3. ============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 divisor
3. the sum of the first N odd integers
4. 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+3x
11. 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 probility
17. 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 inches
24. 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
5. =============================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 is
2*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C
7. 【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。
6. 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the
least 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 the
following? 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4
Twice the sum of three positive integers x,y,z when divided by 7 gives remainder 1 then what is the
remainder 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=16000pi
15 【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=8000pi
A road roller which levels a surface has height as 16 and diameter as 2, then if it revolves for around 500
revolutions. 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 300
revolutions. 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 grams
and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a
package for which the charge is $1.55 ? 答案选B
A 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0.2
Mean of 50 numbers given to be 19.5, and when a number 18.5 from those numbers is replaced by is
replaced 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=0.2
18 【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
7. 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 rate
20 【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 9
Column 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37500
22 【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
8. 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 the
probability of 30 years and older? 5/6
27 【比大小】1/96+1/97+1/98+1/99+1/100 和 1/20 誰比較大，选A
Col A: 1/100+1/99+1/98+1/97+1/96
Col B: 1/20
变体：Column A : Arithmetic mean of 1/96, 1/97, 1/98, 1/99, 1/100
Column 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C
Printer 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：16200
30 【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A
32 【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：C
33【比大小】数字PQRS的平均数是r，标准差是t
A：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t
34 【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
9. 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C
39 【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114
40 【算术题】the discount of 40 percent of the original selling price of an item reduce the price to $72
the 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：13/36
42 【比大小】x+y+z＞0，x+y+1＜0 比较z和1大小 答案：选A z>1
43 【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
10. 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B
50 【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C
ColA: ways of selecting 3 things out of 9
ColB: ways of selecting 6 things out of 9
51 【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 III
53 【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=1/18
54 【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：B
56 【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
11. A man measures the perimeter of a rectangle for 5 times. The first two measures are less than 200 and the
next three are greater than 200.
Col A ：The arithmetic mean of the five measures
Col B：200
57 【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D
x^4=16 colA: x colB: 2
59 【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C
60 【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: B
ColA: 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=1.56
62 【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】
12. 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0.01
65 【比大小】k: Y = 3X – 5 ; m: Y = 3X + 7，比較k和m的slope(斜率) 答案：C
66 【比大小】If a>1，Column A : (a+a^-1)^2 Column B : (a^2 + a^-2) 答案选A
67 【比大小】Arithmetic mean of Group A = 32
Arithmetic mean of Group B = 38
Arithmetic mean of Group C = 40
Arithmetic mean of ALL Groups = 36
Column A : No. of people in Group A
Column 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C
70 【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A
71 【比大小】f(n)=2/n-2/(n+2)然后f(5943)和f(5944)比大小 答案：A
72 【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，1600/3.6
The 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 $1600
Col B: 500 答案：C
13. 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+k
74 【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: D
77 【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^3
78 【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：B
80 【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 year
81 【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:11
82 【计算题】下面那个x值使得1/x最大？
A : 2/7
B : 3/8
14. C : 3/10
D : 7/200
E : 3/500
答: E
83 【比大小】ColA: 7^20，ColB: 20^7 答案: 选A
84 【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D
86 【计算题】Least number which when divided by 6,7,8,9 will leave a remainder of 3 in each case x 选3
88 【计算题】How many numbers are there between 1 and 500 inclusive, which are not divisible by either
4 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 integers
ColA: SD of P,Q,R
ColB: 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 usual
travel 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： 6
93 【比大小】–x|x|>0
ColA: square root of (x-10)^2
ColB: (10-x)
答案：选D
94 【计算题】Maximum number of points where a triangle and a circle can intersect. 答案：选6
95 【比大小】A circle is centred on the origin. Point X and point Y are selected at random from within the
circle.
ColA: probability that X>Y>0
ColB: 1/8
15. 答案C
96 【计算题】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.
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：-29
98 【计算题】Numbers of ways in which 12 students can take 3 different tests of 4 students are to take
each 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 them
together. 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 find
some 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 ans
is col A
104 【比大小】y/x = 5，4x + y = 27
Col A：y+2，Col B：x+2 答案：选A
105 【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?
