___²_د_7.16_by_nina_tux
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  ___²_د_7.16_by_nina_tux ___²_د_7.16_by_nina_tux Document Transcript

  • 七月官方数学整理7月官方非常重要信息!禁止把JJ传到公共场合,太傻,寄托,人人,微博,FACEBOOK上面,禁止公开这些JJ以及公开传递。考试时如果遇到图表题和残题,请着重记一下题目条件及细节,感激不尽!上传散装JJ,请直接点击 http://114.80.209.148/upload.html或所在群群共享即可。【官方组号召帖】亲爱的G友们,看着前辈们用自己的cancel换来的宝贵题目,你好意思不写机经么?看着后面千千万万双可怜巴巴的眼睛,你忍心不带出残体么?看着官方组给你的丰厚奖励,你忍得住不记住新题么?加试部分不要跳过,大家踊跃背机经啦~~~在此先拜谢写机经的同学~~~大家一起加油杀G了~~~O(∩_∩)O~~~每日更新时间:北京时间22:00整理人:Nina, Tux有问题或疑议请联系 凸凸 QQ 13800018update history:7.1 22:00 添加1-127.2 22:00 添加13-23,更新第3题PQ长度7.3 22:00 添加24-37,更新第3、9题答案7.4 22:00 添加38-54, 修改36题笔误,更新1,19,22题。7.5 22:00添加55-72, 更新3,4,19,20,21,26,27,28,297.6 22:00 添加73-77,更新22,59,64,67,69,727.7 22:00 添加78-165,更新26,67和部分题目的英文7.8 22:00 添加166-173, 修改83题答案,更新关于平方根的声明,更新20,59,62,71,78,79, 158,1647.9 22:00 添加174-189, 修改85,140,145,146,161答案,更新24,71,807.10 22:00 添加190,修改180答案,更新19,26,29,637.11 22:00 添加191,更新19,68,77,120,158,1697.12 22:00 添加192-224,更新46,152,154,155,1737.13 22:00 添加225-237,更新23,57,125,187,202,207,208,209,211,214,215,216
  • 7.14 22:00 添加238-239,更新21,59,151,154,2337.15 22:00 添加240-248,更新45,527.16 22:00 添加249-253
  • ============重点易错知识点(感谢6月工作组的同学的整理)=============这里不是jj=====1. Positive factor 正因数2. least common multiple; greatest common divisor3. the sum of the first N odd integers4. the least common denominator 最小公分母 common difference/ratio 公差/比5. decimal expression小数表达; to the nearest四舍五入; thousandth 千分位6. prime number质数; composite number合数;mutual prime number互质数(最大公约数1)7. How many of the positive integers less than 25 are 2 less than an integer multiple of 4.8. ones or units’ digit 个位; tens’digit十位;hundreds’digit百位; thousands’ digit千位; thousandth’s digit千分位; tenths’ digit十分位; hundredths’ digit百分位9. domination of the function 函数定义域quotient商10. 7 less than 5x is 5 more than the product of 3 and x: 5x-7=5+3x11. simple interest= Principle*Interest Rate*Times Compound interest + principle= principle(1+interest Rate)^n, n是期数 Balance 余款12.Median 中数 Mode 众数 Range 值域 Standard deviation 标准方差13.Arithmetic Progression/series 等差级数 Geometric Progression/series 等比级数14.Factorial Notation 阶乘15.Mutually Exclusive events 事件互不相等:AB不能同时发生16.The odds=the probility17. reciprocal倒数18.Dash 连字符19.Vertical angle 对顶角 acute angel 锐角 obtuse angle 钝角 supplementary angle 补角complementary angle 余角 alternate angle 内错角 transversal 两直线的截线isosceles triangles 等腰三角形 equilateral triangles 等边三角形the square 正方形 the rectangle 矩形 angle bisector 角平分线 diagonal 对角线parallelograms平行四边形 the rhombus 菱形 trapezoids梯形 tangent to a circle 圆切线secant to a circle 圆的割线 inscribed angle 圆周角 sector 扇形 vertex 顶点cylinders圆柱体 Cones 圆锥[S=pi*r*l; V=pi*r^3/3]20. slope斜率 intercept 截距21.Drawn to scale 按比例绘制22.Pentagon 五边形 hexagon 六边形octagon 八边形 decagon 十边形23.1 foot= 12 inches24. intercept在ets给的GRE Math Review里面找到了关于斜率的这样一段话,关键地方已经做了高亮:“the x-intercepts of a graph are the x-values of the points at which the graph intersects the x-axis. Similarly,the y-intercepts of a graph are the y-values of the points at which the graph intersects the y-axis.”注意是values of the points, 意思intercept(截距)肯定就是分正负,现在不管什么别的专家不专家怎么说,GRE一切以ETS为基准.(出自:ETS的math review)例:六月jj比较大小第5题:在坐标系里 ax+by+c=0,0<a<b<c,问与x,y轴的截距大小,选B,(截距:intercept)所谓的intercept是有正负的因为0<a<b,所以 x-intercept=-c/a< y-intercept=-c/b所以是B变体:ax+by=c,此时x,y轴两截距均为正数。注意:机经中出现的sqrt是为了方便输入和排版而代替根号的,考试中会直接给出
  • 根号,所以是正的,sqrt(10)就是根号10;而如果题目中出现XX的平方根,squareroot of 。。。是要考虑正负的;特别是在x^2=A的情况下,x要考虑正负。
  • =============================这里开始是七月数学机经==============================1. 【图表题】糖果题,此题有2问。一个图表,x轴是糖果买的价钱,y轴是电分,从1990到2000。图里面是M.N,L,K四种糖果的年价格走势。 第一问,四种糖果从90到00年价格的增长的百分比排序,从低到高,答案是MLKN。第二问,是三个假设,1, 2分别为计算,比较简单,第一个假设是在90年的时候M比K是否在50%到60%之间。第3个假设是说 N糖果的产量(磅数pound)是最低的。问这三个假设是否正确。 五个选项,选只有假设1和2是正确的那项!7月版本:糖果题版本2:在LKMN四个节日当中,全国的糖果销售额从1996-2000的变化趋势 有四条曲线1. 把四个节日,按销售额的增加率从小到大排列MLKN具体数字忘了,方法就是 (销售额@2000-销售额@1996)/销售额@1996,算出来以后排一排就好了2. 一个公司X某年(97年还是什么的)在LKMN某一个节日当中(好像是L节日吧)的销售量是全国销售量的33%,然后该公司在L节日的销售量是全年销售的8%。问这个公司在97年的全年销售额1.5 * 33%/8% 约定于6.2 (1.5是从图中找到的)2. 【比大小】X-Y=偶数 求X^2+1除2的remainder 比上1 ,选 B官方:这个题貌似带出来的题干不太全,希望后来看见的同学能帮忙补一下。3. 【几何题】一个已知的直角坐标系,其中P点坐标为(5,t),Q点坐标为(-5,-t),已知PQ长度为2*sqrt(34)求斜率。 答案是:0.6 (3/5)Two points were given on a straight line (5,t) and (-5,-t) and the distance between the two points is2*sqrt(34). What is the slope of the line?官方:根据PQ的长度求出t的值,距离的平方=(x1-x2)^2+(y1-y2)^2,求出t=±3。根据斜率公式求出斜率即可。这道题有图可以知道是正的斜率。4. 【比大小】定义:K⊕N = 2^(K+N),求 (-1⊕1) 和1比较大小,选C变体:A⊕B = (A^-B)^2 就是A的-B次方之後再2次方之類的官方:把数带进去算就好了5. 【比大小】1575=3^m 5^n 7^q,比较5和m+n+q,选C官方:本题在JJ里面是和5比大小,但是最新同学带出来的题目不是和5比大小,请务必要小心算不要只背答案,这个用短除的方法很简单计算。6. 【比大小】有个CUBE的边长是6,比较表面积和体积的大小,选C7. 【比大小】六边形的内角和和540°比大小,选A。官方:多边形内角和公式(n-2)*180度8. 【几何题】A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x+ 1. Which of the following could be the length of the other side? 选C,要考虑三角不等式还有他给的条件:两边之和大于第三边,两边之差小于第三边,还有题目中提到是两个较短的边的条件。A. 2;B. 4;C. 6;D. 8;E. 10。9. 【算术题】if n is an integer and 99<n^2<200;thn n could hve atmost hw many values? 答案是10,n可以等于±10、±11、±12、±13、±14。如果题目中提到postive integer 答案就是5。
