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标题: GMAT数学高分攻略ZZ [打印本页]

作者: xiongbaobao 时间: 2010-11-8 11:35 标题: GMAT数学高分攻略ZZ

I．       GMAT数学50分+的标准：

1.    拿到一道数学题，能够在10-30秒内（根据个人水平定）把题目读懂：读懂字面意思并同时准确提炼出相应的数学模型
2.    读懂题目后：能够迅速识别这道题它想考我什么（知识点方向）、马虎的陷阱在哪里（马虎是字面的，可以一眼识别）
3.    思维层次：1和2做好后，思路的方向就基本出来了，包括这道题需要“试算”、“特值反例”、直接代公式、集合的venn或二维表、etc，也会知道应该这么去想和应该避免的思路歧义，这步就自然会出现对“思维陷阱”的敏感。
——整个过程：浑然天成！

作者: xiongbaobao 时间: 2010-11-8 11:35

II．    II. 学生容易犯的GMAT数学错误类型：

1．理解问题: 致命却容易被思维好逻辑强的同学忽略！
【表现】：
1）  完全无法读懂字面意思
2）  能读懂字面意思，但是无法在规定时间内完成
3）  能在规定时间内读懂字面意思，但是不能快速整理出数学模型或解题思路。
2．知识点遗忘
【表现】：能读懂题，且有思路的大致方向，但对于完成该思路的工具（如描述统计的公式、集合的2种类型的处理方式，排列组合和概率的公式，etc）完全没有印象或虽然有印象但是不能系统驾驭，导致最终不能完成题目。
3．思维陷阱
【表现】：能够读懂题目且知道思路以及运用的工具，但是由于加入了自己的主观或过去的常识导致自己加了条件，在这样的情况下解题，出现偏差。
Eg：
（DS）x是否能被z整除？
分析：此题很多同学在看2个选项时首先会去想z是否是x的因子，而忽略了本题的前提“x和z必须同时为整数”，而这一点是在判断“是否充分”时不可忽略的。这样的错误源于自己加入了条件“x和z是整数”，或根本不知道“整除”是针对整数而言的（后者这个属于第二类错误）！
4．马虎问题
【表现】：计算错误，把三角形的“height”看成“side”，etc

作者: xiongbaobao 时间: 2010-11-8 11:35

5．解题过程不必要的繁复，浪费时间：该类问题常见于DS题
【根源】：没有搞清楚DS“充分性”的含义！主要有以下两大类（其他占比很小的零碎题型就不总结了）——
(1) what 型：只有能够求出唯一值来回答what才叫充分！
Eg:
What is the value of the integer n ?
(1)
(2)

    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    EACH statement ALONE is sufficient.

    Statements (1) and (2) TOGETHER are NOT sufficient.
【解析】：B
条件1单独不充分，因为求出的n有2个值。
条件2单独充分：能求出一个唯一值（可以用试算）n=3.
【注意】：如果条件2的方程的解>1个，则看1）+2）取交集后是否能够确定唯一值，如果可以，充分选C！
（2）“Is”型：能够确定回答yes或确定回答no都叫充分；可能回答yes也可能回答no叫不充分。

作者: xiongbaobao 时间: 2010-11-8 11:36

Eg：
相关考题（ID 2426）：
If s4v3x7 < 0, is svx < 0?
(1)    v < 0
(2)    x > 0

    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    EACH statement ALONE is sufficient.

