新GRE数学模拟练习题(3)

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GRE数学模拟题目

GRE数学模拟题目近年来，GRE数学部分在考题的设计上越来越注重考察考生的逻辑推理能力和问题解决能力。

下面将为大家提供一些模拟GRE数学题目，并对这些题目进行详细的解析。

题目一：某公司的年度销售额从1997年的50万美元增加到2000年的80万美元。

如果假设年销售额以4%的年增长率递增，那么请推算出该公司在1997年的年度销售额是多少？解析：假设1997年的年销售额为x万美元。

根据题意，该公司的年销售额从1997年到2000年增长了80 - 50 = 30 万美元。

根据题设，年增长率为4%，可得以下等式：x * (1 + 0.04)^3 = x + 30化简得：1.04^3 * x = x + 301.1259 * x = x + 300.1259 * x = 30x = 30 / 0.1259 ≈ 238.39因此，该公司在1997年的年度销售额约为238.39 万美元。

题目二：将一个名为A的集合中的元素逐个地添加到一个名为B的集合中，每次添加时，元素个数增加的量以等比数列递增，首项为1，公比为2。

如果操作6次后，集合B中的元素个数为121个，请问集合A原本有多少个元素？解析：设集合A原本有n个元素。

根据题设，我们可以列出公式：1 +2 + 2^2 + 2^3 + 2^4 + 2^5 = n + 1212^6 - 1 = n + 12164 - 1 = n + 12163 = n + 121n = 63 - 121 = -58由于集合中元素个数不能为负数，所以集合A原本的元素个数不能为-58。

因此，这道题目是不符合实际情况的，解不存在。

题目三：已知一组数据为 {2，4，6，8，10}，若要将该组数据的每个元素都除以相同的正整数x，使得得到的结果仍然构成一个等差数列，求x的最小值。

解析：首先计算原数据元素间的差值为2。

如果要将这组数据除以x得到一个等差数列，那么除数x应该满足以下条件：2 / x = 4 / x - 2 / x = 6 / x - 4 / x = 8 / x - 6 / x = 10 / x - 8 / x化简得：2 / x = 2 / x = 2 / x = 2 / x = 2 / x由此可得x的最小值为2。

2024 GRE考试必备数学历年真题练习

2024 GRE考试必备数学历年真题练习在GRE数学部分的备考过程中，历年真题的练习是非常重要的一环。

通过针对性的练习，考生可以熟悉考试题型，了解考点，提升解题速度和准确性。

本文将为大家提供2024年GRE考试的数学历年真题练习，帮助考生更好地备考。

1. 整数1.1 题目选择下列哪个数是正偶数？(A) -12(B) -5(C) 0(D) 9(E) 271.2 解析正偶数是指能够被2整除的正整数。

从选项中排除负数，在0和正数中，只有0能够被2整除，因此答案选(C)。

2. 几何2.1 题目下图中，正方形ABCD的边长为3。

点E是线段BC的中点，点F是线段BD上的一点，且AF的长度为3。

求射线AF与线段CE的交点P到点E的距离。

[图片描述：一个正方形ABCD，边长为3，线段BC的中点为E，线段BD上的一点为F，AF的长度为3]2.2 解析首先，可以得出正方形ABCD的对角线AC的长度为3的开平方乘以2，即AC=3乘以根号2。

由于AE与CF平行且等长，射线AF可以看作与线段BE平行且等长。

因此，三角形BEP是等腰直角三角形，所以BP = EP = EC的一半。

又因为BC=3，所以EC=3/2。

因此，点P到点E的距离为1.5个单位。

3. 概率与统计3.1 题目某次测试的成绩服从正态分布，平均成绩为80分，标准差为5分。

已知一个学生的成绩在85分以上的概率为0.841，求这个学生的成绩。

3.2 解析根据正态分布的性质，均值加上标准差得到的分数对应的概率是大约0.841。

因此，这个学生的成绩应该在平均成绩80分加上标准差5分的位置，即85分。

通过以上三个部分的例题，希望能够帮助到考生更好地了解2024年GRE考试数学部分的题型和解题思路。

在备考过程中，考生还需深入学习数学知识，掌握解题技巧，并进行大量真题练习，提升解题能力。

祝愿各位考生在考试中取得好成绩！。

gre考试例题

gre考试例题GRE考试的全称为Graduate Record Examination，是一项针对研究生和商学院申请者的标准化考试，主要测试英语语言能力、数学推理能力和批判性思维能力。

以下是GRE数学考试的一些经典例题：1.如果一组数据包含3个数：2，4，9，那么这组数据的第40百分位数是：A. 2B. 4C. 5D. 9E. 202.函数y = f(x)在x = c处的导数f'(c)表示函数在c点的切线斜率。

如果f'(c) = 0，则c可能是函数的拐点。

已知函数y = x^3在x = c处的导数为1，则c等于：A. -1B. 0C. 1D. 2E. -2/33.在等差数列{a_n} 中，a_3 + a_8 > 0，则一定有：A. a_1 + a_10 > 0B. a_6 > -a_7C. a_6 > a_5D. a_1 + a_11 > 0E. a_2 + a_9 > 04.一个箱子中有大小相同的红球、白球和黄球，已知红球10个，白球8个，黄球若干个。

某人闭着眼睛从中随机取出8个球，取出红球和白球的个数刚好和取出黄球的个数相等，则箱子里黄球的个数为：A. 8B. 10C. 12D. 14E. 165.一个正整数N的所有因数中，只有两个是素数，则称N为“半素数”。

例如，28的所有因数是1、2、4、7、14和28，其中素数有2和7，因此28是一个“半素数”。

小于30的所有“半素数”之和为：A. 206B. 273C. 359D. 431E. 453。

新GRE数学代数模拟考试练习题

新GRE数学代数模拟考试练习题1.正整数x，下面哪个选项不和3x相等我选的是E：7-x(sure)2.X~3 * y = 10 ~6 (y > 1), 问X 与 10~2比大小解：x=10~2/y~1/3y>1则y~1/3>1 所以还是10~2大选B3.数列：a1=3, a2=6, a(n)= a(n-1)/a(n-2)，问：a(150)=?解：3, 6, 2, 1/3, 1/6, 1/2, 3, 6, (每6次一个循环，答案应该是1/2吧)另一版本：前人几经有误,我的是：a1=2, a2=6, an=a(n-1)/a(n-2), 求a1502, 6, 3, 1/2, 1/6, 1/3 , 2, 6, 3, …所以我的答案是1/3 (大家看清楚A1的值，自己判断吧)4. 125w+25x+5y+z=264,x,y,z,w,are nonnegative integrate,and no more than 5,what is w+x+y+z?解：用短除法把256写成五进制就是2024，则得到x+y+z+w=2+0+2+4=85.a * x平方+B*X+k=0(a和b已知，k未知)，给出一个X的值，问另一个。

简单，解出K后，再解出X26.a,b,c,-5,-10的平均数和a,b,c,5,10的平均数之差是多少?解：在考场遇到时看清楚谁在前。

答案是-6 ，也许是6。

7. F(X)=2的2X-1方，求F(3+X)F(3-X)解：2的10次方8.-7<=x<=5-5<=y<=3问x^2-y^2的值?(转载自http://，请保留此信息。

)解：当X= -7 ，Y= 0 时，49。

9.有个公式很重要。

求M到N之间是Q的倍数的数有多少个?公式是： [(该范围内Q的倍数-该范围内Q的最小倍数)/Q ] +1今天我碰到两个这样的题，多亏有这个公式，要不然就费劲了10.一个数，被9整除得x1+x2+x3,被12整除得x2+x3,则这个数至少为?能被x1整除?答案：369(x1+x2+x3)=12(x2+x3) x1=3(x2+x3)……..11.数列a1,a2,...a10.除了第一项外的各项都是其前一项的1/2。

gre测试题及答案

gre测试题及答案
GRE测试题及答案
1. 阅读理解题
阅读下面的文章，然后回答问题。

文章：
“在19世纪末，随着工业化的迅速发展，城市化进程加快，导致了人口从农村向城市大规模迁移。

这一现象不仅改变了社会结构，也对经济和文化产生了深远影响。

”
问题：
根据文章，19世纪末城市化进程加快的主要原因是什么？
A. 人口增长
B. 社会结构变化
C. 工业化发展
D. 文化影响
答案：C
2. 词汇题
从下列选项中选择一个与“innovative”意思最接近的词。

A. Traditional
B. Conservative
C. Conventional
D. Creative
答案：D
3. 数学题
如果一个数的两倍加上3等于15，那么这个数是多少？
A. 3
B. 4
C. 5
D. 6
答案：B
4. 逻辑推理题
所有的猫都是哺乳动物。