  • 10.【比大小】col A :the least 5 integers with 4 different prime factors, each greater than 2. col B:1155. 选D官方:机经说的是最小的5个整数和1155作比较,因为5个数字里一个等于1155,另外四个比1155大,所以没法比较。如果题干说的是the 5th least integer with blabla(第5小的整数),那么选A。如果题干说theleast integer with blabla,选C。如果是题干别的意思,请仔细计算。11.【算术题】What is the average of four tenths and five thousandths? 选0.2025官方:(4/10+5/1000)/2 = 0.2025。12 【算术题】The difference between a five-digit integer and its reflection must be divisible by which of thefollowing? 答案:9官方:设这个五位数是10000a+1000b+100c+10d+e, 它的reflection就是10000e+1000d+100c+10b+a, 两个数相减,等于9999a+990b-990d-9999e, 所以肯定能被9整除。13 【算术题】x,y,z,是 正数 ,2(x+y+z)除以7余1,在問(x+y+z)除以7余几 答案是4Twice the sum of three positive integers x,y,z when divided by 7 gives remainder 1 then what is theremainder when x+y+z is divided by 7?官方:简单的做法代个数进去算算就可以了,可以让x+y+z=11;标准做法是把括号里的看做一个整体X,穷举X mod 7分别等于0到6的时候,2X mod 7等于多少,然后把等于1的那些挑出来。mod表示求余函数。14 【算术题】一个管子半径是2feet,高是8feet,问500个管子的体积是多少? 答案是16000pi官方:圆柱体体积公式:底面积×高=pi*r^2*h, pi*2^2*8*500=16000pi15 【算术题】一個压土机的轮子直径是2,長是8;转500圈能压多少面积的土?答案是8000pi官方:求表面积公式:底面周长×高=pi*d*h, pi*2*8*500=8000piA road roller which levels a surface has height as 16 and diameter as 2, then if it revolves for around 500revolutions. What is the area of the land that it covers in 500 revolutions? 答案:16000pi A road roller makes a surface level flat which has a height of 18 and diameter 6, and it revolves for 300revolutions. Find the area of the land covered in 300 revolutions? 答案:32400pi出现多次变体,计算时请注意。16 【算术题】Courier charges for packages to a certain destination are 65 cents for the first 250 gramsand 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of apackage for which the charge is $1.55 ? 答案选BA 1155 B 1145 C 1040 D 950 E 259官方:(1.55-0.65)/0.1=900grams, 900+250=1150grams, 因为最多是1150grams,所以选B.如果再少就用不了这么多钱,就是在1150到1050之间才是$1.55.17 【算术题】五十个算术平均值是x,五十个数中,有一数是18.x,若这个数从18.x变为28.x时,其算术平均值变化多少? 答案是0.2Mean of 50 numbers given to be 19.5, and when a number 18.5 from those numbers is replaced by isreplaced by 28.5, then what is the difference between the new mean and the old mean?官方:一个数从18.x变成28.x,说明这50个数的总数增加了10,那他的算术平均值变化就是10/50=0.218 【比大小】xy坐标系从原点(0,0)经过(x,11/10x)的直线的angle与45度比大小 答案选 A官方:直线的斜率是1.1,45度角的直线斜率是1,所以题目中的角度会大于45度。斜率是夹角的正切值。19 【应用题】关于net profit的题,1992年是y,1996年是2.6y,问四年的arithmetic average 是多少?选
  • 40%1992’s profit is y, 1996’s profit is 2.6y what is the average profit increase?官方:选项里应该是40,50,60,70,80,题目里貌似有说是compounded interest rate20 【比大小】有(10^22)+1 除以11的余数 与2比大小 选C变体:Column A : Remainder of 10^22-1 divided by 9Column B : 2 答案:B官方:上面那个数等于 (10^22-1)+2 也就是 22个9+2,99后面跟很多0是可以整除11的,22个9拆成11组都能整除11,剩下的2就是余数。另外记住, 10的偶數次方除以11都餘1 加1後變成2,10的奇數次方除以11都餘10 加1後變成11就好了。21 【图表题】有圖表題組在講 workforce 公司現在的員工分別是幾年進公司的,图表中给出了1994到2000年的人数比例, 2001年的公司总人数就是1994年至2000年人数总和。問題一:某公司隨機抽兩位2001年的員工解雇, 那這兩位都是1997年進公司的機率有多少? 答案是20% *20% = 0.04問題二:1994到1998年进公司(75%)的薪水为39900,1999和2000年進公司(25%)的薪水為30100.那公司總平均薪水為? 答案:约为3750022 【比大小】好像是a= 5*71*91 ,b= 17*91*69 。比大小,选B。官方:同样的题目有很多,数字不同,问法一样,有的问比较个位数字的大小,那就是个位数字相乘,那选A,有的是直接比大小,也不排除问的是数位,考试时请看清楚,unit digit的意思是个位数。23 【比大小】P圓被面積為18的正方形包住,Q圓是包住面積為9的正方型,問哪個圓半徑大,选C Area=18的正方形内的圆和Area=9的外切圆 diameter 相等24 【算术题】x=97 the least of x/97, x/(x+1), (x+1)/x, (x-1)/x, x/(x-1),选D变体:x=98 which of the following is the least?a. (x-1)/x b. (x-2)/(x-1) and a few other options 答案自己注意,方法一样25 【算术题】[(5.95*601.3)^0.5]/3.91 (a)5 (b)10 (c)15 (d)20 (e)25,选C官方:这个题估计一下就行了,5.95近四成6,601.3近似成600,那么中括号的结果就是60,然后除以一个接近4的数,大概等于15。26 【图表题】表格和饼图,讲某学校faculty的年龄构成,和文科类各级别教员的比例第一个表格 给了各种不同级别的教授和年龄,大致情况如下第一问是60岁以上或有associate professor职位,或两者皆满足的人数是 900(Associate professor + over60 associate professor – Both) = 900
  • 第二个饼状图 说得是art 这个学院的的教授的年龄分布第二问是文科30岁以上的assistant professor 占文科assistant professor比例是:1-11/(120*55%)=5/6 120和55%来自饼图Art department,Total department: 120,55% is assistant professor,When 11 is less than 30, what is theprobability of 30 years and older? 5/627 【比大小】1/96+1/97+1/98+1/99+1/100 和 1/20 誰比較大,选ACol A: 1/100+1/99+1/98+1/97+1/96Col B: 1/20变体:Column A : Arithmetic mean of 1/96, 1/97, 1/98, 1/99, 1/100Column B : 0.01 答案:选A官方:1/20=5/100,1/96到1/99均大于1/100,所以前面的和比较大。28 【几何题】有一題給一段弧长 =π/2 面積 = 2π的扇形, 問半徑是多少? 选A:8官方:扇形弧长=2r*pi(θ/2pi) 扇形面积=pi*r^2(θ/2pi) 一比就可以得出半径是8。29 【比大小】3秒2页,5小时几页与12000页比大小, 选CPrinter makes 2 copies per 3 second变体:Xerox machine prints 3 pages in 2 secs. How many pages can the machine can print in 3 hours?答案:1620030 【比大小】y^2=9 A: y^2 B: y+? (某个数)官方:这不是难为官方么,请后来的同学看到把题目补全,计算的时候请注意y=±3,不要忽略了负数的情况31 【几何题】xy轴坐标,圆心在(1, 5),圆上的每个点都是nonnegative,问圆的最大面积?A:π B:2π C:... D:25π 答案:选A32 【比大小】某一年某人买5000ponds的纸,平均价格是0.96,隔年买6000ponds,平均价格0.9,问A:两年差价 B:600 答案:C33【比大小】数字PQRS的平均数是r,标准差是tA:P+1,Q+1,R+1,S+1的标准差 B:t+1 答案:选B官方:每个数+1,平均数会+1,标准差不会改变,还是t34 【几何题】___________ M___N O____P______ __ -2 -1 x 0 Y 1 2问x*y的值会落在哪里?A:M B: N C: O D: P 答案选:B官方:x*y肯定是负值,因为y<1, 必然乘积在x靠近0的一方35【比大小】一台車 前面兩中鐘頭平均時速是每小時五十公里休息之後再出發 平均時速是每小時四十公里。問整個平均速度 跟 每小時41公里比大小官方:没法比较,因为行驶时间跟休息时间都没有给出,无法计算平均速度。如果考场上看到有别的额外信息的话自己算一下,这道题不排除带出来机经不全的可能。36 【算术题】3/4的x比2/3的x大9, 问1/2的x是多少?答案:选54
  • A.6 B.12 C.36 D.54官方:2/3 x + 9 = 3/4 x,可以算出x=108,那么1/2 x 就是54。37 【几何题】问图中有多少个长方形? 答案:选E 9个官方:图大概就是这个样子,数一下就好了。38 【比大小】w < x < y < z,四个数的average=median,比较x-w和z-y的大小,选C39 【比大小】5边形,知道一个角是84°,其他四个角都是X,比较x和112。 答案选A官方:X应该是11440 【算术题】the discount of 40 percent of the original selling price of an item reduce the price to $72the original selling price of the item = $120官方:$72是60%的钱。discount of 40 percent还剩60%的钱41 【算术题】求1/2,1/3,1/4的平均数 答案:13/3642 【比大小】x+y+z>0,x+y+1<0 比较z和1大小 答案:选A z>143 【比大小】有四个数,两个大于120,两个小于120,比较它们平均数和120比大小 答案:D 没法比较44 【几何题】圆心坐标(0, 2)和圆上一点坐标(2, -1),求直径? 答案是:2*sqrt(13)官方:两点之间距离公式求出半径45 【算术题】5478.0235,问千分位是什么 答案:3官方:注意千分位的英文,thousandths’ digit,有人看成千位。46 【几何题】 P1P2P3P4 四个象限 P1234分别在4各象限 比较P1P3 和P2P4的斜率 答案:A官方:斜率是有正负的47 【比大小】0<x<1,比较1+x和1/(1-x),选B官方:请注意后面是1-x还是x-1,结果会差很多48 【比大小】2^70+2^70+2^70+2^70 和 2^72 比大小,选C