    Statements (1) and (2) TOGETHER are NOT sufficient.
【解析】：E
本题知道v或x都没有用，关键是s，因为题干已经可以确定vx<0了，所以，最终取决于s与0的关系，每个选项单独以及结合起来都得不到s的信息，所以对于问题依然可能回答yes也可能回答no，因此无论如何都无法充分。

III． GMAT数学备考策略

首先：水平测试——
用PREP模考软件数学部分测试一下：
1）  如果能够保证错误在3个以内且不超时、pace稳定，就可以直接完成下述三个层次的第三个，大考前需要看一遍OG review，即可。
2）  如果错误率超过1）的标准，或做题感觉很艰难（包括pace不稳定、读题困难、题目思路把握不准确，etc），就按照如下三个层次来，在进行过程中，可以不断用I的三个标准来判断自己的进步和水平现状，当找到相应感觉以后，就可以进入下一个层次。

作者: xiongbaobao 时间: 2010-11-8 11:36

GMAT数学备考的三个层次：
1. 基础训练与错误点的寻找：OG
1）OG review + DS和PS题目开始前的guide（DS是P273-276：了解出题规则），只有知己知彼才能百战百胜。
2）OG DS和PS——DS160道，PS250道左右。分别把后面的100道做一遍，总结出自己的理解问题，这是基础积累过程；
A）如果各做100道：一次做完；如果都做完，就分2次完成，两次的时间间隔不能太长，DS和PS搭配着来
B）错题总结：按照错误类型总结——
a）思维陷阱
b）马虎问题
c）理解问题：并把阻碍理解的表达积累起来
e）“DS的充分性”没有把握好

作者: xiongbaobao 时间: 2010-11-8 11:36

2.    理解能力训练、pace训练和知识点遗忘的克服：PREP数学的破解（博森小班专区资料下载会有题目和部分讲解的下载）
（1）    资料：PREP破解 DS和PS——最接近实战的英文题
（2）    怎么练：
A）每天37道，自己组合成套题配合着语文和作文来做，计时。
B）每天做完以后：总结错题，猜的但猜对了的不管。
按照错误类型进行总结：马虎问题、思维陷阱、理解问题、知识点遗忘。
尤其是知识点遗忘部分，建议把相应知识点的题目放在一起，积累到一定程度以后，会发现这一类知识点的出题思路和解题思路。
C）定时复习。
（3）    练到什么程度：当发现3个标准的题感有了，就可以酌量减少，一周做2套什么的维持下感觉，根据自己的模考计划而定。
哪部分差做哪部分，时间紧的建议做完DS 2个practice，PS practice1。
3.    思维训练：机经
（1）    资料：当月JJ；if没有，就用上月JJ
（2）    对待JJ的心态：
不是背答案，因为考场压力可能迫使你完全忘记了答案。平时反复整理JJ的目的是让你实现以下几个方面：
A）找到自己知识点的漏洞：练习方法我下面会讲
B）熟悉GMAC近期出题的思路方向：JJ的趋势较红书时代有所变化，这就是为什么用JJ的参考价值更大。以这个出题方向为纲引导你形成一种思想套路之类的东西，也就是：看到这类题就会自然而然地产生一个思考的方向，且这个方向90%以上是准确的。

作者: xiongbaobao 时间: 2010-11-8 11:37

【经验】：考场上，特别是有JJ时，很可能做得比较好，此时会遇到一些新的难题，这些题虽然陌生，一定逃不出你整理过的某个知识点，运用做JJ时给你的感觉和思路，一定可以激发平时没有的考场灵感，这就是数学和语文最大的不同。
C）提高考场效率：一定是建立在水到渠成的基础上。不是直接背了就去，除非心态极佳不怕变体或记忆力超群且识别变体的能力超群。
（3）目标：最后上考场的感觉是JJ的思路已经进入了骨髓，觉得是不上51都难的感觉。
（4）如何使用相应月份的JJ：
1）自己先做一遍：这一遍就是找出自己的错题，同时按如下两条线进行分类
2）无需按照PS或DS来分。
两条线——
A）错误类型：
a）马虎问题和理解问题：
前者：如果时间不够充裕的，就按我后面说的方式进行，我后面会专门讲数学的备考
后者：基础不好且有时间的可以看看红书；没有时间的就按照我说的备考进行——积累和熟练为主。
b）思维陷阱：
c）知识点遗忘：单独一部分进行
d）DS充分性把握不好
e）悬而未决：有争议的；大家都搞不定的难题
f）记住答案的：有些题目需要大量计算的，可以先用计算器算好了，直接背，不是刻意，多看几遍一定就印象深刻了。
B）知识点类型：我在10.16的答疑部分的讲义有所演示如何进行这部分分类