16. ANS: D=6
A=5,B=7,C=1,D=6
835+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A
109 【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6.86
111【比大小】z is a positive odd integer
ColA：number of positive factors for 2z，ColB： twice the number of factors of z 答案：C
112【比大小】if two sides of a triangle are 6 and 8, then
ColA：area of the triangle，ColB： 27
ANS: B
113【比大小】ColA：1/(1-0.03)， ColB：1.03
ANS:A
114【比大小】k/5099=0.0382, unit digit of k.
ANS: 4
115 【计算题】Guests at a recent party ate a total of 15 pork chops. Each guest who was neither a student
nor a vegetarian at exactly 1 pork chop. No pork chop was eaten by any guest who was a student, a
vegetarian or both. The vegetarians attended the party at a rate of 2 students to every 3 non-students, half
the 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 are
to 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：17
ANS: D
118【计算题】Something on average weight of a 20 member group increased by 3kg, when a person
weighing around 68 was replaced by a new member. Weight of the new member?
ANS:128
119【比大小】ColA：25% of sqrt(983.33)， ColB： sqrt(98.333)
ANS: B
17. 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 more
than 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: C
123 【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2
124 【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 the
value of a? 答案: ±6
125 【比大小】 ColA：x+y ColB：90 答案：B
126 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 to
formed, out of which 6 are girls.
Col A: The probability that 7th member is also a girl
Col B: 3/5
答案：B
官方：A计算出来概率是2/7
128 【比大小】Given that x^2 > -y
Col A: x Col B: y 答案：D
129 【计算题】Given two overlapping swimming pool of radius 6 each. Find the perimeter of the swimming
pool?
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：6
131 【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
18. Col B: Half the population in 1995
答案：A
132 【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：63.65
134 【计算题】If K = 105/L, L is an integer, then
Col A: The number of positive integer values of L, K
Col B: 7
答案A，8>7
135 【计算题】If x = 10!, then how many zeros the number x has? 答案：2
136 【计算题】A bag contains 20 red and 30 white balls. If 3 balls are picked at random, then what is the
probability that all of them are red? 答案： 57/980
137 【比大小】Col A: |6| + |-3| + |-3| Col B: 0 答案：A
138 【计算题】A square inscribed in a circle, one side of the square is given, question asked is to find the
radius of the circle?
官方：没有数字带出来，计算方法应该是(side*sqrt2)/2
139 【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 days
they can complete the work, if they work together? 答案：1
141 【比大小】If LCM (least common multiple) of two numbers is 105, then
Col A: The greatest prime factor of the two numbers
Col B: 5
答案：A
142 【计算题】Given that a/b = 1.25, where a and b are integers. Which among the following cannot be
true:
I.a+b is an odd integer
II.ab is an odd integer
III.a+b is an even integer
答案：II
143 【比大小】If |x|/x = -1, then
Col A: x
Col B: -x
答案：B
19. 144 【比大小】Given that m - 6z > 0 and 5z - m > 0.
Col A: m
Col B: 0
答案：B
145 【计算题】If N = (-2) ^x, where x is a negative integer and -5 < x < -1. What is the difference between
maximum and minimum possible values of N? 答案：3/8
146 【比大小】The average weight of 65 women is F and average weight of 75 men is M, given that F > M
Col A: Average weight of 140 members
Col B: (F+ M)/2
答案：B
147 【几何题】All the sides of a quadrilateral have different lengths, at most how many angles can be 90
degrees?
答案：2
148 【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)/2
149【计算题】Volume of a cube given as 27 which is painted totally, and are cut into small pieces of unit
volume. Area of the unpainted surface? 答案：108
150 【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：D
151【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 integer
II. ab is an odd integer
III.(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
22. 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B
170 【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C
173 【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。C
X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 many
books are on the shelf?