  • 49 【比大小】f(n)=3n+1, n 为偶数,f(n)=2n,n为奇数。比较f(f(2)) 和 f(f(3))的大小官方:f(f(2))=14, f(f(3))=19, 注意哪个是A哪个是B50 【比大小】比较从9张画里选3张和从9张面里选6张的大小 答案选CColA: ways of selecting 3 things out of 9ColB: ways of selecting 6 things out of 951 【比大小】x<y<z,比较xy和yz 答案选D官方:就目前信息,不知道正负没法比较。如果题目中提到<0 or >0, 则可以比较,请仔细看题计算。52 【图表题】 美国雇用人数的那题,1988年和2000年,左边是10个county的employment数据(用的是一个ratio来表示人口,例如:1.00,1.22,0.63) 右边是的每个county的工资sum in million.问题一:1988年employment人数相同的两个county的工资sum相差多少,(in billion), 两个相同county的ratio=0.63,算一下相减就行,算出来答案是2.47,选项是2.5问题二:I. 2000年所有的平均值在29800以上(错,其中一年是25200左右)II.美国town的人数均值是13.2million? (错,这里有个故弄玄虚的地方,美国的总量好像是132,这里列举了10个town,其实应该用所有的town的数量来除)III.COUNTY D的1988到2000增长率是超过2倍。答案选: only III53 【算术题】三个人画画,1、2、3一起画一张要6天,1、2画要9天,问3自己画需要几天 答案:18天官方:把1和2看成一个整体,知道了合速度和其中一个速度,求另一个速度1/6-1/9=1/1854 【算术题】x y z一起工作需要9个小时做完,y 和z 一起工作需要12小时完成,问如果x一个人工作需要多少小时完成? 答案:36小时官方:解法与53相同55 【比大小】有4个小朋友,都大于3岁,现在总年龄是36,问3年前他们的年纪和与30比大小。答案:B56 【比大小】一个花园perimeter的5次测量,2次大于200, 3次小于200,问平均和200比较 答案:不能确定
  • A man measures the perimeter of a rectangle for 5 times. The first two measures are less than 200 and thenext three are greater than 200.Col A :The arithmetic mean of the five measuresCol B:20057 【算术题】某材料密度是 2.5g/cm^3,一根这种材料的棒子重800g, 棒子宽3cm, 长是高的3倍,问棒子高最接近什么? 答案:应该是6 其它选项是9,45,53有一种材料density为500g/cm3, 有一个长方形的东东是这个材料做成的,mass 是400g,然后宽是3cm,长是高的三倍,问高是多少?答案算出来约是0.3官方:题目中的描述是the width is 3cm and three times as long as the height is,不排除是一道题因为带出来的数有错误,但肯定是一回事。密度x体积=质量,体积=长x宽x高,然后就是计算问题了。58 【比大小】x^4=16 的x与2比较大小 答案选Dx^4=16 colA: x colB: 259 【比大小】某公司内employee 其中女员工55%,公司内某职位22%,女性员工中的secretary占了40%,比较女性员工中的secretary所占%与公司内某职位22%两者大小。 答案C一个公司 x%是 women, women里面有y%是secretary,有z%是executives.ColA: women secretary 人数 x% * y% =22%ColB: executives的人数…也是22% 选C60 【应用题】5%浓度的盐水500立方cm,问充进多少浓度为3.5%的盐水后,浓度变为4%?答案是1000.变体:5%浓度的盐水K,问充进500浓度为3.5%的盐水后,浓度变为4%?官方:用总溶质除以总溶液就好了61 【几何题】 如图一个等边三角形中间三个相切圆弧,问黑色部分的面积和3*sqrt(3)/4哪个大,答案: BColA: Area of the shaded region ColB:3*sqrt(3)/4官方:首先感谢这位同学辛苦的画图。三角形的面积是根号3=1.732,非黑色部分的面积是pi/2=1.5662 【比大小】G事件发生的概率3/5,E发生的概率是5/7,两个事件相互独立,问G发生同时E不发生的概率和 1/6 比大小 答案选A官方:概率为(3/5)(2/7)63 【几何题】
  • 这是个圆,半径为r,ST 长度为pi/2,OST面积为pi,问r是多?答案:r=4变体: If the arc length of is 2π and the area is π/2 then what is the radius of the circle? 答案: r=1/2官方:再次感谢画图的同学,扇形面积=(1/2)*r*l,l为弧长。请注意题目中的数值有可能会变。这两天出来的说OST的面积给的是2pi,那么r=8,方法是一样的。64 【算术题】100 < X < 999,X的all 3 digits are the same number,請問X有幾種可能的答案?答案:8种 官方:别问我为什么变体:从100<X<999中随机抽出一个数,三个数字重复出现的概率是多少(包括100和999),答案是0.0165 【比大小】k: Y = 3X – 5 ; m: Y = 3X + 7,比較k和m的slope(斜率) 答案:C66 【比大小】If a>1,Column A : (a+a^-1)^2 Column B : (a^2 + a^-2) 答案选A67 【比大小】Arithmetic mean of Group A = 32Arithmetic mean of Group B = 38Arithmetic mean of Group C = 40Arithmetic mean of ALL Groups = 36Column A : No. of people in Group AColumn B : No. of people in Group C 答案:选A变体:1班分数82 2班88 3班90 整个平均分是86 问1班和3班哪个班学生多 选1班学生多68【图表题】美国雇用人数,有10个town和employment数据, town的数据最下面是美国的sum.问题一:1998年(?)employment人数相同的两个town,他们的增长率的比值?答案是 M<<K问题二:I. 2000年所有的平均值在26000以上(错,其中一年是25000左右)II.美国town的人数均值是13million? (错,这里有个故弄玄虚的地方,美国的总量好像是130,这里列举了10个town,其实应该用所有的town的数量来除)III.忘记了。求跟增长率一致的说明是只有3.官方:貌似跟52是一道题,不知是不是变体。69 【比大小】X@Y=X^(-Y) ,Column A : (2@3)^2,Column B : (2@2)^3 选C70 【计算题】For what x value is x^12 - x^10 +x^8 – x^6 > 1(a) -2 (b) -1 (c) -0.5 (d) 0.5 (e) 1 答案A71 【比大小】f(n)=2/n-2/(n+2)然后f(5943)和f(5944)比大小 答案:A72 【应用题】一本书36块,10%的profit,问要赚1600块需要卖多少本书和500比大小 答案选B官方:大概是444本,1600/3.6The cost of a book is $32. A person gets 10% profit on each of the book sold.Col A : The number of books sold by the shopkeeper to get a profit of $1600Col B: 500 答案:C
  • 官方:觉得是一道题,估计是有同学把数字记错了,大家仔细一点就好了73 【几何题】直線坐標上2點分別叫p ,k, p<0,k>0求两者间的距离? 答案是lpl+k74 【图表题】学生奖学金的,一个是方图是说的是列出了每几年领取奖学金的人数,第二个图是饼图,说的是筹集的资金的使用比例图。第一问我填了900(我没有看题目就写了答案了),第二问是求某段时间平均每个学生领多少钱?我是用饼图可以求出钱数,方图可以知道人数官方:74题来自同学回忆,第二问的数字不记得了,请看到类似题目的同学带出更多信息。75 【比大小】某人跑步5laps,第一圈12mins,之后每圈都是前一圈用时的5/6,最后问总时间与50mins作比较。答案:B官方:等比数列求和公式:Sn=a1(1-q^n)/(1-q) =12(1-(5/6)^5)/(1-5/6),有没有发现计算量很大啊?其实有更简单的方法就是,第一圈12,第二圈10,后面每圈都要小于10,5圈下来肯定小于50。76 【比大小】(x-2)(y-4)=0 ,问x大小与2比较 。 答案:D无法比较变体: (x-2)(y+3)=0 ColA: x ColB: 2 答案: D77 【计算题】X,Y,Z为非零实数,问下面有可能为0的是 I. X^2+Y^2+Z^2; II. X^3+Y^3+Z^3; III.X^4+Y^4+Z^4,答案是II. X^3+Y^3+Z^378 【计算题】某正态分布数列95%落在二标准差内,问下列何者在二标准差外 答案 2%官方:正态分布中,约95%的面积在平均值左右的二个标准差范围内,范围外的5%是在左右两边的,每一边为2.5%,所以2%是在二标准差外。如图所示79【比大小】d是x, y, z 的标准差(或者方差,不确定)Col A: x+1, y+1, z+1 的标准差Col B: d+1答案:B80 【比大小】Find greater interest gain @ interest rate=7% A: 6,000, 2年 B: 12,000, 1年 答: A 变体:12% interest rate compounded. Column A: interest gained on $6000 after2 years; Column B:interest gained on 12000$ after 1 year81 【计算题】Each people read a unique amount of books. Find median of people who read:- less or equal to 6 books (4 people)- 7 to 11 books, inclusively (5 people)- more or equal to 12 books (6 people)答: 10 选项A:7 B:8 C:9 D:10 E:1182 【计算题】下面那个x值使得1/x最大?A : 2/7B : 3/8
