achieve her desired average. In order to minimize the score on the third test, we assume that Isabella will receive all 100 points on the fourth test. Therefore, the lowest Isabella could have scored on the third test would be192-100=92.

中文解析:

前两次考试成绩分别是97和91， 第四次最高可以是100， 四次考试成绩的平均分目标是95. 因此第三次考试的成绩可以是： 92分。 答案是B。

Problem 8

Answer: D

Solution:

First ,use the 20% discount of coupon, then use the half price of the advertise. Your should pay (1-20%)*0.5=0.4 for any item. Thus the discount is 1-0.4=0.6=60%.

中文解析：

半价后的价格是50%。 再使用20% 的额外折扣券，则购买价格是原始价格的：50%*80%=40%。 即60% off. 答案是D。

Problem 9

Answer: C

Solution:

Let the number of two-legged birds be x and the number of four-legged mammals be y. We can now use systems of equations to solve this problem.

Write two equations:

2x+4y=522;

x+y=200;

solving the equations, we get x=139.

中文解析：

假设两条腿的动物有x个，四条腿的动物有y个。 这些动物的头数有: x+y=200个。 这些动物的腿数有: 2x+4y=522.

求解这个方程组，解得x=139, y=61. 因此两条腿的动物有139个。 答案是C。

Problem 10

Answer: D

Solution:

For this problem, all we need to do is find the amount of valid 4-digit numbers that can be made from the digits of 2012. There can be only two leading digits, namely 1 or 2.

When the leading digit is 1, you can make 3 such numbers.

When the leading digit is 2, you can make 6 such numbers.

Summing the amounts of numbers, we find that there are 9 such numbers.

中文解析：

四位数的千位数必须是1或者2. 如果千位数是1： 剩下的3个数是0，2，2， 由于2个2 ，因此是3！/2 ，即该种情况下有3种不同的安排。 如果千位数是2， 剩下的3个数是0，1，2 . 有3！，即6种不同的安排。 综合起来： 有3+6=9种不同的安排，答案是D。

Problem 11

Answer: D

Solution:

Notice that the mean of this set of numbers, in terms of x, is: (3+4+5+6+6+7+x)/7=(31+x)/7.

Because x should be a whole number, thus x could be 4, 4+7, 4+7*2…. Because we know that the mode must be 6 (it can't be any of the numbers already listed, as shown above, and no matter what x is, either 6 or a new number, it will not affect 6 being the mode), and we know that the mode must equal the mean, we can set the expression for the mean and 6 equal: (31+x)/7=6 , =>x=11.

中文解析：

这组数的Mode,是唯一的，因此x不可能是3，4，5，或者7. 同时注意x只能是正整数。x可以是比3小的正整数，可以是6， 或者是比7大的正整数。 如果x比3小，则这组数的mode=6, 这组数的median是 5. median和mode不相等，不符合题意。 如果x=6， 则mode=6, median=6, mean=37/7 . mean和median，mode不相等，不符合题意。 如果x比7大， mode=6, 则mean也是6，即（3+4+5+6+6+7+x)/7=6. 求得x=11. 答案是D。

Problem 12

Answer: A

Solution:

3^1=>3; 3^2=>9; 3^3=>7; 3^4=>1; 3^5=>3…

We observe that there is a pattern for the units digit which recurs every four powers of three. Using this pattern, the remainder of 2012/4 is 0, thus, the units digit of 3^2012 is 1. The units digit of 13^2012 is 1 too.

中文解析:

各位数是3. 我们找找3的乘方的规律。 3的1次方是3， 3的二次方是9， 3的3次方的各位数是7， 3的4次方的各位数是1， 3的五次方的各位数是3，和3的1次方的个位数相同，即循环的规律出现了，每4次循环1次。 2012 /4的余数是0. 因此3的2012次方的各位数是1. 答案是A。

Problem 13

Answer: C

Solution:

We assume that the price of the pencils remains constant. Since the price of the pencils is more than one penny, we can find the price of one pencil (in cents) by taking the greatest common divisor of 143 and 187, which is 11. Therefore, Jamar bought 143/11=13 pencils, d Sharona bought 187/11=17 pencils. Thus, Sharona bought 17-13=4 more pencils than Jamar.