如果一个动物不是哺乳动物，那么它不可能是猫。

以下哪项陈述与上述信息相矛盾？
A. 所有的狗都是哺乳动物。

B. 一只鸟不是猫。

C. 一只猫是哺乳动物。

D. 一只不是哺乳动物的动物不是猫。

答案：A
5. 写作题
请根据以下提示写一篇短文，描述你认为的全球化对教育的影响。

提示：
- 全球化使得教育资源更加丰富。

- 全球化促进了不同文化之间的交流。

- 全球化可能导致本土文化的丧失。

（此处省略写作内容）
结束语：以上是GRE测试题及答案的示例，希望能够帮助考生更好地准备GRE考试。

gre练习题

gre练习题GRE（Graduate Record Examinations）是一项广泛用于研究生院入学申请的标准化考试，它包括了数学、阅读和写作三个部分。

以下是一些模拟练习题，可以帮助你准备GRE考试。

# 数学部分练习题1. 整数问题如果一个整数除以4余1，除以5余1，那么这个整数加1后一定是5的倍数。

这种说法正确吗？为什么？2. 百分比问题如果一个商品打8折后的价格是原价的80%，那么原价与打折后价格的差额占原价的百分比是多少？3. 几何问题一个圆的半径是10厘米，求这个圆的面积。

4. 代数问题如果方程 \( ax^2 + bx + c = 0 \) 有两个实数根，且 \( a \), \( b \), \( c \) 都是正数，那么 \( b^2 - 4ac \) 必须大于、等于还是小于0？5. 概率问题一个袋子里有5个红球和3个蓝球。

如果随机抽取2个球，至少有一个是红球的概率是多少？# 阅读部分练习题1. 主旨大意题阅读以下段落，并概括其主旨大意："In recent years, the debate over the role of technologyin education has intensified. Advocates argue that incorporating technology into the classroom can enhance learning experiences and prepare students for the digital age. Critics, on the other hand, contend that an over-reliance on technology can detract from critical thinking andinterpersonal skills."2. 推断题根据上述段落，推断作者可能对技术在教育中的作用持什么态度？3. 词汇题段落中提到的“enhance”一词，最接近的同义词是什么？4. 细节理解题根据段落，哪些论点是支持者提出的？哪些是批评者提出的？5. 逻辑关系题段落中提到的两种观点之间存在什么逻辑关系？# 写作部分练习题1. 论证有效性分析阅读以下论证：“由于越来越多的人选择在线购物，实体店铺将很快消失。

GRE数学的模拟试题

GRE数学的模拟试题GRE数学的模拟试题1. x+y=5&2x+2y=8之间最短距离与1比较<12 .3/0.0001 与 3/0.000099 比大小?(答案：<)3. 在一个图表题里考到了median。

这题比较不好做，还是罗马数字题。

是有关选民选举的比例，两块饼饼统计图，一饼是参选人x,y的支持率，另一块是选民们的收入income (?)。

从图中收入少于3000的选民有58% ，所以说选民收入median在收入少于3000的里面。

4. 有一题问下面这个数里能找出的最2的最大次方的factor 是多少?(2^5)(12^10)(18^6)，指数可能不是这个了，不过意思是这个意思。

5.1-10中选出两个数，可重复，问是都是偶数的概率。

(答案：3/4)6.以40miles/hour速度经过一1.5miles的路，若超速则罚款fine=50+(速度-40)*10，现一人用108秒通过此路，问她的'fine=?(key 150 )7.xyz togather finish the task for 9 hour, xy togather need 12 hour,z alone needs ? hour. key 368. 直线l.在X轴截距是3，在Y轴截距是4。

直线m.在X轴截距是4，在X轴截距是3。

比两个直线的sloop. 注意都为负 m19. 从一堆6个什么东东(blesket?不认识的单词)里取4个共会有15种不同的可能，如果从8个里面取4个会比从6个里面取多多少种可能?我选的是55.这题有点怪，不知为什么它还要把15说出来。

难道是我理解有误?10. 一个表3分钟慢一秒钟，问慢3分钟要过多少分种?(答案：540分钟 )。

gre模拟考试题及答案

gre模拟考试题及答案GRE（Graduate Record Examinations）模拟考试题及答案GRE模拟考试题一、词汇题（Vocabulary）1. The professor's lecture was so ________ that the students were captivated by every word.A) mundaneB) enthrallingC) tediousD) inconsequential2. Despite the ________ of his argument, the lawyer was unable to convince the jury.A) cogencyB) fallacyC) redundancyD) triviality答案解析：1. 正确答案：B) enthralling解释：enthralling 意为“迷人的”，符合句子中“学生们被每一句话吸引”的语境。

2. 正确答案：A) cogency解释：cogency 意为“说服力”，尽管律师的论点很有说服力，但未能说服陪审团。

二、阅读理解题（Reading Comprehension）Passage:The Renaissance was a period of great cultural change and achievement in Europe that spanned the period roughly from the 14th to the 17th century. It marked the transition from the Middle Ages to Modernity, and during this time, there was a renewed interest in science, art, and literature.Question:What was the Renaissance known for?A) The decline of cultural achievementsB) The transition from the Middle Ages to ModernityC) The focus on religious themes in artD) The lack of interest in science and literature答案解析：正确答案：B) The transition from the Middle Ages to Modernity 解释：文章明确指出文艺复兴是从中世纪到现代性的过渡时期，标志着文化的巨大变化和成就。

GRE数学模拟的练习题

GRE数学模拟的练习题
GRE数学模拟的练习题
GRE数学模拟的练习题
1、n个数从小到大排列，求/4，设商为i，余数为j，则可求得1st Quartile为：/4+j/4
2、4个，2个?的排列方式 15
3、 5双袜子，同时去2只，刚好配对的概率。

4、40人说French,60人说Russian,80人说Italy,说两种语言的有50人,说三种语言的有10人. 共有125人,问不说这些语言的`有几人. Key:125-=15
5、等腰直角三角形边长2加2倍根号2，求面积。

6、某种溶液浓度为125gram per liter, 转换成 ounce per gallon,求表达式。

已知 1 ounce=28.xxx gram and 1 gallon=3.875 liter
7、x,y,z 均方差为d, 求x+10,y+10,z+10的均方差
8、1的概率是0.8,2的概率是0,6,问是1或是2或是both的概率,1-0.60.8=0.92.
9、还有一组测量数据中,12.1比mean低1.5个标准差,17.5比mean高3.0个标准方差.问mean是多少.13.9
10、图表题,1992年总和是50,96年是60,每年至少增长1,问最大的年增长:7.0。

GRE(QUANTITATIVE)计算题模拟试卷3(题后含答案及解析)