  • C : 3/10D : 7/200E : 3/500答: E83 【比大小】ColA: 7^20,ColB: 20^7 答案: 选A84 【计算题】-2<x<9 and -4<y<10, maximum value of x-y 选13官方:这个题目有一点小问题,答案不保证对。有可能题目中提到是整数,或者不等号是带着等号的,遇到请仔细。85 【比大小】P>a+b,Q>a+b,ColA: P+Q,ColB: a+b 选D86 【计算题】Least number which when divided by 6,7,8,9 will leave a remainder of 3 in each case x 选388 【计算题】How many numbers are there between 1 and 500 inclusive, which are not divisible by either4 or 7? 答案:选321。官方:500减去4的倍数,减去7的倍数,加上28的倍数89 【计算题】考虑关于PETER这个名字的错误拼写, 拼对的概率是多少?官方:这个题目可能是给这5个字母random拼出来PETER的概率,答案是:1/(5!/2!)=1/60。90 【比大小】P,Q,R are positive integersColA: SD of P,Q,RColB: SD of P-6, Q, R+6答案:D。官方:需要P,Q,R的关系。91 【几何题】parallel lines and how many parallelograms can be formed.官方:信息不完全,估计原题中有图。92 【计算题】Travelling at 3/4 of a person’s usual speed, he is late by 1 hr 30 mins. What is his usualtravel time? 答案:4.5 hr变体:If a person traveling by 75% of his speed gets late by 2 hours, then what is the normal travel time?答案: 693 【比大小】–x|x|>0ColA: square root of (x-10)^2ColB: (10-x)答案:选D94 【计算题】Maximum number of points where a triangle and a circle can intersect. 答案:选695 【比大小】A circle is centred on the origin. Point X and point Y are selected at random from within thecircle.ColA: probability that X>Y>0ColB: 1/8
  • 答案C96 【计算题】3 different co-ordinate points are given with k as a y intercept in one and the three points arecollinear. Value of K is asked.官方:应该是给了同一条直线上3个点的坐标带着k的,然后给了y轴截距,目前信息不全。97 【计算题】-11, 12, -13, 14, -15, 16………..Sum of first 37 terms.答案:-2998 【计算题】Numbers of ways in which 12 students can take 3 different tests of 4 students are to takeeach test.官方觉得是12个学生可以参加3个不同的考试,每一个考试有四个人参加的的方法有多少种,是排列组合,应该是(12选4)*(8选4)=12!/(4!*4!*4!)吧,考试的时候再仔细看看题目99 【图表题】A venn diagram given showing percentages of 3 magazines individually and three of themtogether. The question said to find the percentage subscribed to at least 2 of the magazines.官方:题目信息不全,请带出更多的信息。100 【图表题】a city having 6 different industries and their pollution rate with respect to 4 different years.官方:残题请大家带出更多信息101 【图表题】comparing a pie chart and a bar graph of criminal rate of country X and was asked to findsome probability.官方:同样是残题102 【比大小】A shop sells an item for 125 dollar and another shop sells an item for 75 dollar.ColA: percentage gained over 125 dollar if the item is bought from the shop selling at 75 dollar.ColB: 40%答案:选A 官方:50/75 *100% > 40 %103 【比大小】slope of a line passing from origin and having a point (a,4a/3) is z.col A:Z,col B:4/5。 答案:A答案: slope for (0,0) and (a,4a/3) is 4/3=z=1.33...in col B the option should be 4/5 not 45...4/5=0.8...so ansis col A104 【比大小】y/x = 5,4x + y = 27Col A:y+2,Col B:x+2 答案:选A105 【计算题】Cost price of 11 pens are equal to selling price of 9 pens, what is profit percent?答案:22.2%106【计算题】Sum of n consecutive integers is said to even. Some options were given like 8, 12, 16, 20,24 (all multiples of 4) and the question is that which could be the sum of the value of n.官方:题目信息有些问题。我们怀疑是求那个sum,如果是那样,就选不是4的倍数的那个。107【计算题】83A+DBB=CAC2, where A,B,C,D are different digits, what is D?
  • ANS: D=6A=5,B=7,C=1,D=6835+677=1512两个三位数加起来等于四位数,四位数的最高位一定是1,把C=1作为突破口。108 【比大小】a/b=3.12, remainder was 24.ColA:b, ColB:100 答案:选A109 【计算题】A pyramid had a square base. The sides of the squares are 20. Height of pyramid?官方:条件不全没法算吧。110 【计算题】A person is travelling from two cities at 8mph and back at 6mph, average speed was asked.答案:48/7约等于6.86111【比大小】z is a positive odd integerColA:number of positive factors for 2z,ColB: twice the number of factors of z 答案:C112【比大小】if two sides of a triangle are 6 and 8, thenColA:area of the triangle,ColB: 27ANS: B113【比大小】ColA:1/(1-0.03), ColB:1.03ANS:A114【比大小】k/5099=0.0382, unit digit of k.ANS: 4115 【计算题】Guests at a recent party ate a total of 15 pork chops. Each guest who was neither a studentnor a vegetarian at exactly 1 pork chop. No pork chop was eaten by any guest who was a student, avegetarian or both. The vegetarians attended the party at a rate of 2 students to every 3 non-students, halfthe rate of non-vegetarians. If half of the guests were vegetarians, how many guests attended the party?A. 25,B. 30,C. 45,D. 70,E. 90。答案:选D官方:题目貌似有问题,据说答案没问题,考场上请仔细计算。116 【计算题】A permutation problem, where a teacher sets some questions and only some questions areto be answered with some choices, number of ways answering the question.官方:全是some啊。。。117 【比大小】m*n=64, where m and n are positive integers,ColA:m+n, ColB:17ANS: D118【计算题】Something on average weight of a 20 member group increased by 3kg, when a personweighing around 68 was replaced by a new member. Weight of the new member?ANS:128119【比大小】ColA:25% of sqrt(983.33), ColB: sqrt(98.333)ANS: B
  • 官方:考试时应该会已根号的形式给出,正负可以直接判断。120【计算题】A probability question where 2 dice are rolled and sum of the number obtained were morethan 7; probability that sum is an odd number官方:答案是6/15 = 2/5。121【计算题】4^30-2^50, when divided by 5, what is the remainder官方:原式子=2^60 - 2^50,又因为2^4 divided by 5的remainder是1,所以可以把指数除以4取余数,那么就是 2^4-2^2 = 12,那么除以5的余数是2。122 【比大小】If x<0, then ColA: -x-IxI ColB: 0 Ans: C123 【计算题】When (1+22^24) is divided by 23 then what is the remainder? 答案: 2官方: 把上式变换为(23-1)^24+1, 括号中展开是一个25项式, 最后一项是1, 其余各项都至少包含1个23为系数,因此均能被23整除, 所以整个式子最后余2124 【计算题】If a function is defined by a@b=a^2-2ab+b^2 and given that a@3a=144 then what is thevalue of a? 答案: ±6125 【比大小】 ColA:x+y ColB:90 答案:B126 If the length of each side of the regular hexagon is 2 then what is the y coordinate of point P?官方:这道题应该有个图知道P点位置,然后根据正六边形的对应关系即可。127 【比大小】Of the 20 students in a class, half of the students are boys. A 7 member committee is toformed, out of which 6 are girls.Col A: The probability that 7th member is also a girlCol B: 3/5答案:B官方:A计算出来概率是2/7128 【比大小】Given that x^2 > -yCol A: x Col B: y 答案:D129 【计算题】Given two overlapping swimming pool of radius 6 each. Find the perimeter of the swimmingpool?官方:应该是有图没有带出来130 In how many ways, three X and two Y can be arranged in a line, such that no Y are together? 答案:6131 【比大小】The population of a town is increased at a constant rate of 30% from 1990 to 1998.Col A: The population in 1993