中文解析：

买同样的铅笔，一个人花了143分，另一个人花了187分。 因此铅笔的单价应该是143和187的公因数。 这两个数的最小公因数（GCF)是11. Jamar买了143/11=13根铅笔， Sharona买了187/11=17根铅笔。 多买17-13=4根。 答案是C。

Problem 14

Answer: B

Solution:

This problem is very similar to a handshake problem. We use the formula n(n-1)/2 to usually find the number of games played (or handshakes). Now we have to use the formula in reverse.

So we have the equation n(n-1)/2=21 . Solving, we find that the number of teams in the BIG N conference is 7.

中文解析：

假设有n个球队， 每个球队之间仅安排一场比赛，则比赛的总场次应该是C（n,2)次, 即n*（n-1）/2次。 题目告知是21次，即n*(n-1)/2=21. 可以求得n=7. 答案是B。

Problem 15

Answer: D

Solution:

To find the answer to this problem, we need to find the least common multiple of 3,4,5,6. The least common multiple of the four numbers is 60, and by adding 2, we find that that such number is 62.

中文解析：

这个数除以3，4，5，6后的余数都是2. 假设这个数是n, 则n-2能被3，4，5，6整除。求3，4，5，6的最小公倍数， 是60. 因此这个数是62. 答案是D。

Problem 16

Answer: C

Solution:

In order to determine the largest number possible, we have to evenly distribute the digits when adding. The two numbers that show an example of this are 97531 and 86420. The digits can be interchangeable between numbers because we only care about the actual digits. Only C is OK .

中文解析：

这两个5位数都尽量大，则其和能最大。 为了让这两个5位数最大，尽量让高位的数字大。 其万位数分别是9和8. 千位数分别是7和6， 百位数是5和4， 十位数是3和2， 个位数是1和0. A选项的万位数是7，不符合要求。 B选项的百位数是7， 不符合题意，百位数必须是5或4. D选项的百位数是2 也不符合题意。 E选项的十位数是0也不符合题意。 答案只有C。

Problem 17

Answer: B

Solution:

The first answer choice A(3), can be eliminated since there must be 10 squares with integer side lengths. We then test the next smallest side length which is 4. The square with area 16 can be partitioned into 8 squares with area 1 and two squares with area 4, which satisfies all the conditions of the problem. Therefore, the smallest possible value of the length of the side of the original square is 4.

中文解析：

由于分成的10个小正方形，至少有8个面积是1， 则10个小正方形的面积大于10. 因此，原始的大正方形的面积要大于10，其边长大于3. 如果大正方形的边长是4， 其面积是16. 减去8个面积是1的正方形后，还剩下的面积是8. 可以分成2个面积是4的小正方形。 符合题意，原始正方形的边长最小可以是4. 答案是B。

Problem 18

Answer: A

Solution:

The problem states that the answer cannot be a perfect square or have prime factors less than 50. Therefore, the answer will be the product of at least two different primes greater than 50. The two smallest primes greater than 50 are 53 and 59. Multiplying these two primes, we obtain the number 3127, which is also the smallest number on the list of answer choices.

中文解析：

这个数的最小的质因数（prime factor）比50大。 比50大的最小的prime number是53. 由于这个数不是prime number, 因此这个数不能是53。这个数不是square, 因此也不能是53*53. 比50大的prime number 最小的两个分别是53和59. 因此这个数是53*59=3127. 答案是A。

Problem 19

Answer: C

Solution:

Let n be the number of marbles, there are n-6 red marbles, n-8 green marbles,n-4 blue marbles. At the same time (n-6)+(n-8)+(n-4)=n. thus, n=9.

中文解析：

假设有n个marbles. 有n-6个红色的， n-8个绿色的，n-4个蓝色的。 另外n=(n-6)+(n-8)+(n-4). 求得n=9.