GRE（QUANTITATIVE）计算题模拟试卷3(题后含答案及解析) 题型有：1. 知识模块：计算6．x/4 = -Solve for x.正确答案：-24解析：To solve this problem, multiply both sides by 4 to get rid of the fraction and isolate the x on the left side: x = -24. 知识模块：计算7．If x= 15, then 4x-_____= 42正确答案：18解析：You are given the value of x, and asked to calculate a missing number in the equation. Because x = 15, then 4x = 60. The equation is now 60 -(some number)= 42. The difference between 60 and 42 is 18. 知识模块：计算8．Two trains running on parallel tracks are 600 miles apart. One train is moving east at a speed of 90 mph, while the other is moving west at 75 mph. How long will it take for the two trains to pass each other?正确答案：3.64 hours解析：This is a standard Rate ×Time = Distance problem. Since the two trains start 600 miles apart, the combined distance traveled by both trains must equal 600. Using the R ×T = D formula, you know that(Rate of Train 1 ×Time of Train 1)+(Rate of Train 2 x Time of Train 2)= 600. You are given that the rate of travel is 90 mph for the first train and 75 mph for the second train, and the distance traveled is 600 miles; therefore, you must solve for T, as follows:90T+ 75T= 600165T= 600T =(approximately)3.64 hours 知识模块：计算9．3(x - 4)= 5x -Solve for x.正确答案：4解析：To solve this problem, first do the multiplication on the left side of the equation to get 3x - 12 = 5x - 20. Next, put the like terms together. To do this, subtract 3x from both sides, and add 20 to both sides to get 8 = 2x. Divide both sides by 2 to get x = 4. 知识模块：计算10．For x = 4, 3x2 - 5x + 9 =_____正确答案：37解析：To solve the equation, substitute 4 for x:3(42)- 5(4)+ 9 =3(16)- 20 + 9 = 48 - 20 + 9 = 37 知识模块：计算11．(5X3 + 3x - 12)-(2x3 - 6x + 17)=_____正确答案：3x3 + 9x - 29解析：To add or subtract polynomials, combine like terms(remember to keep track of the negative signs!):(5x3 + 3x - 12)-(2x3 - 6x + 17)(5x3 - 2x3)+(3x + 6x)-(17 + 12)3x3 + 9x - 29 知识模块：计算12．(4x2 + 2x)(x - 6)=_____正确答案：4x3 - 22x2 - 12x解析：Use the Distributive Property to multiply each term of one polynomial by each term of the other(remember to use the FOIL method).(4x2 + 2x)(x - 6)First terms:(4x2)(x)= 4X3Outside terms:(4x2)(-6)= -24x2Inside terms:(2x)(x)= 2x2Last terms:(2x)(-6)= -12xNow place the terms in decreasing order of the exponents:4x3 - 22x2 - 12x 知识模块：计算13．What are the solution sets for x2 + 2x - 48?正确答案：(x - 6)and(x + 8)解析：Find two numbers whose product is -48 and sum is 2. 8 and -6 are the only possible numbers. Therefore, the solution sets are(x - 6)and(x + 8). 知识模块：计算14．(x - 4)and(2x + 3)are the solution sets for what equation?正确答案：2x2 - 5x - 12解析：The solution sets are given, so multiply the two sets together to find the original equation, using the FOIL method:(x - 4)(2x + 3)= 2x2 + 3x - 8x - 12= 2x2 - 5x - 12 知识模块：计算15．x- 2y = 14 x- 4y = -8正确答案：x= 36y= 11解析：When solving systems of equations, the best thing to do first is to isolate one of the variables. In this problem, you can do so by changing the sign on the bottom equation:x - 2y = 14 -x + 4y = 8Add the two equations together(note that the x terms cancel out):2y= 22y= 11Choose one of the original equations and substitute 11 in for y. Solve for x:x- 2(11)= 14x- 22 = 14x= 36It is a good idea to test your answers by substituting x and y values into both of the original equations. 知识模块：计算16．4x - 2y = 6 -6x + 5y= 7正确答案：x=11/2y=8解析：This problem is a little trickier than the first, as you cannot simply changethe sign of one of the equations to isolate one of the variables. In this situation, you have to make the coefficients the same through multiplication. Since you know that 4 and 6 both go into 12, use the x term. Multiply the top equation by 3, and the bottom by 2:12x - 6y = 18 -12x + 10y = 14Add the two equations together(note that the x terms cancel out):4y= 32 y=8Finally, choose one of the original equations, substitute 8 for y, and solve for x.4x - 2(8)= 6 4x - 16 = 6 4x= 22x=22/4, or 11/2 知识模块：计算17．3x-y = 18 4x = 24 - 6y正确答案：x=6y=0解析：The first step is rearranging the equations to align like terms:3x - y=18 4x + 6y = 24Multiply the top equation by 6 and add the equations:18x - 6y = 1084x + 6y = 2422x = 132x =6Now choose one of the original equations, substitute 6 in for x, and solve fory:3(6)-y= 18 18 -y= 18 -y=0 y=0 知识模块：计算18．8(y + x)= 12 4x - 3y = -22正确答案：x=-5/2y=4解析：First, distribute the 8 to get 8y + 8x = 12. You can then multiply the second equation by -2 to isolate one of the variables, and rearrange the equations to line up the like terms:8x + 8y = 12 -8x + 6y= 44Add the equations together(note that the x terms cancel out):14y = 56 y = 4Now choose one of the original equations, substitute 4 for y, and solve for x.8x + 8(4)= 12 8x + 32 = 128x = -20x=[*]x=[*] 知识模块：计算19．4x - y = 63 3y + x = 6正确答案：x=15y=-3解析：Line up the like terms in both equations:4x - y = 63 x + 3y = 6Multiply the top equation by 3 and add the equations:12x - 3y = 189x + 3y = 6Note that the y terms cancel out:13x = 195 x = 15Now substitute 15 for x in one of the equations.x + 3y = 6 15 + 3y= 6 3y= -9 y=-3 知识模块：计算20．For -5xmeans “less than or equal to” and x + 3 xx, what is the value of f(2)?正确答案：5解析：To solve, substitute 2 for x in the function:f(2)=f(2)=f(2)=10/2 f(2)= 5 知识模块：计算29．For the function f(x)= x2 + x, what is the value of f(-5)?正确答案：20解析：To solve, substitute -5 for x in the function:f(-5)=(-5)2 +(-5)f(-5)= 25-5f(-5)= 20 知识模块：计算30．What is the y-intercept of the line with the equation 2y = 4x + 6?正确答案：3解析：First, rearrange the equation into the slope-intercept form by isolating y on the left side; divide both sides by 2:y = 2x + 3You know that in the slope intercept formula, y = mx + b, b is the y-intercept. Because b = 3, the correct answer is 3. 知识模块：计算。

GRE(QUANTITATIVE)综合模拟试卷3(题后含答案及解析)