答案：56
175 【比大小】(x-3)^2=-(y+2)^4 and 2x+3y+4z=0,
ColA：z
ColB：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=-2
176【计算题】Sides of a square measured to the nearest centimeter are 6 cm long, least possible value of
the 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=6
177【计算题】Greatest prime factor of 4^17-2^28 答案：7
178 【计算题】Property assesses at 60% of appraised value and taxed at the rate of 4 dollars per 100
dollars of assessed value. A taxpayer is assessed 240 dollars per quarter in property taxes, what is
appraised value of the property? 答案：40000
官方：(0.6x)*0.04=240/0.25
179【计算题】Exam held, 70% passed in chemistry, 73% passed in Maths and 64% passed in both. 63
failed 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 = 300
180【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。
23. 181【计算题】500 candidates gave test, avegare score was 72. Bottom 16% will have to take retest, 10
candidate 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：D
183 【计算题】A rectangle PQRS given with length PQ=17 and width QR=5. T is a point on RS. What is
the probability that QT>13 答案：5/17
184【比大小】X<0, ColA：sqrt(–x|x|)， ColB：-x 答案：C
185【比大小】 x < 0, Column A: x-|x|, Column B: 0 答案：B
186 【几何题】there was a figure of a cuboid cut into cubes each of side 1 cm... basically you had to add
the lengths of each of those cubes to find the length, breadth n height of the cuboid. YOU had to determine
the 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C
188【比大小】the length and breadth of a room are 12 and 8 resp. if a circular carpet has to be placed on
it, what is the max area the circle can have?
ColA: max area of circle ColB: 24pi 答案：B
189 【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：A
191【比大小】0< x<1, 比较1/(1-x) 和1+x 答案：A
192【计算题】1mile=5280 feet，1foot =12inches，一个 cube 边长 3 feet
road ：longth 1/2 miles，wideth 24 feet，highth 4inches
question: 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
24. 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：15
197【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：C
200【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：B
202【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：B
205【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：D
206【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：C
207【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
26. 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：A
223【比大小】 BC=AC=DC=5，角BCA等于30度，比大小：AB与AD
答案：D
224【比大小】ColA：0.375/1 ColB：3/8，答案C
225【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：B
227【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?
29. 【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 units
ColA: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. Area
of the unpainted surface?
答案：1*6*27-3*3*6=108
4. 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 said that which could be the sum of the value of n.
答案： 24可以，7+8+9
5. 【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: 100
a=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?
30. 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)=48/7
9. 【比大小】z is a positive odd integer
ColA: 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<=24
11. 【比大小】a direct question came from powerprep,
ColA: 1/1-0.03 ColB: 1.03 答案A
12. 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：4
14. 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 be
answered 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*4
17. Something on average weight of a 20 member group increased by 3kg, when a person weighing
around 68 or 72 kg (do not remember exactly the person’s weight) was replaced by a new member. Weight
of 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。。2/5
20. 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 people
were trying 2 different candies. One question was on percentage increase in one type of candy from 1st
year given to last year. Another question was on inference based, with 3 options out of which two were
related 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
31. out the ratio of income:expenditure of the two families whose percent increase in income was greatest
and least respectively. Another was a simple on which told to find out the median of expenditure of the ten
families in the 2nd and 4th year.
a. 【比大小】ColA: 7^20 ColB: 20^7 答案A
b. -2<x<9 and -4<y<10, maximum value of x-y
答案 13 -10<-y<4 -12<x-y<13
c. P>a+b Q>a+b 比较P+Q和a+b 答案A
d. 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3
e. 【比大小】1575=3^m5^n7^p
ColA: m+n+p ColB: 5 答案 C
f. 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 probability
that the name was still correct was asked.
答案 2/(5A5)=1/60
h. 【比大小】P,Q,R are positive integers
ColA: 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=4.5
k. 【比大小】–x|x|>0
ColA: square root of (x-10)^2 ColB: (10-x) 答案C
l. Maximum number of points where a triangle and a circle can intersect. 答案 3
m. 【比大小】A circle is centred on the origin. Point X and point Y are selected at random from within the
circle.
ColA: probability that X>Y>0 ColB: 1/8 答案选C
n. 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.
32. q. A venn diagram given showing percentages of 3 magazines individually and three of them together. The
question 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=5
2.【计算题】What is the remainder when 7^0+7^1+7^2……+7^25 is divided by 14?
3. DI
4. DI
5. Guests at a recent party ate a total of 15 pork chops. Each guest who was neither a student nor a
vegetarian at exactly 1 pork chop. No pork chop was eaten by any guest who was a student, a vegetarian
or both. The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the 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
6. 【比大小】A figure given, which is exactly same as a question I have encountered in Kaplan Online Test
ColA: Perimeter of Triangle ABC
ColB: 4
7. In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 cards of each number in the
deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is
the 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: a
ColB: 4
9. 【比大小】Y-X=2
ColA: Y+4
ColB: X+5
10. 【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 B
ColB: 12
11. There are three secretaries who work for four departments. If each of the four departments has one
report to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all
33. three secretaries are assigned at least one report?