  • Col B: Half the population in 1995答案:A132 【计算题】The Unit digit of 37^37 is .........答: 7变体:The unit digit of 89^98 is ................... 答:1官方:个位数是9,3,1,7,9,3,1,7.......9,3,1,7的循环,共36个133 【计算题】The mean of 20 values was 65, one value 69 is misread as 96. Find the correct mean? 答案:63.65134 【计算题】If K = 105/L, L is an integer, thenCol A: The number of positive integer values of L, KCol B: 7答案A,8>7135 【计算题】If x = 10!, then how many zeros the number x has? 答案:2136 【计算题】A bag contains 20 red and 30 white balls. If 3 balls are picked at random, then what is theprobability that all of them are red? 答案: 57/980137 【比大小】Col A: |6| + |-3| + |-3| Col B: 0 答案:A138 【计算题】A square inscribed in a circle, one side of the square is given, question asked is to find theradius of the circle?官方:没有数字带出来,计算方法应该是(side*sqrt2)/2139 【计算题】A probability question on some deck of cards is asked.官方:信息没有带全,请后面的同学补全。140 【计算题】Given that 3 persons can complete a work individually in 3 days, then in how many daysthey can complete the work, if they work together? 答案:1141 【比大小】If LCM (least common multiple) of two numbers is 105, thenCol A: The greatest prime factor of the two numbersCol B: 5答案:A142 【计算题】Given that a/b = 1.25, where a and b are integers. Which among the following cannot betrue:I.a+b is an odd integerII.ab is an odd integerIII.a+b is an even integer答案:II143 【比大小】If |x|/x = -1, thenCol A: xCol B: -x答案:B
  • 144 【比大小】Given that m - 6z > 0 and 5z - m > 0.Col A: mCol B: 0答案:B145 【计算题】If N = (-2) ^x, where x is a negative integer and -5 < x < -1. What is the difference betweenmaximum and minimum possible values of N? 答案:3/8146 【比大小】The average weight of 65 women is F and average weight of 75 men is M, given that F > MCol A: Average weight of 140 membersCol B: (F+ M)/2答案:B147 【几何题】All the sides of a quadrilateral have different lengths, at most how many angles can be 90degrees?答案:2148 【计算题】The sum of first 100 positive integers is 5050, what is the sum of first 300 positive integers?答案:45150官方:等差数列求和Sn=n(a1+an)/2149【计算题】Volume of a cube given as 27 which is painted totally, and are cut into small pieces of unitvolume. Area of the unpainted surface? 答案:108150 【计算题】100<X, X+7除以3的余数是2,问X除以2的余数和0比较。答案:D151【计算题】Given that a(b+1)=odd 问下列哪个是正确的?(说明a是odd, b是even)I.a+b is an odd integerII. ab is an odd integerIII.(a+1)b is an even integer答案:选I&III对的那个(好像是第四个选项)152 【计算题】 有一道数轴题,在一条数轴上分布了很多点,只有大概位置,最后求一个算式(rt+s)/(m^2+u)的值最接近MRSTU什么点,答案:是s点,就是比较靠近0,在负的那一边。官方:除了u点位置不确定,在1和2之间,其他位置应该没有问题。153 【比大小】x-x^2>0 问x与1谁大 答案B
  • 154 【图表题】 有一个V区域有五个其他区域 外地出生人口所占比重绘制了一个饼形图 一个区域X有几个邻区 邻区的总人数和外地人口总数绘制了一个表,左边是表格,有UVRTX等等城市,要注意右边的饼图,什么foreign-born的人口比例,表格里有European,Asia等等地区的人口。在计算的时候我没有用到表只用了饼状图第一问问1990年V区域中外国出生人口是欧洲的人的比重29%第二问 中国人口占亚洲外国出生的1/3 问那么中国占全部外国出生人口的比例是1/8155 【比大小】F的斜率是3,G的斜率是2,两条直线在(1, 1)相交,问F(2)-G(2)和2比大小。 答案:选B官方:F(2)-G(2)=1,目前有计算形式出现的情况。156 【比大小】f(x)=ax+5 g(x)=bx+2 a>0;b<0 问f和g的x轴的截距谁大 答案:g的大157 【比大小】某高校百分制的考试中三年级和二年级的同学一起参加考试,二年级的平均分是88,三年级的平均分是92,问总体平均分和90谁大 答案:D变体:初中平均分88,高中平均分92,总平均分和90比较。 答案:D一学校有140人,低年级学生平均分92,高年级学生平均分88,问总体平均分与90比大小 答案:D158 【比大小】If x = 30! and y = 5, then Col A: x/y Col B: 29! 答案:A159 【图表题】 是几个公司full-time 和part-time 的工作的人数和平均每小时的工资绘制的表格F公司比G公司的part-time 多付187000的工资,假设每个公司每个员工工作的时间是相同的问两个公司的员工工作多少小时? 答案:17个小时260个员工,有190人有房,220人有车,该公司的每个人不是有房就是有车要不就是都有,问有多少人只有车没有房?答案:70人160 【计算题】1935的最大质因数(prime factor)是多少? 答案:43161【计算题】3个委员会各有8,10,13个人,问拉一组不同的人三个委员会都有,最少多少人?答案:24 选项是:13,15,21,24,31162 【计算题】A set包含3-90中3的倍数,包括3和90;B set中包含5-75中5的倍数,包括5和75。问,Aset中既是3的倍数又是5的倍数的数字的总数占A的百分之多少。1/10
  • 官方:答案由同学带出。官方觉得题目有点问题,可能信息不全。163【几何题】 如图:AB=6,BC=16,CD=10,角B和角C都是直角,问你AD距离? 答案:16*sqrt(2)官方:很多情况是与16*sqrt(2)比大小,选C164【几何题】 如图:一个长方体,高是4,体对角线是13,面对角线有一条是5,问你体积? 答案:144165 【几何题】 如图:图中角ADB=角DBE = 角BEC,三个命题AD=BE, BD=CE, AD=DB, 问哪几个是命题是对的? 答案:选都不正确那个选项貌似是D166 【图表题】墨西哥的一个数据和全球数据。。问12月出的墨西哥的那个数据和12月末的比较墨西哥的人口 和 全世界的人口:问1994 年 年初到年末 墨西哥人口减少了多少?官方:残题,望带出更多数据。167 【计算题】1 / x - (1-x)* 1/x 答案:选1168 【比大小】(2^200+2^200)/(4^50+4^50+4^50+4^50)和2^100比大小。选B169 【比大小】 一个3条平行线与x轴平行分别与y轴交1,2,3然后
  • 两个三角形,一个高是3,一个高是2,比较ABC的面积和3/4的ADC的面积的大小。答案:选B170 【计算题】2x+y=a, 2y+x=b,a和b都是具体数,具体多少不记得了,求x+y是多少,相加除三即可。答案:(a+b)/3算出来的结果171 【比大小】定义f(x)=1/x-1/(x+1),Col A: f(2)+f(3)+…f(8) Col B: 1/8 答案:A答案:第一列的大小是1/2-1/9=7/18,这题存在变体,但计算方法相同,考试时请仔细计算。172 【比大小】r percent of s percent of T is 7,比较T跟70000/rs。选C173 【比大小】24的最大质因数 和-7<x<-1 的乘积 和-58 比大小。选A变体:x是>24的质数,y是-1到-7之间的整数,求xy的最大值和-58比大小。CX是大于24的质数,-5<Y<-1,比较xy和 -58. 答案是D官方:目前变体的两个版本不知道是不是一道题,题目不难,考试时请仔细。174 【计算题】Books standing on a row, a dictionary are 30th book from left and 33rd book from right.2 books to the left of dictionary removed and 4 books to the right of it are also removed, then how manybooks are on the shelf?答案:56175 【比大小】(x-3)^2=-(y+2)^4 and 2x+3y+4z=0,ColA:zColB:0答案:C官方:完全平方非负数,所以方程左右两边有且仅有=0的时候才能相等,因此x=3,y=-2176【计算题】Sides of a square measured to the nearest centimeter are 6 cm long, least possible value ofthe area of the square? 答案:选选项里在30.25-36之间的比较小的官方:5.5<边长<6.5的情况下才能说近似=6177【计算题】Greatest prime factor of 4^17-2^28 答案:7178 【计算题】Property assesses at 60% of appraised value and taxed at the rate of 4 dollars per 100dollars of assessed value. A taxpayer is assessed 240 dollars per quarter in property taxes, what isappraised value of the property? 答案:40000官方:(0.6x)*0.04=240/0.25179【计算题】Exam held, 70% passed in chemistry, 73% passed in Maths and 64% passed in both. 63failed in both, total number of examinees? 答案:300官方:C only = 70-64 = 6%,M only = 73-64 = 9%,both fail = 100-6-9-64 = 21%so, no of students = 63/0.21 = 300180【计算题】F(x)=1/[x-3], which cannot be the range of this function. 答案:0官方:方程不会等于0。range是指方程的值域,domain是指方程的定义域,如果题目中是the range of x也应该是指定义域。