GRE（QUANTITATIVE）综合模拟试卷3(题后含答案及解析) 题型有：1. 2.1．正确答案：B解析：In this question you are asked to compare the area of a parallelogram with an area of 24, given two side lengths and the measure of one interior angle of the parallelogram. Since the measure of the interior angle given is 125°, you can conclude that the parallelogram is not a rectangle. Recall that the area of a parallelogram is found by multiplying the length of a base by the height corresponding to the base. It is helpful to draw the vertical height from vertex C to base AD of the parallelogram, as shown in the figure below. Note that the newly drawn height is a leg in a newly formed right triangle. The hypotenuse of the triangle is a side of the parallelogram and has length 6. Thus, the leg of the triangle, which is the height of the parallelogram, must be less than the hypotenuse 6. The area of the parallelogram is equal to the length of base AD, which is 4, times the height, which is less than 6. Since the product of 4 and a number less than 6 must be less than 24, the area of the parallelogram must be less than 24. Quantity B is greater than Quantity A, and the correct answer is Choice B.2．正确答案：A解析：From the histogram, you can observe that all of the measurement intervals are the same size, the distribution has a peak at the measurement interval 6-10, and more of the measurement intervals are to the right of the peak than are to the left of the peak. Since in the histogram the 95 measurements have been grouped into intervals, you cannot calculate the exact value of either the average or the median; you must compare them without being able to determine the exact value of either one. The median of the 95 measurements is the middle measurement when the measurements are listed in increasing order. The middle measurement is the 48th measurement. From the histogram, you can see that the measurement interval 1-5 contains the first 15 measurements, and the measurement interval 6-10 contains the next 35 measurements(that is, measurements 16 through 50). Therefore, the median is in the measurement interval 6-10 and could be 6, 7, 8, 9, or 10. Estimating the average of the 95 measurements is more complicated. Since you are asked to compare the average and the median, not necessarily to calculate them, you may askyourself if you can tell whether the average is greater than or less than the median. Note that visually the measurements in the first three measurement intervals are symmetric around the measurement interval 6-10, so you would expect the average of the measurements in just these three measurement intervals to lie in the 6-10 measurement interval. The 30 measurements in the remaining four measurement intervals are all greater than 10, some significantly greater than 10. Therefore, the average of the 95 measurements is greater than the average of the measurements in the first three measurementintervals, probably greater than 10. At this point it seems likely that the average of the 95 measurements is greater than the median of the 95 measurements. It turns out that this is true. To actually show that the average must be greater than 10, you can make the average as small as possible and see if the smallest possible average is greater than 10. To make the average as small as possible, assume that all of the measurements in each interval are as small as possible. That is to say, all 15 measurements in the measurement interval 1-5 are equal to 1, all 35 measurements in the measurement interval 6-10 are equal to 6, etc. Under this assumption, the average of the 95 measurements isThe value of the smallest possible average,1,015/95, is greater than 10. Therefore, since the average of the 95 measurements is greater than 10 and the median is in the measurement interval 6-10, it follows that the average is greater than the median, and the correct answer is Choice A3．正确答案：D解析：One way to approach this question is to plug in numbers for the variables and see what the relationship between the two quantities is for each of the numbers you plug in. If you plug in x = 2, you see that Quantity A is 3x+1= 33 or 27, and Quantity B is 4x = 42, or 16. In this case, Quantity A is greater than Quantity B. If you plug in x = 3, you see that Quantity A is 3x+1 = 34, or 81, and Quantity B is 4x= 43, or 64. In this case, Quantity A is greater than Quantity B. If you plug in x = 4, you see that Quantity A is 3x+1 = 35 or 243, and Quantity B is 4x = 44, or 256. In this case, Quantity B is greater than Quantity A. Since for x = 2 and for x= 3, Quantity A is greater than Quantity B, and for x= 4, Quantity B is greater than Quantity A, it follows that the relationship between the two quantities cannot be determined. The correct answer is Choice D. Since both quantities are algebraic expressions, another way to approach this problem is to set up a placeholder relationship between the two quantities and simplify it to see what conclusions you can draw.For any value of x, the value of 3x is positive, so dividing by 3x does not change any inequality that could be put in the placeholder. Since each step in this simplification is reversible, this reduces the problem to comparing 3 with ;(4/3)x. You can see that because 4/3 is greater than 1, the value of(4/3)x becomes greater as x becomes larger. In particular, it is greater than 3 for large enough values of x.For the smallest value of x, x = 2, the relationship is(4/3)2= 16/9 To say that the value 650 is at the 60th percentile of the distribution means, graphically, that 60 percent of the area between the normalcurve and the horizontal axis lies to the left of the vertical line segment at 650. To say that 850 is at the 90th percentile of the distribution means that 90 percent of the area between the normal curve and the horizontal axis lies to the left of the vertical line segment at 850. The value 750 is halfway between 650 and 850. However, because the curve is decreasing in that interval, the area between 650 and 750 is greater than the area between 750 and 850. Since the value at the 75th percentile should divide in half the area between the value at the 60th percentile(650)and the value at the 90th percentile(850), this value is closer to 650 than to 850. Thus you can conclude that Quantity A, the value at the 75th percentile of the distribution of X, is less than Quantity B. The correct answer is Choice B.6．正确答案：C解析：Set S consists of all integers from 1 to 80, except those that are equal to the square of an integer. So, Quantity A, the number of integers in set S, is equal to the number of positive integers that are less than 81 minus the number of positive integers less than 81 that are equal to the square of an integer. Clearly, there are 80 positive integers that are less than 81. One way to determine the number of positive integers less than 81 that are squares of integers is by noticing that 81 is equal to 92 and concluding that the squares of the integers from 1 to 8 are all positive integers that are less than 81. You can also draw this conclusion by squaring each of the positive integers, beginning with 1, until you get to an integer n such that n2 is greater than or equal to 81. Either way, there are 8 positive integers less than 81 that are squares of integers. Therefore, the number of integers in set S is 80 - 8, or 72, which is equal to Quantity B. So Quantity A is equal to Quantity B, and the correct answer is Choice C.7．A manager is forming a 6-person team to work on a certain project. From the 11 candidates available for the team, the manager has already chosen 3 to be on the team. In selecting the other 3 team members, how many different combinations of 3 of the remaining candidates does the manager have to choose from?A．6B．24C．56D．120E．462正确答案：C解析：To determine the number of different combinations of 3 of the remaining candidates that the manager has to choose from, you first have to know the number of remaining candidates. Since you know that the manager has already chosen 3 of the 11 candidates to be on the team, it is easy to see that there are 8 remaining candidates. Now you need to count how many different combinations of 3 objects can be chosenfrom a group of 8 objects. If you remember the combinations formula, you know that the number of combinations is(which is denoted symbolically asor). You can then calculate the number of different combinations of 3 of the remaining candidates as follows.The correct answer is Choice C.8．Which of the following could be the grap>h of all values of x that satisfy the inequality[*]?[*]A．B．C．D．E．正确答案：C解析：To determine which of the graphs is the correct answer, you first need to determine all values of x that satisfy the inequality. To do that you need to simplify the inequality until you isolate x. You can begin by multiplying both sides of the inequality by 3 to obtain(3)(2 - 5x)-(6x - 5). Note that when you multiply by 3, the right-hand side of the inequality becomes -(6x - 5), not -6x - 5. The rest of the simplification is as follows.Note that when an inequality is multiplied(or divided)by a negative number, the direction of the inequality reverses. The graphs in the answer choices are number lines on which only the number 0 is indicated. Therefore, you do not need to locate 1/9 on the number line; it is nough to know that 1/9 is a positive number. Choice C is the only choice in which the shaded part of the line is equal to or greater than a positive number. Therefore, the correct answer is Choice C.9．If 1+x + x2 + x3 = 60, then the average(arithmetic mean)of x, x2, x3 , and x4 is equal to which of the following?A．12xB．15xC．20xD．30xE．60x正确答案：B解析：A quick inspection of the answer choices shows that it is not necessary to solve the equation 1 + x + x2 + x3 = 60 for x to answer this question. You are being asked to express the average of the four quantities x, x2, x3, and x4 in terms of x. To express this average in terms of x, you need to add the 4 quantities and divide the result by 4; that is,.The only information given in the question is that the sum of the 4 quantities, 1 +x+ x2+ x3, is 60, so you need to think of a way to use this information to simplify the expression.Note that the numerator of the fraction is a sum of 4quantities, each of which has an x term raised to a power. Thus, the expression in the numerator can be factored as x + x2+ x3+ x4= x(1+ x + x2+ x3). By using the information in the question, you can make the following simplification.Therefore, the correct answer is Choice B.10．Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are(2,4)and the coordinates of point Q are(8, 6). What are the coordinates of point R ?A．(3,2)B．(3,3)C．(4,4)D．(5,2)E．(6,2)正确答案：E解析：Since OPQR is a parallelogram, line segments PQ and OR have the same length and the same slope. Therefore, in the figure above, PQM and ORN arc congruent right triangles. From the coordinates of P and Q, the lengths of the legs of triangle PQM are PM = 8 - 2 = 6 and QM = 6-4 = 2. Thus, the lengths of the legs ON and RN of triangle ORN are also 6 and 2, respectively. So the coordinates of point R are(6, 2). The correct answer is Choice E.11．The relationship between the area A of a circle and its circumference C is given by the formula A = kC2, where k is a constant. What is the value of k ?A．B．C．1/4D．2πE．4π2正确答案：A解析：One way to approach this problem is to realize that the value of the constant k is the same for all circles. Therefore, you can pick a specific circle and substitute the circumference and the area of that particular circle into the formula and calculate the value of k. Say, for example, that you pick a circle with radius 1. The area of the circle is n and the circumference of the circle is 2π. Inserting these values into the formula gives n = k(2π)2. Solving this equation for k gives k=, and the correct answer is Choice A. Another way to approach the problem is to express A and C in terms of a common variable and then solve the resulting equation for k. Recall the commonly used formulas for the area and the circumference of a circle: A = πr2 and C = 2πr. Note that in these formulas, both A and C are expressed in terms of the radius r. So, in the formula A = kC2, you can substitute expressions for A and C in terms of r. Substituting πr2 for A and 2πr for C gives πr2 = k(2πr)2. Now you can determine the value of k by solving the equation for k as follows.The correct answer is Choice A.12．The sequence of numbers a1,a2,a3,...,an,... is defined byfor each integer n1. What is the sum of the first 20 terms of this sequence?A．B．C．D．E．正确答案：B解析：This question asks for the sum of the first 20 terms of the sequence. Obviously, it would be very time-consuming to write out the first 20 terms of the sequence and add them together, so it is reasonable to try to find a more efficient way to calculate the sum. Questions involving sequences can often be answered by looking for a pattern. Scanning the answer choices and noting that they contain fractions with denominators 2, 20, 21, and 22, and nothing in between, seems to confirm that looking for a pattern is a good approach to try. To look for a pattern, begin by adding the first two terms of the sequence.Now, if you add the first three terms of the sequence, you getNote that you can simplify the sum by canceling the fraction 1/3; that is, the sum of positive 1/3 and negative 1/3 is 0.If you add the first four terms, you getAgain, you can simplify the sum by canceling. This time, you can cancel the fractions 1/3 and 1/4.If you write out the next two sums and simplify them, you will see that they areWorking with the sums makes it clear that this pattern continues to hold as you add more and more terms of the sequence together and that a formula for the sum of the first k terms of the sequence isTherefore, the sum of the first 20 terms of the sequence is equal toThe correct answer is Choice B.13．The table above shows the frequency distribution of the values of a variable Y. What is the mean of the distribution?Give your answer to the nearest 0.01.______正确答案：1.29解析：The mean of the distribution of the variable Y is the sum of all the values of Y divided by the number of values of Y. However, before you begin the summing process, you need to understand how the information is presented in the question. Information about the variable is given in a table, where any repetitions of values have been summarized in the column labeled “Frequency.”Reading from the table, you can see that the value 1/2 occurs twice, the value 3/4 occurs seven times, and so on. To sum all the values of Y, you could add the value - twice, add the value 3/4 seven times, and continue the addition process in this manner. It is easier, however, to multiply the values by their corresponding frequencies and then sum the individual products, as shown below.To find the average, you need to divide the sum, 44, by the number of values of Y. The number of values can be found by looking at the columnof frequencies in the table. The sum of the numbers in this column, 2 + 7 + 8 + 8 + 9, or 34, is the number of values of Y. Thus, the mean of the distribution is 44/34, which, as a decimal, equals 1.2941….Rounded to the nearest 0.01, the correct answer is 1.29.14．Let S be the set of all positive integers n such that n2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?Indicate all such integers.A．12B．24C．36D．72正确答案：A，C解析：To determine which of the integers in the answer choices is a divisor of every positive integer n in S, you must first understand the integers that are in S. Note that in this question you are given information about n2, not about n itself. Therefore, you must use the information about n2 to derive information about n. The fact that n2 is a multiple of both 24 and 108 implies that n2 is a multiple of the least common multiple of 24 and 108. To determine the least common multiple of 24 and 108, factor 24 and 108 into prime factors as(23)(3)and(22)(33), respectively. Because these are prime factorizations, you can conclude that the least common multiple of 24 and 108 is(23)(33). Knowing that n2 must be a multiple of(23)(33)does not mean that every multiple of(23)(33)is a possible value of n2, because n2 must be the square of an integer. The prime factorization of a square number must contain only even exponents. Thus, the least multiple of(23)(33)that is a square is(24)(34). This is the least possible value of n2, and so the least possible value of n is(22)(32), or 36. Furthermore, since every value of n2 is a multiple of(24)(34), the values of n are the positive multiples of 36; that is, S = {36, 72, 108, 144, 180,...}. The question asks for integers that are divisors of every integer n in S, that is, divisors of every positive multiple of 36. Since Choice A, 12, is a divisor of 36, it is also a divisor of every multiple of 36. The same is true for Choice C, 36. Choices B and D, 24 and 72, are not divisors of 36, so they are not divisors of every integer in S. The correct answer consists of Choices A and C.15．The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.Which of the following statements individually provide(s)sufficient additional information to determine the range of the heights of all the students in the class?Indicate all such statements.A．The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.B．The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.C．The average(arithmetic mean)height of the male students in the class is 4.6inches greater than the average height of the female students in the class.正确答案：A解析：Choice A tells you that the tallest male student is 5.8 inches taller than the tallest female student. You can combine this information with the given information about the male and female height ranges to place four students—the shortest male, the shortest female, the tallest male, and the tallest female—in relative order according to height, as shown in the figure below. You can see from the figure that the tallest student must be a male and the shortest student must be a female. You can also see the difference in height between those two students, which is the range of the heights of the entire class. Therefore, Choice A provides sufficient additional information to determine the range. Choice B provides information about one of the centers of the data—the median; it does not say anything about how spread out the data are around that center. You are given that the median height of the males is 1.1 inches greater than that of the females. First note that it is possible for two different sets of data to have the same median but have very different ranges. Choice B gives the difference between the medians of the male heights and the female heights, without giving the actual medians. However, even if you knew the medians, the fact that the ranges can vary widely indicates that the range of the heights of the entire class can also vary widely. It is possible to construct examples of heights of students that satisfy all of the information in the question and in Choice B but have different ranges for the heights of the entire class. Here are two such examples, each of which has only three females and three males. Although the examples are small, they illustrate the fact that the range of the heights of the entire class can vary. In both examples, the range of female heights is 13.2, the range of male heights is 15.4, and the difference between the median heights is 1.1 inches.Example 1Female heights: 50.0 56.6 63.2 which have a median of 56.6 Male heights: 50.0 57.7 65.4 which have a median of 57.7 Range of heights of entire class: 15.4Example 2Female heights: 50.0 56.6 63.2 which have a median of 56.6 Male heights: 51.0 57.7 66.4 which have a median of 57.7 Range of heights of entire class: 16.4Therefore, Choice B does not provide sufficient additional information to determine the range of the heights of the entire class. Choice C provides information about another center of the data—the average. You are given that the average height of the males is 4.6 inches greater than that of the females. However, like Choice B, the statement gives no information about how spread out the data are around that center. Again, it is possible for two different sets of data to have the same average but have very different ranges. Examples similar to the two examples above can be constructed that satisfy all of the information in the question and in Choice C but have different ranges for the heights of the entire class. Therefore, Choice C does not provide sufficient additional information to determine the range of the heights of the entire class. The correct answer consists of Choice A.。