A. 2/3
B. 1/3
C. 8/9
D. 4/9
E. 2/9
12. How many 3-digit positive integers are divisible by 78 or 91?
A. 17
B. 19
C. 20
D. 21
E. 22
13. 【比大小】ColA: 10% of sq root of 573.28
ColB: sq root of 57.328
14. A certain holiday is always on the 4th Tuesday of month X. If month X has 30 days, on how many
different 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 the
circle.
ColA: probability that A>B>0
ColB: 125/1000
16.【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: x
ColB: z
17. 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 4
students.
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 constant
rate 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 of
the 4th year. By how many feet did the oak tree increase each year?
A. 2/5
B. 3/10
C. 2/3
D. �br> E. 6/5
19. Amanda travels from home to work, a distance of ‘d’ miles in ‘h’ hours. She returns home along the
same route and covering exactly the same distance but at an average speed that is 40% more than her
average 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
34. R, whose co-ordinates are (6,0), is a point on a line segment generated by this program, what is the
probability that the line will not pass through the square region ABCD? Figure provided on the exam.
A. �br>
B. br>
C. 3/8
D. 5/8
E. 7/8
21. 【比大小】ColA: No of ways for selecting 3 things out of 9
ColB: No of ways for selecting 6 things out of 9
22. 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 deviation
of set Y?
23. 【比大小】ColA: Area of the region enclosed by the lines |2x|+|3y|=12
ColB: 36
24. DI
25. DI
26. 【比大小】ColA: How many parallelograms are formed if a set of 10 parallel lines intersects another set
of 10 parallel lines?
ColB: 90
27. 【比大小】ColA: 0.99998/0.99999
ColB: 1.00001/1.00002
28. 【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 is
pulled out of the necklace at random
ColA: Probability that the selected bead is green
ColB: Probability that the selected bead is blue
1. C [ 1575 = 3^2 . 5^2 . 7^1 ]
2. 8 [ 1+7 + 14(1+ ...) = 8 + 14(something)]
3. DI
4. DI
5. Not clear
6. Figure
7. A [(4 + 10)/(52 + 12)]
8. D [a can be -4 or 4]
35. 9. A [Y+4 = X+6]
10. B
b=+-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 12
11. D [explained above..2 posts back]
12. C
78 * 10 = 780 (thats 9 numbers excluding 78) ...another two multiples before it
crosses 1000.
91 * 10 = 910 (thats 9 numbers)
Total = 20
13. 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. B
Prob of choosing 1st quad from 4 is 1/4 ie 250/1000
When 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 0.5
multiplying the two... we get slightly less than 125/1000...therefore B
16. 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. time
tot dist = 2d
say t1(which is equal to h),t2...
s=d/t1
1.2s=d/t2 => s = d/1.2t2
d/t1 = d/1.2(t2)
t2 = t1/1.2 = 5/7(t1)
speed = 2d / (h + 5/7b) = 2d/(12/7 * h) = 7/6 d/h
20. no figure
21. C [C(9,3) = C(9,6)]
22. -aM/b [std. deviation formulas...dont think this is there for the gre..]
36. 23. A [ two triangles of base 12 and height 4...area is 48]
24. DI
25. DI
26. 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, means
theres 1 extra of red,geen, white compared to blue and yellow.]
1.【比大小】ColA: ways of selecting 3 things out of 9
ColB: ways of selecting 6 things out of 9
2.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 the
rate 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 what
is the new mean of 50 numbers?
5.A very confusing problem on some secretaries assigned with some tasks in an office. It was a
permutation 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: 1/5
7.【比大小】In a company, 40% of female employees were graduates and 35% of male employees were
non-graduates.
ColA: % of graduates in the company
ColB: 55
8.A question with a diagram showing two overlapping circles forming a swimming pool, and was asked to
find 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 square
is being formed. A point is randomly selected and was asked to find the probability that the line will not pass
through the square region.
11.Perimeter of a triangle was given as 10, and it was mentioned that the different sides are integers. It
was asked to find the difference between the maximum and minimum possible values of a particular side
mentioned.
37. 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 questions
out of which 4 have to be answered. It was asked to find out the total number of ways in which they can be
answered 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 triangle
ColB: some values (5 or 6)
16.Greatest prime factor of 3^38-2^28
17.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~~~