  • 181【计算题】500 candidates gave test, avegare score was 72. Bottom 16% will have to take retest, 10candidate scored 92 or higer, what is the score below which a candidate must take a retest?官方:题目好像信息不全,也没有选项答案可以参考。182 【比大小】(x+y)<20 and y<20, ColA:x and ColB:20 答案:D183 【计算题】A rectangle PQRS given with length PQ=17 and width QR=5. T is a point on RS. What isthe probability that QT>13 答案:5/17184【比大小】X<0, ColA:sqrt(–x|x|), ColB:-x 答案:C185【比大小】 x < 0, Column A: x-|x|, Column B: 0 答案:B186 【几何题】there was a figure of a cuboid cut into cubes each of side 1 cm... basically you had to addthe lengths of each of those cubes to find the length, breadth n height of the cuboid. YOU had to determinethe surface area of the cuboid.官方:信息不全,估计看见图不是很难。187 【比大小】 2Z=X+Y x,y,z 的平均数与Z比大小。选C188【比大小】the length and breadth of a room are 12 and 8 resp. if a circular carpet has to be placed onit, what is the max area the circle can have?ColA: max area of circle ColB: 24pi 答案:B189 【计算题】有一辆车走完全程需要60分钟,速度是a(忘记了)。如果另一辆车前面45分钟的速度是30迈,那么后面30分钟它的速度是多少?官方:答案貌似是45,由同学带出。根据答案倒推a是45。190 【比大小】有个cheese的题,说是100kg milk 可以做10kg的cheese,问1.2millionkg的milk能做多少cheese,和12000比大小。 答案:A191【比大小】0< x<1, 比较1/(1-x) 和1+x 答案:A192【计算题】1mile=5280 feet,1foot =12inches,一个 cube 边长 3 feetroad :longth 1/2 miles,wideth 24 feet,highth 4inchesquestion: 多少cube 可以把路铺了?答案:7040要铺1/2 inch长,24km宽,4 inch的路,问要用多少的cube(单位貌似是inch,隐藏在题干里)官方:因为是新题,大家的信息都有些出入,请遇到的同学留意。193【几何题】一个球体里面有两个圆切面都过圆心, 两圆面之间的夹角为30度,问:其夹角所包含部分占球的几分之几。答案是: 1/6官方:原题应该有图,请仔细计算。194【计算题】A国钱=1.5 B国钱,1 B国钱=1.4 C国钱,1 C国钱=1.3D国钱问50A国钱是多少D国钱? 答案:136.5
  • 195【计算题】班级原来有1/3男生,然后走了2女生,剩下的人2/5是男生,问班级有多少人?答案:12官方:注意一下问原来还是现在,原来是12人,现在是10人。196【计算题】 一个圆柱侧面积是150pi, 上圆面积是25pi,问圆柱的高。 答案:15197【比大小】切橘子,图中给了一个球的两个横截面,两面成30°,问切下来的部分是橘子的多少与1/10比较 答案:A官方:答案由同学带出,说计算后得1/9,原题应该有图,遇到请仔细计算。198【几何题】平行四边形题求周长,忘了题怎么叙述的,反正得出的理论是下面的三角形是等腰三角形, 周长得16官方:残题,应该有图。199【比大小】一个学校35%上instrument班,25%的人上poem班,instrument班中有5/7的学piano,问学piano的人和学poem的人数比大小。 答案:C200【计算题】一个折扣店正常按商品定价低20%销售商品,在这个商店折扣期间再按低25%的折扣出售商品,问在本店折扣期的商品价格是正常定价的多少? 答案:60%201【比大小】(x+10)^2-2=0,(y-10)^2-2=0,比较x与y大小 答案:B202【比大小】2^16做3次开平方运算,与4比大小。答案:C官方:考试时请注意原题描述。203【图表题】 求的是差值最大的地方有多少官方:是个新题,但是目前信息很残,请遇到的同学留意。204【比大小】定义 X@Y=(x^2+y^2)/2,比较3@4,和16 的大小 答案:B205【比大小】x除以5的余数是3,问x除以2的余数 和1(还是0来着) 比较, 答案:D206【比大小】通过原点的直线斜率是-2, 上面有一点(2,y),比较y和-4 答案:C207【计算题】书店买书 regular价格就比原来的书便宜20%,on sale时候又打了10%的折扣,问 on sale 时候的价格比原来价格的百分比。 答案:72%208【图表题】1999年世界各国produce和export玉米的排名,各取前十。第一题,简单的计算,1.英国少于8million 2. 美国多于1/3 3. 所有其他国家加起来少于5%, 都是对的. 第二题, Tailand有多少ponds,tailand好像0.1 metro tons, given 1 short ton = 0.907 metro tons = 200 pons 答案是220
  • 209 【图表题】 捐款题,每个机构在每个领域捐款的表、扇形图。第一问如果四个领域(教育、住建、艺术、还有什么education35%, service 20几%)平均分,教育得到的会比现在少多少?选1.1million,似乎是最后一个,因为1.1 million=11 million*(35%-25%);第二题基于一个表格,表格里面有4个机构的捐款,让你把这个表格转化为扇形图,求B机构的圆心角。答案似乎是20.7左右。(11/191)*360209【比大小】分式化简,分子分母都是x的几次方乘以Y的几次方,其中有y的-3次方之类的,约分化简就行,结果是两个分式相等。x y都是7次方啥的,不过化简后为-2,所以C官方:题目残,但应该不难,注意负指数实际就是分数形式。210【比大小】一个正方形,上面画了个正三角形,给出三角形边长,求正方形面积。答案无法确定。因为人家没告诉你是按照比例画图的,即不一定是正三角形,虽然看着很标准。官方:答案由同学带出,官方没有进一步的信息判断。211【比大小】89!-88!与87!*88^2比大小 答案:C。212【比大小】有个条件y>-2,貌似选A。反正就是分式比大小,分母都是正的,分母越小,分数越大。213【比大小】定义x=n(n+1)/2,比较(-1)^x与(-1)^(x+2)。n为整数。 答案:C变体:比较 (-1)^x与(-1)^(5x)的大小,选C214【计算题】A box has 4 @, inclusive, @有8个P, inclusive, P有3个wayer。句子有点难读,但是 其实就是把4*8*3=A (由于数字4,8,3记不清了,先写A)问下面的数有多少个A运东西,大包装能装4个中包装, 中包装能装3个小包装,每个小包装里面有8件,问一大批的件数不可能是哪个数,就是说哪个不是96的倍数。答案:是64000215【计算题】求1到650这些数中在130到389中且尾数是12345其中之一的数占的百分比? 答案:20%216【比大小】 某种测试的结果频数,一共24次,取值10的4次,20的x,30的y,40的10次,20和30的平均值是28,然后问全部measurement的算术平均值 A:15 B:20 C:25 D:30 E:35 选30217【计算题】8个人里面找5人组的可能性是56种,问找3人组的可能性。 答案:56官方:有可能是比大小218【计算题】直线(3,0)(7,2)两点,求此直线公式 答案:y=1/2x-3/2
  • 219【计算题】一梯形,上底8,下底16,左边底角45°,已知面积72,求右边侧边。 答案:2*sqrt(10)官方:由面积得高为6,把高从上底两个端点做一下会出来两个三角和一个矩形,左边三角在底边上的长度是6(与高相等),底边第二段就是上底长度8,剩下一个是2,加上高是6,相当于求右边三角的斜边220【计算题】一个商品的销售额是一个数,其中有一半是减价50%销售,问原价买的话销售额多少 Total sale 1200+ 然后有一半sale是50%discont的,问如果不,一共多少,我选的1900+答案:1.5倍当前销售额221【计算题】一个重量单位,大概2000kg等于不到1那个单位,估计一下什么东西有多重。答案:220官方: 应该是范围推断,答案由同学带出。222【比大小】一个班上有25个学生,3月里出生的数量是大于任意其他一个月的。问最少在3月出生的人数和2比大小 答案:A223【比大小】 BC=AC=DC=5,角BCA等于30度,比大小:AB与AD答案:D224【比大小】ColA:0.375/1 ColB:3/8,答案C225【图表题】图表题是一个折线图从19xx到2000的美国电脑用户数量,第一问问1997年有78%的电脑用户有娃,这其中又有18%的娃玩电脑,问1997年美国有多少娃玩电脑,用1997年的数据*78%*18%即可(因为是估算所以直接乘0.2和0.8就行)第二问是说2000年美国共有***个家庭,问任取美国一个家庭用电脑的概率。用图中数据/xxxx即可这道图表题俩图结果两问就用了一个图226【比大小】 坐标原点是O,M坐标(1, y),N坐标(2, 5),OM=ON,y和6比大小 答案:B227【比大小】the average weight of a collection of boxes is 18 pounds, it consists of two different boxes,one is 10 pounds and another is 20 pounds,Q: What is the relationship between the number of 20 pounds of boxes and 8?