GRE(QUANTITATIVE)模拟试卷3(题后含答案及解析)

GRE（QUANTITATIVE）模拟试卷3(题后含答案及解析)题型有：1. 2. 3.1．Column A Column BThe least common denominator of 1/2, 1/3 and 1/4 15A．if the quantity in Column A is greaterB．if the quantity in Column B is greaterC．if the two quantity are equalD．if the relationship cannot be determined from the information given正确答案：B解析：解：本题的正确答案为(B)。

“the least common denominator”是最小公分母，也就是分母的最小公倍数。

2，3和4的最小公倍数是12，所以1/2,1/3和1/4的最小公分母为12。

2．d=5. 03894 and |d| is the decimal expression for d rounded to the nearest thousandth.Column A Column BThe number of decimal places where d and |d| differ4A．if the quantity in Column A is greaterB．if the quantity in Column B is greaterC．if the two quantity are equalD．if the relationship cannot be determined from the information given正确答案：B解析：d=5.03894且|d|是d四舍五入到千分位的小数表达(decimal expression)。

解：本题的正确答案是(B)。

新GRE数学模拟练习题(3)

新GRE数学模拟练习题(3)1．A,B,C,D,E,F排在1,2,3,4,5,6六个位置上,问A不在1, B不在2, C不在3的情况下,共有多少种排法?(A) 720(B) 450(C) 180(D) 216(E) 3202．一直线L过点A(5,0), B(0,2), 坐标原点为O, 点P(X,Y)为三角形OAB中一点, 问：Y(A) 1/4(B) 3/8(C) 1/2(D) 5/8(E) 3/43．In an insurance company, each policy has a paper record and an electric record．For those policies having incorrect paper record, 60% also having incorrect electric record; For policies having incorrect electric record, 75% also having incorrect paper record．3% of all policies have both incorrect paper and incorrect electric records．If we randomly pick out one policy,what’s the probability that the one having both correct paper and correct electric records?(A) 0．80(B) 0．94(C) 0．75(D) 0．88(E) 0．924．If Bob can do a job in 20 days and Jane can do the job in 30 days, they work together to do this job and in this period, Bob stop work for 2．5 days and Jane stop work for x days, and the job be finished for 14 days, what is x?(A) 1．6(B) 3．2(C) 1．5(D) 1．25(E) 1．155．The probability of A is 60% and the probability of B is 50%, what is the most possible probability that neither A nor B would happen?(A) 0．80(B) 0．40(C) 0．75(D) 0．55(E) 0．686．There are 1200 respondents to a poll, each favoringtheir preference for candidates A,B, and C．54% favored A, 48% favored B, and 42% favored C, and there is 30% favored both A and B．what’s the largest possible number of respondents favoring C, but not C&B, nor C&A?(A) 25%(B) 30%(C) 28%(D) 38%(E) 40%参考答案：1．解：首先考虑总的可能性为，再考虑A在1，B在2，C在3的可能性分别为，中重复计算了三者交集，分别为AB在1，2，AC在1，3，BC在2，3，所需将三种情况加回，即，但考虑这三种加回的交集又重复计算了ABC在1，2，3的情况，所以应减去P332．解：在平面直角坐标系中，T3．解：设总数为x，设incorrect paper record有y,incorrect electric record有z，则：x·y·60%=3%·x y=5%x·z·75%=3%·x z=4%则，两者至少有一个错误的百分比为5%+4%-3%=6%，所准确答案为94%4．解：1/20(14-2．5)+1/30(14-x)=1，得出x=1．255．解：划出图表来能够一目了然：A， B均不发生的概率为40%，最小概率为0．6．解：A和B的并集为：54%+48%-30%=72%，所C为28%．。