Problem 20

Answer: B

Solution:

The value of 7/21 is 1/3. 5/19 is less than 5/15 (5/15=1/3). 9/23 is greater than 9/27(9/27=1/3). Thus 5/19 <7/21 <9/23.

中文解析：

7/21=1/3. 5/19 < 5/15 =1/3. 因此 5/19 < 7/21. 9/23 >9/27=1/3. 因此 9/21>7/21. 因此答案是B。

Problem 21

Answer: D

Solution:

If Marla evenly distributes her 300 square feet of paint between the 6 faces, each face will get 300/6=50 square feet of paint. The surface area of one of the faces of the cube is 10*10=100 square feet. Therefore, there will be 100-50=50 square feet of white on each side.

中文解析：

正方体的边长长是10， 因此每个面的面积是10*10=100. 绿色的颜料可以涂的面积是300，平分到每个面，则每个面可以涂300/6=50的绿色。 每个面是100，绿色部分涂50，剩下的面积是100-50=50 平方英尺。 答案是D.

Problem 22

Answer: D

Solution:

First, we find that the minimum value of the median of will be 3 . Then, we find that the maximum value of the median of R will be 9. The median could be 3, 4, 5,6,7,8,9. Thus the answer is 7.

中文解析：

9个数字的中位数是第5个。 这组数已知6个，如果另3个数都比2小，这时的中位数最小，是3. 如果另外3个数都比14大，则这时的中位数最大， 是9. 在3和9之间，3，4，5，6，7，8，9都可能是中位数，共有7个数都有可能。 因此答案是D。

Problem 23

Answer: C

Solution:

Area of equilateral triangle is s*s*sqrt(3) which s is the side length. A hexagon is composed of 6 little equilateral triangles. Let the side length of the triangle be 2s, the side length of the hexagon is s. The area of little equilateral (side length is s) of hexagon is 1/4 of the area of bigger equilateral triangle. (side length is 2s). Thus the area of hexagon is 6*1/4*4=6.

中文解析：

三角形的周长和六边形的周长相同，因此三角形的边长是六边形边长的2倍。 把六边形分成6个三角形，其中每个小三角形都是等边三角形，六边形中的小三角形的边长是大等边三角形的边长的一半，则小三角形的面积是大三角形面积的1/4. 大三角形的面积是4，因此小三角形的面积是1， 六边形有6个小三角形，面积是6. 答案是C。

Problem 24

Answer: A

Solution:

Draw a square around the star figure. The side length of this square is 4, because the side length is the diameter of the circle. The square forms 4-quarter circles around the star figure. This is the equivalent of one large circle with radius 2, meaning that the total area of the quarter circles is 4Pi. The area of the square is 16. Thus, the area of the star figure is16-4Pi. The area of the circle is 4Pi. Taking the ratio of the two areas, we find the answer is (4-Pi)/Pi.

中文解析：

如上图所示： 正方形的边长是圆形半径的2倍，即4. 正方形的面积是： 4*4=16.

圆形的面积是： Pi*2*2=4Pi. 4个1/4圆的面积合起来即是1个圆形的面积4Pi。 题目所求星形的面积是正方形的面积减去4个1/4 圆形的面积,即： 16-4Pi . 其和圆形的面积的比值是: (16-4Pi)/4Pi。 即： （4-Pi)/Pi。 答案是A。

Problem 25

Answer: C

Solution:

The total area of the four congruent triangles formed by the squares is 5-4=1. Therefore, the area of one of these triangles is 1/4. The height of one of these triangles is a and the base is b. Using the formula for area of the triangle, we have ab/2=1/4. Multiply by 2 on both sides to find that the value of ab is 1/2.

中文解析：

位于大正方形和小正方形之间的四个小的直角三角形的面积之和是: 5-4=1. 其中任意一个小直角三角形的底是a,高是b， 面积是1/2*ab. 因此： 4*（1/2 *ab)=1, 求得ab=1/2. 答案是C。

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