  • 一批boxes重量的算术平均值是18 lb,每个boxes的重量不是10 lb就是20 lb。ColA:重量是20lb盒子的数量 ColB:8 答案:D228【比大小】说3^k=5^m 然后比较k+m 和1的大小。选D229【计算题】n除以6余数为4,问n的6次方的余数和4比大小。C230【计算题】Y=2x + 3 问xy<0时,x的range是多少。答案是 -3/2 <x <0。231 【计算题】第一天比price少了20%,第二天比price少了40%, 问第二天比第一天少的比例。选25%232 【比大小】还有一个1meter=39inch,1foot=12inch,然后45meter和150foot比较。选B233【比大小】Given Xy>0, 问x^4*y^3和0的大小,选D234 【比大小】235 【比大小】a>0,a^2+a^-2 和(a+a^-1)^2 比大小 选B236【图表题】 说一间商店的音乐商品销售情况小的那部分是vocal revenue 占39% 大的那部分是61%(图一)237 【图表题】还有一个是1999年(50,000tons)和2009年(60,000tons)的饼图, 有banana, rice,pineapple之类的。问下列哪个是99年加09一起percentage最大的,选最后一个选项pineapples,其实图里面是banana和rice最多,但是选项里没有这2个。还有问下列那个是从99年到09变化最多的?注意要用percentage乘以tons.238 【计算题】一辆车75分钟平均时速5?公里记不得多少了,前45分钟是60,问后半个小时是多少,选45239 【几何题】一个钝角,两条边是6和8,问长的那一条和10哪个大? 比10大240 【计算题】Lisa的工资是 B某的 1.3倍。问B某的工资是Lisa的百分之多少。77%
  • 241 【几何题】 第一个圆以O为圆心其的弧EF是长是2pi.第二个圆以P为圆心,弧AB的长是Pi,比较∠EOF和∠APB。 答案应该是无法比较选D。242 【计算题】有一道|x-2|<2, 求x的range, 我选的是0<x<4243 【图表题】有个电视台的1996年pie chart. 5个programs占不同percentage的比重, news是30%,drama是18%,其他忘了.饼图右边是电视台收视调查这类的,分Approvaling和Disapprovaling.下面一堆数据...问题一:如果news和drama如果来年平分percentage是多少, 选25%问题二: 电视台的预测收视=(19*r), r=收视Approvaling/Disapprocaling.........问news的预测收视减去实际收视是多少....news的app=1250,,,disapp=625,.....19*(1250/625)=38%, 然后减去实际的30%, 等于8%244 【计算题】2*sqrt(9) * 9*sqrt(2) 选EA.108 B.18*sqrt(11) C. 18*sqrt(6) D.18*sqrt(2) E. 54*sqrt(2)245 【计算题】x+y+z>0,x+y+1<0 比较z和1大小 答案:选A z>1246 【计算题】a#b 如果a大于b 则a#b等于2n加1如b 大则。。。。记不住了247 【计算题】sqrt(6)*(sqrt(2)-sqrt(3)) 和2*sqrt(3)-3*sqrt(2)。选C248 【计算题】正方形内切圆,正方形边长是2,问圆形占正方形比率和3/4比大小圆形占正方形比率是pi/4,所以选A249 【计算题】有一题给出一个数150km每hour,与25m每min,前者是后者的几倍(具体数记不清)。答案250250 【计算题】两组数,第一组是从1加到N, 第二组是从N加到2N,问第二组减第一组的差是什么,选N的平方251 【比大小】@表示一种运算,a>b时a@b= 2a,a<b时a@b=b+1:A:(3@2)@7 B: 3@(2@7)答案:B252 【比大小】给出一个关于y的x的等式,然后比较x+4 还是什么的,两个之间的大小,答案要选D,因为x不一定是正数或负数,所以大小无法确定253 【比大小】一道排列组合题目,10个dimes,还有X个quarters,中任意取一个quarters,是0.6的几率,问有多少个quarters?答案:15
  • 【官方组号召帖】亲爱的G友们,看着前辈们用自己的cancel换来的宝贵题目,你好意思不写机经么?看着后面千千万万双可怜巴巴的眼睛,你忍心不带出残体么?看着官方组给你的丰厚奖励,你忍得住不记住新题么?加试部分不要跳过,大家踊跃背机经啦~~~在此先拜谢写机经的同学~~~大家一起加油杀G了~~~O(∩_∩)O~~~===下面这些是阿三机经,官方只整理过其中的一部分,有一些前面已经出现,不知道机经来源可靠不可靠,有时间就看看,不用过于纠结里面的内容==1. Cost price of 11 pens are equal to selling price of 9 pens, what is profit percent?答案:(1/9-1/11)/(1/11) = 22.2%2. 【比大小】Distance y to x 10 units , z to x 20 unitsColA:Distance Z to X ColB:30选D,应该是小于等于3. Volume of a cube given as 27 which is painted totally, and are cut into small pieces of unit volume. Areaof the unpainted surface?答案:1*6*27-3*3*6=1084. Sum of n consecutive integers is said to even. Some options were given like 8, 12, 16, 20, 24 (allmultiples of 4) and the question said that which could be the sum of the value of n.答案: 24可以,7+8+95. 【计算题】83A+DBB=CAC2, where A,B,C,D are different digits, what is D? 答案: D=6官方:C必然等于1,因为D如果取9,C还是1; A+B=2或12.可以假设A,B分别为0和2,排除A+B=2的可能。所以个位数进了一位去十位数,所以3+B=C-1.而c=1.所以b等于7. 而a+b=12,所以a等于5。所以dbb=cac2-83a=1512-835=677.6. 【比大小】a/b=3.12, remainder was 24. 答案A(题目应说明a,b是整数)ColA: b ColB: 100a=3.12b=xb+24,x为整⇒b=24/(3.12-x), 当x=3, b=200,a=624。只有x为3时才使得a,b为整7. A pyramid had a square base. The sides of the squares are 20. Height of pyramid?
  • 官方:这个题目条件不全吧8. A person is travelling from two cities at 8mph and back at 6mph, average speed was asked.答案 2/(1/8+1/6)=48/79. 【比大小】z is a positive odd integerColA: number of positive factors for 2z ColB: twice the number of factors of z 答案D有不同情况10. 【比大小】if two sides of a triangle are 6 and 8, then ColA: area of the triangle ColB: 27 答案B三角形面积=1/2*6*8*sin夹角<=2411. 【比大小】a direct question came from powerprep,ColA: 1/1-0.03 ColB: 1.03 答案A12. 4^30-2^50, when divided by 5, what is the remainder官方:原式子=2^60 - 2^50,又因为2^4 divided by 5的remainder是1,所以可以把指数除以4取余数,那么就是 2^4-2^2 = 12,那么除以5的余数是2。13. k/5099=0.0382, unit digit of k.答案:414. A question on hamburgers, which was similar to Dr Raju’s 1st July’s pork chops question.15. A permutation problem, where a teacher sets some questions and only some questions are to beanswered with some choices, number of ways answering the question.16. 【比大小】m*n=64, where m and n are positive integers, ColA: m+n ColB:17 答案D 8*8 or 16*417. Something on average weight of a 20 member group increased by 3kg, when a person weighingaround 68 or 72 kg (do not remember exactly the person’s weight) was replaced by a new member. Weightof the new member?18. 【比大小】ColA: 25% of sq rt of 983.33, ColB: sq rt of 98.333 答案B两边平方比大小19. A probability question where 2 dice are rolled and sum of the number obtained were more than 7;probability that sum is an odd number.枚举法。。2/520. 这个感觉是图表题,不知道是不是糖果那个there was on some country and in 4 different years peoplewere trying 2 different candies. One question was on percentage increase in one type of candy from 1styear given to last year. Another question was on inference based, with 3 options out of which two wererelated to mean and median increase, last option was given on probability.21. 这应该是另一个图表题Another DI was on income and expenditure of 10 families in 4 different years, first question asked to find
  • out the ratio of income:expenditure of the two families whose percent increase in income was greatestand least respectively. Another was a simple on which told to find out the median of expenditure of the tenfamilies in the 2nd and 4th year.a. 【比大小】ColA: 7^20 ColB: 20^7 答案Ab. -2<x<9 and -4<y<10, maximum value of x-y 答案 13 -10<-y<4 -12<x-y<13c. P>a+b Q>a+b 比较P+Q和a+b 答案Ad. Least number which when divided by 6,7,8,9 will leave a remainder of 3 in each case这个我不会算,你觉得得3靠谱不?每一个都是商0余3e. 【比大小】1575=3^m5^n7^pColA: m+n+p ColB: 5 答案 Cf. How many numbers are there between 1 and 500 inclusive, which are not divisible by either 4 or 7?304不知道对不对,这个要讨论下g. A comparison question was given regarding the misspell of a person’s name PETER and the probabilitythat the name was still correct was asked.答案 2/(5A5)=1/60h. 【比大小】P,Q,R are positive integersColA: SD of P,Q,R ColB: SD of P-6, Q, R+6不确定。。是否pqr是按大小顺排列i. A question on parallel lines and how many parallelograms can be formed.j. Travelling at 3/4th of a person’s usual speed, he is late by 1 hr 30 mins. What is his usual travel time?答案:4.5hr,3/4V(t+1.5)=vt⇒t=4.5k. 【比大小】–x|x|>0ColA: square root of (x-10)^2 ColB: (10-x) 答案Cl. Maximum number of points where a triangle and a circle can intersect. 答案 3m. 【比大小】A circle is centred on the origin. Point X and point Y are selected at random from within thecircle.ColA: probability that X>Y>0 ColB: 1/8 答案选Cn. 3 different co-ordinate points are given with k as a y intercept in one and the three points are collinear.Value of K is asked.o. -11, 12, -13, 14, -15, 16………..Sum of first 37 terms.p. Numbers of ways in which 12 students can take 3 different tests of 4 students are to take each test.