GRE数学实战模拟练习

GRE数学实战模拟练习一、整数整数是数学中最基本的数学概念之一。

它包括正整数、负整数和零。

在GRE数学考试中，我们经常需要进行整数的运算、比较和求解问题。

1.1 整数的四则运算整数的四则运算包括加法、减法、乘法和除法。

加法：整数的加法是指将两个整数相加，得到一个新的整数。

如3+ 4 = 7。

减法：整数的减法是指将一个整数减去另一个整数，得到一个新的整数。

如5 - 2 = 3。

乘法：整数的乘法是指将两个整数相乘，得到一个新的整数。

如2× 3 = 6。

除法：整数的除法是指将一个整数除以另一个整数，得到一个新的整数或小数。

如6 ÷ 2 = 3。

1.2 整数的比较和求解在GRE数学考试中，经常需要将整数进行比较和求解问题。

比较：将两个整数进行比较，可以通过比较它们的大小关系来判断它们的大小。

如5 > 3，表示5大于3。

求解：对于一些问题，需要通过计算和推理来求解整数的值。

如已知方程2x + 3 = 7，求x的值。

通过化简方程，可得2x = 4，进而得到x = 2。

二、分数分数是指一个数与另一个非零数的比值，其中分子是被除数，分母是除数。

在GRE数学考试中，我们经常需要进行分数的运算、比较和化简。

2.1 分数的四则运算分数的四则运算包括加法、减法、乘法和除法。

加法：分数的加法是指将两个分数相加，得到一个新的分数。

如½ + ¼ = ¾。

减法：分数的减法是指将一个分数减去另一个分数，得到一个新的分数。

如¾ - ¼ = ½。

乘法：分数的乘法是指将两个分数相乘，得到一个新的分数。

如½ × ¼ = ⅛。

除法：分数的除法是指将一个分数除以另一个分数，得到一个新的分数。

如¾ ÷ ½ = 1½。

2.2 分数的比较和化简在GRE数学考试中，经常需要将分数进行比较和化简。

新GRE模考题

新G R E模考题(总12页)--本页仅作为文档封面，使用时请直接删除即可----内页可以根据需求调整合适字体及大小--新GRE 模考题Sect ion 3For Questions 1 to 5, select one entry for each blank from the corresponding column of choices. Fill all blanks in the way that best completes the text.1. Cynics believe that people who ______ compliments do so in order to be praised twice.(A) bask in(B) give out(C) despair of(D) gloat over(E) shrug off2. The Chinese, who began systematic astronomical and weather observations shortly after the ancient Egyptians, were assiduous record-keepers, and because of this, can claim humanity’s longest continuous ______ of natural events.(A) defiance(B) documentation(C) maintenance(D) theory(E) domination3. Nineteenth-century scholars, by examining earlier geometric Greek art, found that classical Greek art was not a magical ______ or a brilliant ______ blending Egyptian and Assyrian art, but was independently evolved by Greeks in Greece.4. Their mutual teasing seemed ______, but in fact it ______ a long-standing hostility.5． The astronomer and feminist Maria Mitchell’s own prodigious activity and the vigor of the Association for the Advancement of Women during the 1870’s ______ any assertion that feminism was ______ in that period.Questions 6 to 7 are based on the following reading passage.From the 1900’s through the 1950’s waitresses in the United States develo ped a form of unionism based on the unions’ defining the skills that their occupation included and enforcing standards for the performance of those skills. This “occupational unionism” differed substantially from the “worksite unionism” preva lent among factory workers. Rather than unionizing the workforces of particular employers, waitress locals soughtto control their occupation throughout a city. Occupational unionism operated through union hiring halls, which provided free placement services to employers who agreed to hire their personnel only through the union. Hiring halls offered union waitresses collective employment security, not individual job security—a basic protection offered by worksite unions. That is, when a waitress lost her job, the local did not intervene with her employer but placed her elsewhere; and when jobs were scarce, the work hours available were distributed fairly among all members rather than being assigned according to seniority.6. The primary purpose of the passage is to(A) analyze a current trend in relation to the past(B) discuss a particular solution to a long-standing problem(C) analyze changes in the way that certain standards have been enforced(D) apply a generalization to an unusual situation(E) describe an approach by contrasting it with another approach7. The author of the passage mentions “particular employers” (line 5) primarily in order to(A) suggest that occupational unions found some employers difficult to satisfy(B) indicate that the occupational unions served some employers but not others(C) emphasize the unique focus of occupational unionism(D) accentuate the hostility of some employers toward occupational unionism(E) point out a weakness of worksite unionismQuestions 8 to 9 are based on the following reading passage.The dark regions in the starry night sky are not pockets in the universe that are devoid of stars as had long been thought. Rather, they are dark because of interstellar dust that hides the stars behind it. Although its visual effect is so pronounced, dust is only a minor constituent of the material, extremely low in density, that lies between the stars. Dust accounts for about one percent of the total mass of interstellar matter. The rest is hydrogen and helium gas, with small amounts of other elements. The interstellar material, rather like terrestrial clouds, comes in all shapes and sizes. The average density of interstellar material in the vicinity of our Sun is 1,000 to 10,000 times less than the best terrestrial laboratory vacuum. It is only because of the enormous interstellar distances that so little material per unit of volume becomes so significant. Optical astronomy ismost directly affected, for although interstellar gas is perfectly transparent, the dust is not. For the following question, consider each of the choices separately and select all that apply.8. It can be inferred from the passage that the density of interstellar material is(A) equal to that of interstellar dust(B) unusually low in the vicinity of our Sun.(C) not homogeneous throughout interstellar space.9. Select a sentence in the passage which gives the reason why stars can be obscured even by very sparsely distributed matter.For Questions 10 to 13, select the two answer choices that, when used to complete the sentence, fit the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.10. Industrialists seized economic power only after industry had______agriculture as the preeminent form of production; previously such power had resided in land ownership.(A) sabotaged(B) overtaken(C) toppled(D) joined(E) supplanted(F) surrogated11. Many industries are so______ by the impact of government sanctions, equipment failure, and foreign competition that they are beginning to rely on industrial psychologists to salvage what remains of employee morale.(A) estranged(B) beleaguered(C) overruled(D) encouraged(E) restrained(F) besieged12. Not wishing to appear ______, the junior member of the research group refrained fromventuring any criticism of the senior members’ plan f or dividing up responsibility for the entire project.(A) reluctant(B) inquisitive(C) presumptuous(D) pretentious(E) censorious(F) moralistic13. The natures of social history and lyric poetry are antithetical , social history always recounting the ______and lyric poetry speaking for unchanging human nature, that timeless essence beyond fashion and economics.(A) bygone(B) evanescent(C) unnoticed(D) unalterable(E) transitory(F) eternalQuestions 14-16 are based on the following passage.The 1973 Endangered Species Act made into legal policy the concept that endangered species of wildlife are precious as part of a natural ecosystem. The nearly unanimous passage of this act in the United States Congress, reflection the rising national popularity of environmentalism, masked a bitter debate. Affected industries clung to the former wildlife policy of valuing individual species according to their economic usefulness. They fought to minimize the law’s impact by limiting definitions of k ey terms. But they lost on nearly every issue. The act defined “wildlife” as almost all kinds of animals—from large mammals to invertebrates—and plants. “Taking” wildlife was defined broadly as any action that threatened an endangered species; areas vital to a species’ survival could be federally protected as “critical habitats”. Though these definitions legislated strong environmentalist goals, political compromises made in the enforcement of the act were to determine just what economic interests would be set aside for the sake of ecological stabilization.For the following question, consider each of the choices separately and select all that apply.14. According to the passage, all of the following statements are defined as a “critical habitat” EXCEPT(A) A natural ecosystem that is threatened by imminent development(B) A natural area that is crucial to the survival of a species and thus eligible for federal protection.(C) A wilderness area in which the “taking” of wildlife species is permitted rarely and only under strict federal regulation15. It can be inferred from the passage that if business interests had won the debate on provisions of the 1973 Endangered Species Act, which of the following would have resulted(A) Environmentalist concepts would not have become widely popular.(B) The definitions of key terms of the act would have been more restricted.(C) Enforcement of the act would have been more difficult.(D) The act would have had stronger support from Congressional leaders.(E) The public would have boycotted the industries that had the greatest impact in defining the act.16. The author refers to the terms “wildlife” (line 11), “taking” (line 13), and “critical habitats” (line 16) most likely in o rder to(A) illustrate the misuse of scientific language and concepts in political processes(B) emphasize the importance of selecting precise language in transforming scientific concepts into law(C) represent terminology whose definition was crucial in writing environmentalist goals into law(D) demonstrate the triviality of the issues debated by industries before Congress passed the Endangered Species Act(E) show that broad definitions of key terms in many types of laws resulted in ambiguity and thus left room for disagreement about how the law should be enforcedQuestions 17-19 are based on the following passage.Allen and Wolkowitz’s research challenges the common claim that homework-waged labor performed women worker’s needs and preferences. By focusing on a limited geographical area in order to gather in-depth information, the authors have avoided the methodological pitfalls that have plagued earlier research on homework. Their findings disprove accepted notions about homeworkers: that they are unqualified for other jobs and that they use homework as a short-term strategy for dealing with child care. The authors conclude that the persistence of homework cannot be explained by appeal to such notions, for in fact, homeworkers do not differ sharply from other employed women. Most homeworkers would prefer to work outside the home but are constrained from doing so by lack of opportunity. In fact, homework is driven by employers’ desires to minimize fixed costs: homeworkers receive no benefits and are paid less than regular employees.17. The passage is primarily concerned with(A) advocating a controversial theory(B) presenting and challenging the results of a study(C) describing a problem and proposing a solution(D) discussing research that opposes a widely accepted belief(E) comparing several explanations for the same phenomenonFor the following question, consider each of the choices separately and select all that apply.and Wolkowitz’s research suggests which of following statements are true about most homeworkers(A) They do not necessarily resort to homework as a strategy for dealing with child care.(B) They perform professional-level duties rather than manual tasks or piecework.(C) They do not prefer homework to employment outside the home.19. The ratio of divorces to marriage has increased since 1940. Therefore, there must be a greater proportion of children living with only one natural parent than there was in 1940.Which of the following, if true, most strongly weakens the inference drawn aboveA. the number of marriages entered into by women twenty-five to thirty-five years old has decreased since 1940.B. when there is a divorce, children are often given the option of deciding which parent they will live with.C. since 1940 the average number of children in a family has remained approximately steady and has not been subject to wide fluctuations.D. before 1940 relatively few children whose parents had both died were adopted into single-parent families.E. the proportion of children who must be raised by one parent because the other has died has decreased since 1940 as a result of medical advances.For Questions 20, select one entry for each blank from the corresponding column of choices. Fill all blanks in the way that best completes the text.20. Scientists (i)___________ disposition (ii)____________ the impact of human activities on climate has been greatly mitigated-- perhaps even counterbalanced—by the natural trend over the past several centuries toward much cooler weather. This optimistic conclusion seems unrealistic to other scientists, who find it difficult to believe either that the greenhouse effect could be (iii)_________, or that such a fortunate combination of event is likely.Sect ion 5For Questions 1 to 4, select one entry for each blank from the corresponding column of choices. Fill all blanks in the way that best completes the text.1. The current demand for quality in the schools seems to ask not for the development of informed and active citizens, but for disciplined and productive workers with abilities that contribute to civic life only _______, if at all.(A) indirectly(B) politically(C) intellectually(D) sensibly(E) sequentially2. Certain weeds that flourish among rice crops resist detection until maturity by ______ the seedling stage in the rice plant’s life cycle, thereby remainingindistinguishable from the rice crop until the flowering stage.(A) deterring(B) displacing(C) augmenting(D) imitating(E) nurturing3. A major goal of law, to deter potential criminals by punishing wrongdoers, is not served when the penalty is so seldom invoked that it______to be a ______threat.4. Doreen justifiably felt she deserved recognition for the fact that the research institute had been ________a position of preeminence, since it was she who had ________ the transformation.Proportionally, more persons diagnosed as having the brain disorder schizophrenia were born in the winter months than at any other time of year. A recent study suggeststhat the cause may have been the nutrient-poor diets of some expectant mothers during the coldest months of the year, when it was hardestfor people’s to get, or afford, a variety of fresh foods.5. Which of the following, if true, helps to support the conclusion presented aboveA. over the years the number of cases of schizophrenia has not shown a correlation with degree of economic distress.B. most of the development of brain areas affected in schizophrenia occurs during the last month of the mother’s pregnancy.C. suicide rates are significantly higher in winter than in any other season.D. the nutrients in fresh foods have the same effects on the development of the brain as do the nutrients in preserved foods.E. a sizable proportion of the patients involved in the study have a history of schizophrenia in the family.Questions 6 to 7 are based on the following passage.Upwards of a billion stars in our galaxy have burnt up their internal energy sources, and so can no longer produce the heat a star needs to oppose the inward force of gravity. These stars, of more than a few solar masses, evolve, in general, much more rapidly than does a star like the Sun. Moreover, it is just these more massive stars whose collapse does not halt at intermediate stages (that is, as white dwarfs or neutron stars). Instead, the collapse continues until a singularity (an infinitely dense concentration of matter) is reached. It would be wonderful to observe a singularity and obtain direct evidence of the undoubtedly bizarre phenomena that occur near one. Unfortunately in most cases a distant observer cannot see the singularity; outgoing light rays are dragged back by gravity so forcefully that even if they could start out within a few kilometersof the singularity, they would end up in the singularity itself6. the passage suggests which of the following about the Sun(A) the Sun could evolve to a stage of collapse that is less dense than a singularity.(B) in the Sun, the inward force of gravity is balanced by the generation of heat.(C) the sun emits more observable light than does a white dwarf or a neutron star.7. which of the following sentences would most probably follow the last sentence of the passage(A) thus, a physicist interested in studying phenomena near singularities would necessarily hope to find a singularity with a measureable gravitational field.(B) accordingly, physicists to date have been unable to observe directly any singularity.(C) it is specifically this startling phenomenon that has allowed us to codify the scant information currently available about singularities.(D) moreover, the existence of this extra ordinary phenomenon is implied in the extensive reports of several physicists.(E) although unanticipated, phenomena such as these are consistent with the structure of a singularity.Questions 8 to 9 are based on the following passage.The transfer of heat and water vapor from the ocean to the air above it depends on a disequilibrium at the interface of the water and the air. Within about a millimeter of the water, air temperature is close to that of the surface water, and the air is nearly saturated with water vapor. But the differences, however small, are crucial, and the disequilibrium is maintained by air near the surface mixing with air higher up, which is typically appreciably cooler and lower in water-vapor content. The air is mixed by means of turbulence that depends on the wind for its energy. As wind speed increases, so does turbulence, and thus the rate of heat and moisture transfer. Detailed understanding of this phenomenon awaits further study. An interacting—and complicating—phenomenon is wind-to-water transfer of momentum that occurs when waves are formed. When the wind makes waves, it transfers important amounts of energy—energy that is therefore not available to provide turbulence.8. according to the passage, wind over the ocean generally does which of the following(A) causes relatively cool, dry air to come into proximity with the ocean surface.(B) maintains a steady rate of heat and moisture transfer between the ocean and the air.(C) causes frequent changes in the temperature of the water at the ocean’s surface.9. the passage suggests that if on a certain day the wind were to decrease until there was no wind at all which of he following would occur(A) the air closest to the ocean surface would become saturated with water vapor.(B) the air closest to the ocean surface would be warmer than the water(C) the amount of moisture in the air closest to the ocean surface would decrease.(D) the rate of heat and moisture transfer would increase.(E) the air closest to the ocean would be at the same temperature as air higher up.For Questions 10 to 13, select the two answer choices that, when used to complete the sentence, fit the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.10. Marison was a scientist of unusual _______ and imagination who had startling succeeded in discerning new and fundamental principles well in advance of their general recognition.(A) restiveness(B) perspicacity(C) precision(D) aggression(E) candor(F) insight11. It is assumed that scientists will avoid making ______ claims aboutthe results of their experiments because of the likelihood that they will be exposed when other researchers cannot duplicate their findings.(A) hypothetical(B) fraudulent(C) verifiable(D) radical(E) deceptive(F) evaluative12. As early as the seventeenth century, philosophers called attention to the ______ character of the issue, and their twentieth-century counterparts still approach it with uneasiness.(A) absorbing(B) unusual(C) complicated(D) auspicious(E) involved(F) fanciful13. The value of Davis’ sociological research is compromised by his unscrupulous tendency to use materials selectively in order to substantiate his own claims, while ______ information that points to other possible conclusions.(A) deploying(B) disregarding(C) weighing(D) refuting(E) emphasizing(F) discountingQuestions 14 to 16 are based on the following passage.The molecules of carbon dioxide in the Earth’s atmosphere affect the heat balance of the Earth by acting as a one-way screen. Although these molecules allow radiation at visible wavelength, where most of the energy of sunlight is concentrated, to pass through, they absorb some of the longer-wavelength, infrared emissions radiated from the Earth’s surface, radiation that would otherwise be transmitted back into space. For the Earth to maintain a constant average temperature, such emissions from the planet must balance incoming solar radiation. If there were no carbon dioxide in the atmosphere, heat would escape from the Earth much more easily. The surface temperature would be so much lower that the oceans might be a solid mass of ice.Today, however, the potential problem is too much carbon dioxide. The burning of fossil fuels and the clearing of forests have increased atmospheric carbon dioxide by about 15 percent in the last hundred years, and we continue to add carbon dioxide to the atmosphere. Could the increase in carbon dioxide cause a global rise in average temperature, and could such a rise have serious consequences for human society Mathematical models that allow us to calculate the rise in temperature as a function of the increase indicate that the answer is probably yes.Under present conditions a temperature of -18 ℃ can be observed at an altitude of 5 to 6 kilometers above the Earth. Below this altitude (called the radiating level), the temperature increases by about 6 ℃ per kilometer appro aching the Earth’s surface, where the average temperature is about 15 ℃. An increase in the amount of carbon dioxide means that there are more molecules of carbon dioxide to absorb infrared radiation. As the capacity of the atmosphere to absorb infrared radiation increases, the radiating level and the temperature of the surface must rise.One mathematical model predicts that doubling the atmospheric carbon dioxide would raise the global mean surface temperature by ℃. This model assumes that the atmosphere’s relative humidity remains constant and the temperature decreases with altitude at a rate of ℃ per kilometer. The assumption of constant relative humidity is important,because water vapor in the atmosphere is another efficient absorber of radiation at infrared wavelength. Because warm air can hold more moisture than cool air, the relative humidity will be constant only if the amount of water vapor in the atmosphere increases as the temperature rises. Therefore, more infrared radiation would be absorbed and reradiated back to the Earth’s surfac e. The resultant warming at the surface could be expected to melt snow and ice, reducing the Earth’s reflectivity. More solar radiation would then be absorbed, leading to a further increase in temperature.14. according to the passage, the greatest part of the solar energy that reaches the Earth is(A) concentrated in the infrared spectrum(B) concentrated at visible wavelengths(C) absorbed by carbon dioxide molecules(D) absorbed by atmospheric water vapor(E) reflected back to space by snow and ice15. according to the passage, atmospheric carbon dioxide performs which of the following functions(A) absorbing radiation at visible wavelengths(B) absorbing infrared radiation(C) absorbing outgoing radiation from the Earth16. select a sentence in the third or the last paragraph which indicts the premise of the mathematical model mentioned in the passage17. When school administrators translate educational research into a standardized teaching program and mandate its use by teachers, students learn less and learn less well than they did before, even though the teachers are the same. The translation by the administrators of theory into prescribed practice must therefore be flawed.The argument above is based on which of the following assumptionsA. teachers differ in their ability to teach in accordance with standardized programs.B. the educational research on which the standardized teaching programs are based is sound.C. researchers should be the ones to translate their own research into teaching programs.D. the ways in which teachers choose to implement the programs are ineffective.E. the level of student learning will vary from state to state.18. A common defense of sport hunting is that it serves a vital wildlife-management function, without which countless animals would succumb to starvation and disease. This defense leads to the overly hasty conclusion that sport hunting produces a healthier population of animals.Which of the following, if true, best supports the author’s claim that sport hunting does not necessarily produce a healthier population of animalsA. for many economically depressed families, hunting helps keep food on the table.B. wildlife species encroach on farm crops when other food supplies become scarce.C. overpopulation of a species causes both strong and weak animals to suffer.D. sport hunters tend to pursue the biggest and healthiest animals in a population.E. many people have strong moral objections to killing a creature for any reason other than self-defense.For Questions 19 to 20, select one entry for each blank from the corresponding columnof choices. Fill all blanks in the way that best completes the text.19. (i)_________ thinkers are often accused by more (ii)___________ thinkers of building castles in the air based more on lofty ideals and (iii)___________ than on a solid foundation in reality.20. Several geographers and historians have speculated that temperate climates foster the(i)_________ of civilization, but that after a civilization has developed past the(ii)___________ stage, it is more likely to flourish in (iii)_____________ because challenges are needed that must be overcome for further progress to occur.。