  • q. A venn diagram given showing percentages of 3 magazines individually and three of them together. Thequestion said to find the percentage subscribed to at least 2 of the magazines.1.【比大小】1575=3^m5^n7^p 比较 m+n+p 和5 选C 157=3^2*5^2*7^1 m+n+p=2+2+1=52.【计算题】What is the remainder when 7^0+7^1+7^2……+7^25 is divided by 14?3. DI4. DI5. Guests at a recent party ate a total of 15 pork chops. Each guest who was neither a student nor avegetarian at exactly 1 pork chop. No pork chop was eaten by any guest who was a student, a vegetarianor both. The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate ofnon-vegetarians. If half of the guests were vegetarians, how many guests attended the party?A. 25B. 30C. 45D. 70E. 906. 【比大小】A figure given, which is exactly same as a question I have encountered in Kaplan Online TestColA: Perimeter of Triangle ABCColB: 47. In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 cards of each number in thedeck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what isthe probability to pull out a card with a number 10 on it?A.1/4.B. 4/16.C.6/29.D. 4/11.E. 1/3.8. 【比大小】(0,0),(a,0) and (3,4) are the vertices of a triangle of area 8.ColA: aColB: 49. 【比大小】Y-X=2ColA: Y+4ColB: X+510. 【比大小】Given the equation of circle x^2+y^2=49 with two points A (4a, 3) and B (0,-b) on the circle.ColA: Distance between points A and BColB: 1211. There are three secretaries who work for four departments. If each of the four departments has onereport to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all
  • three secretaries are assigned at least one report?A. 2/3B. 1/3C. 8/9D. 4/9E. 2/912. How many 3-digit positive integers are divisible by 78 or 91?A. 17B. 19C. 20D. 21E. 2213. 【比大小】ColA: 10% of sq root of 573.28ColB: sq root of 57.32814. A certain holiday is always on the 4th Tuesday of month X. If month X has 30 days, on how manydifferent dates of month X can the holiday fall?Options: Do not remember (Sorry)15. 【比大小】A circle is centred on the origin. Point A and point B are selected at random from within thecircle.ColA: probability that A>B>0ColB: 125/100016.【比大小】Line P and Q pass through (1,1). The slope of P is less than slope of Q. P passes through(0,x) and Q passes through (0,z).ColA: xColB: z17. A and B represent the following:A: Number of ways in which 12 students can take 3 different tests of 4 students are to take each test.B: Number of ways in which 12 students can be divided into 3 teams so that each team consists of 4students.What is the value of A+B?Options: Really weird options, do no remember anything.18. The height of an oak tree when it was planted was 4 feet. The height of the tree increases by a constantrate each year for the next 6 years. At the end of 6 years the tree was 1/5th taller than it was at the end ofthe 4th year. By how many feet did the oak tree increase each year?A. 2/5B. 3/10C. 2/3D. �br> E. 6/519. Amanda travels from home to work, a distance of ‘d’ miles in ‘h’ hours. She returns home along thesame route and covering exactly the same distance but at an average speed that is 40% more than heraverage speed while travelling from home to work. What is Amanda’s average speed for the round trip?Options were given in terms of d and h.20. A certain computer program randomly generates equations of lines in the form of y=mx+b. If a point
  • R, whose co-ordinates are (6,0), is a point on a line segment generated by this program, what is theprobability that the line will not pass through the square region ABCD? Figure provided on the exam.A. �br>B. br>C. 3/8D. 5/8E. 7/821. 【比大小】ColA: No of ways for selecting 3 things out of 9ColB: No of ways for selecting 6 things out of 922. X is the set of n natural numbers (x1,x2…….xn) and Y is another set of n natural numbers(y1,y2…….yn), such that ax+by+c=0. If the standard deviation of set X is ‘M’, what is the standard deviationof set Y?23. 【比大小】ColA: Area of the region enclosed by the lines |2x|+|3y|=12ColB: 3624. DI25. DI26. 【比大小】ColA: How many parallelograms are formed if a set of 10 parallel lines intersects another setof 10 parallel lines?ColB: 9027. 【比大小】ColA: 0.99998/0.99999ColB: 1.00001/1.0000228. 【比大小】A necklace is made by stringing 68 beads together in the repeating pattern: red, green,white, blue and yellow. The necklace design begins with a red bead and ends with a white bead. A bead ispulled out of the necklace at randomColA: Probability that the selected bead is greenColB: Probability that the selected bead is blue1. C [ 1575 = 3^2 . 5^2 . 7^1 ]2. 8 [ 1+7 + 14(1+ ...) = 8 + 14(something)]3. DI4. DI5. Not clear6. Figure7. A [(4 + 10)/(52 + 12)]8. D [a can be -4 or 4]
  • 9. A [Y+4 = X+6]10. Bb=+-7, -7 is too close reject, take +7. B(0,-(+7)) = B(0,-7).Radius = 7 implies distance from (0,0) to (4a,3) is 7...by distance formula/pythogoras theoram...4a =sqrt(40).distance between (0,-7) and (4a,3) is sqrt(140) which is less than 1211. D [explained above..2 posts back]12. C78 * 10 = 780 (thats 9 numbers excluding 78) ...another two multiples before itcrosses 1000.91 * 10 = 910 (thats 9 numbers)Total = 2013. B [ sqrt(573) is less than 25... 10% of 25 is 2.5, sqrt(57) is greater than 7]14. 7 [ the month can start in any one day of the week. tues,wed,thur...etc ]15. BProb of choosing 1st quad from 4 is 1/4 ie 250/1000When choosing two numbers, prob of choosing a>b is 1-(prob of choosing a <= b)prob of a>b = a<b, but prob(a>b) < prob(a<b AND a=b)therefore, prob of (a>b) is slightly less than 0.5multiplying the two... we get slightly less than 125/1000...therefore B16. B [ -x-1/-1 < -z-1/-1 => -x-1 > -z-1 => -x > -z => x < z ]17. 352800 [ 2 * C(12,4).C(8,4).C(4,4)]18. C [ x+6a = 1.2(x+4a) => x = 4ft = 6a => a = 2/3]19. 7/6 (d/h)avg. speed = tot. dist / tot. timetot dist = 2dsay t1(which is equal to h),t2...s=d/t11.2s=d/t2 => s = d/1.2t2d/t1 = d/1.2(t2)t2 = t1/1.2 = 5/7(t1)speed = 2d / (h + 5/7b) = 2d/(12/7 * h) = 7/6 d/h20. no figure21. C [C(9,3) = C(9,6)]22. -aM/b [std. deviation formulas...dont think this is there for the gre..]
  • 23. A [ two triangles of base 12 and height 4...area is 48]24. DI25. DI26. A [comes to 81 = 9*9]27. B [basic maths prop.]28. A [Since there are more green beads than blue...it has to follow order, if it ends with white, meanstheres 1 extra of red,geen, white compared to blue and yellow.]1.【比大小】ColA: ways of selecting 3 things out of 9ColB: ways of selecting 6 things out of 92.Something about a tree which was growing for a constant rate for 6 years. Height of the tree was given.At the end of 6th year the tree was around one fifth taller than it was in fourth year. Was asked to find therate of increase per year.3.【比大小】A shop sells an item for 125 dollar and another shop sells an item for 75 dollar.ColA: percentage gained over 125 dollar if the item is bought from the shop selling at 75 dollar.ColB: 40%4.Mean of 50 numbers given to be 18.5, and when a number is replaced by some values (28.5), then whatis the new mean of 50 numbers?5.A very confusing problem on some secretaries assigned with some tasks in an office. It was apermutation combination problem.6.【比大小】A person’s name is STEVE.ColA: If any 2 letters are interchanged, what is the probability that the spelling is still correct.ColB: 1/57.【比大小】In a company, 40% of female employees were graduates and 35% of male employees werenon-graduates.ColA: % of graduates in the companyColB: 558.A question with a diagram showing two overlapping circles forming a swimming pool, and was asked tofind the area of the swimming pool. Radius of the both circles were given as 4.9.Two graphs were given and were asked to find whether they represent a function or not.10.A very strange question was given on a computer program generating a straight line and then a squareis being formed. A point is randomly selected and was asked to find the probability that the line will not passthrough the square region.11.Perimeter of a triangle was given as 10, and it was mentioned that the different sides are integers. Itwas asked to find the difference between the maximum and minimum possible values of a particular sidementioned.
  • 12.Remainder was asked to find out when 3^64 is divided by 28.13.F(x+3)=F(n), given F(-1)=6, F(0)=5 and value of F(1) was also given. Asked to find the value of F(19).14.Another permutation or combination problem was given, where a teacher sets 5 objective type questionsout of which 4 have to be answered. It was asked to find out the total number of ways in which they can beanswered if first 3 questions have 4 choices and last 3 have 3 choices.15.【比大小】Some co-ordinate geometry problem, points X,Y,Z forming a triangle.ColA: Perimeter of the triangleColB: some values (5 or 6)16.Greatest prime factor of 3^38-2^2817.k/60125= sq root 0.02681, it was asked to find the unit digit of k【官方组号召帖】亲爱的G友们,看着前辈们用自己的cancel换来的宝贵题目,你好意思不写机经么?看着后面千千万万双可怜巴巴的眼睛,你忍心不带出残体么?看着官方组给你的丰厚奖励,你忍得住不记住新题么?加试部分不要跳过,大家踊跃背机经啦~~~在此先拜谢写机经的同学~~~大家一起加油杀G了~~~O(∩_∩)O~~~