新GRE数学11道练习题及答案解析

新GRE数学11道练习题及答案解析导读：本文新GRE数学11道练习题及答案解析，仅供参考，如果觉得很不错，欢迎点评和分享。

1：还有数列题：a1=2，a2=6，an=an-1/an-2，求a150.解答: an=an-1/an-2,所以an-1=an-2/an-3,带入前式得an=1/an-3,然后再拆一遍得到an=an-6,也就是说,这个数列是以6为周期的,则a150=a144=...=a6,利用a1,a2可以计算出a6=1/3.如果实在想不到这个方法,可以写几项看看很快就会发现a150=a144,大胆推测该数列是以6为周期得,然后写出a1-a13(也就是写到你能看出来规律),不难发现a6=a12,a7=a13,然后那,稍微数数,就可以知道a150=a6了,同样计算得1/3.2：问摄氏升高30度华氏升高的度数与62比大小.key:F=30*9/5=543：那道费波拉契数列的题:已知,a1=1 a2=1 an=an-1+an-2 ，问a1,a2,a3,a6四项的平均数和a1,a3,a4,a5四项的平均数大小比较。

解答:费波契那数列就是第三项是前两项的和,依此类推得到a1-a6为:1 123 5 8 13 21 a1+a2+a3+a6=12, a1+a3+a4+a5=11,所以为大于.4：满足x^2+y^2key: 按照X的可能情况顺序写出:X= Y=1 1-92 1-93 1-94 1-95 1-86 1-87 1-78 1-9 1-4 =>Myanswer:加起来=695：24，36，90，100四个数中,该数除以它的所有的质因子，最后的结果是质数的是那个：Key:906:0.123456789101112….，这个小数无限不循环地把所有整数都列出来.请问小数点后第100位的数字是多少?Key: 位数0 1 2 3 4 5 6 7 8 9 1010 11 12 ………………………19 2020 21……………………………29 2030………………………………39 2040………………………………49 2050 51 52 53 54 55 56 ――――――第101位=5??7：2904x=y2(y的平方)，x、y都是正整数，求x的最小值。

2019年新GRE数学11道练习题及答案解析

2019 年新GRE 数学11 道练习题及答案解析1 ：还有数列题：a1=2，a2=6，an=an-1/an-2 ，求a150.解答：an=an-1/an-2, 所以an-1=an-2/an-3, 带入前式得an=1/an-3, 然后再拆一遍得到an=an-6, 也就是说, 这个数列是以 6 为周期的,则a150=a144=...=a6,利用a1,a2能够计算出a6=1/3.如果实在想不到这个方法, 能够写几项看看很快就会发现a150=a144,大胆推测该数列是以6为周期得，然后写出a1-a13（也就是写到你能看出来规律）,不难发现a6=a12,a7=a13,然后那，稍微数数，就能够知道a150=a6 了,同样计算得1/3.2：问摄氏升高30度华氏升高的度数与62比大小.key: F=30*9/5=54Myanswer：加起来=695：24，36，90，100四个数中, 该数除以它的所有的质因子，最后的结果是质数的是那个：Key：906: 0.123456789101112….，这个小数无限不循环地把所有整数都列出来.请问小数点后第100位的数字是多少?Key：位数0 1 2 3 4 5 6 7 8 9 1010 11 12 ……………………… 19 2020 21 ....................................... 29 2030 ............................................. 39 2040 ............................................. 49 2050 51 52 53 54 55 56 第101 位=5??7：2904x=y2(y 的平方) ，x、y 都是正整数，求x 的最小值。

因为：X A2X Y A2X Z A2=(X X Y X Z)A2所以把2904 除呀除=2X2X2X3X 11X 11=2八2乂1M2X6 再乘一个6就OK了2A2X11A2X6X6=(2X11X6)A2=132A2Key:最小的x=68：序列An=1/n-1/(n+1),n>=1, 问前100项和.解答：An =1/n-1/(n+1)An-1=1/(n-1)-1/nAn-2=1/(n-2)-/(n-1)A1=1-1/2把左边加起来就是An+An-1+……+A仁1-1/(n+1) ... 消掉了好多好多项之后的结果Key:把n=100带入得前100 项之和为100/1019:等腰三角形，腰为6.底边上的高为x,底边为y,问4x2+y2和144 谁大解答:勾股定理得(y/2)2+x2=62, 所以4x2+y2=14410: -1Key:我想的办法只能是尝试：原式=r(1+t*t) 恒小于零1) r -1 ，t 0 则原式-12) r -1 ，t -1 则原式-23) r 0 ，t 0 则原式0 例如：r=-0.9 t=-1/3 时,原式=-1, 若此时-0.9-1. 11：有长方形4feet*8feet, 长宽各截去x inch, 长宽比2：5，解答：列出方程4*12-x)/(8*12-x)=2/5 => x=16。

英语证书考试美国研究生入学考试(GRE)2022年模拟题3

英语证书考试美国研究生入学考试（GRE）2022年模拟题3(总分：170.00，做题时间：180分钟)一、数值比较题(总题数：7，分数：56.00)1.x2=81Quantity A: xQuantity B: 8（分数：8.00）A.Quantity A is greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given. √解析：x2=81，那么x=±9，一个大于8，一个小于8，所以无法与8比较大小，选择D。

2.Quantity A: The Standard Deviation of 1, 3, 5,7,9, 11, 13, 15, 17, 19Quantity B: The Standard Deviation of 2, 4, 6, 8, 10, 12, 14, 16, 18, 20（分数：8.00）A.Quantity A is greater.B.Quantity B is greater.C.The two quantities are equal. √D.The relationship cannot be determined from the information given.解析：如果做这道题目时把两边的值硬算出来的话，显然是不明智的。

我们仔细观察一下这两个数列，第二个数列中的数对应项比第一个数列中的数都大1，那么根据标准方差的性质，这两个数列的standard deviation完全相等，所以选择C。

3.Quantity A: The probability that event R occurs is 0.38 the probability that events R and W both occurQuantity B: 0.4（分数：8.00）A.Quantity A is greater.B.Quantity B is greater. √C.The two quantities are equal.D.The relationship cannot be determined from the information given.解析：事件R发生的概率是0.38，事件R和W同时发生的概率必然小于单个事件发生的概率，不管这两个事件独立与否，因此两者同时发生的概率最大为0.38，小于0.4，所以选择B。