作者: xiongbaobao 时间: 2010-11-8 11:37

【注意几点】：
A）马虎问题：
我觉得比较好的：整理JJ的工作可以和做PREP同步进行。所以，就把自己这段时间以来的PREP的错题（之前已经分类）中马虎问题集中起来做一遍，总结出一种对GMAT数学prefer的一些马虎点的感觉，然后再拿出JJ中的马虎问题看2遍，记住自己容易出错的地方
B）理解问题：
做PREP时就要注意积累一些自己不熟悉的表达，做JJ时遇到理解问题，继续积累收藏，考前看看就OK了。
C）思维陷阱：以JJ为纲，按知识点整理出一类题自己怎么爱犯错的。如果基础再差一点儿，可以加上PREP的相同类型错误的题目一起整理。考前反复看几遍，把这种敏感融入到题感之中。（比如，概率中的有没有放回，是否是独立事件；余数问题：）。
D）悬而未决：
有争议的、大家都没辙的难题——放了，依靠考场灵感。
E）知识点遗忘：看看自己薄弱的知识点在哪一部分，有针对性地补——博森的数学书“知识点讲解”部分或任意下载一些整理好的数学知识点中文总结即可，OG的math review是基础仅仅提供广度和系统性的了解，但在这个范围内各考点的深度需要利用中文资料自己进一步弥补，建议使用好google和维基百科等网络工具来查漏补缺。

作者: xiongbaobao 时间: 2010-11-8 11:37

（4）重视讨论帖：自己先看，通过整理机井+看讨论后依然不明白的，放到答疑专区，并并写清楚您的问题是什么，我们好有的放矢地解决。

（5）考前把自己最后的错题分类总结快速看一遍：早上考的，头晚系统看看；下午考的，第二天上午看看。
主要看什么：自己之前解决的难题，简单的就不用看了；有争议的也看看：不是记住答案，而是告诉自己，遇到这些要小心，这是没有确定的，需要我自己好好思考的，不要考场上乱点。
这一遍会让机经带给你的解题感觉在脑中清晰和系统化，有助于临阵不乱。

4. 考场上：不要去想GMAC是怎么评分的，一切都是未知和徒劳，专气致柔如婴儿是在做好上述准备后获得高分的唯一要诀。

5. 对于知识基础扎实、题目阅读理解顺畅、pace很好的同学：
备考前把OG的math review过一遍，直接进入JJ整理（当月或前月均可，经验反复证明：机经对于前面月份相同题目的重复经常存在），在此基础上，在上述4步中挑选你认为有必要的步骤进行补充训练即可。

作者: xiongbaobao 时间: 2010-11-8 11:37

IV．    附录：

附件1：理解问题专题集锦
【注】：以下题目均来源于PREP破解1和2，下面只分析读题，有兴趣解题的同学可以查阅破解版相应题目的答案。

I．       比例问题、比较问题+集合问题（含浓度问题）
【怎么读】：
1. 比例问题：读出分子分母
1）遇到percentage和fraction：注意跟在这两个词后的of后的部分（包含其修饰语）就是分母；
2）ratio：ratio of A to B——A是分子，B是分母
2. 集合：读出分类标准，并且能够通过英文表述准确识别是否是全集、有没有交集或并集
1）一个标准分类的：通常用韦恩图或公式直接求解
2）两个标准分类的：通常用二维表解决较为简单明了
3. 比较问题：准确读出比较对象

96.    10591-!-item-!-187;#058&007292
According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice.[l1] How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice[l2] ?

(A)  25
(B)  34
(C)  50
(D)  67
(E)  100

142.    14580-!-item-!-187;#058&010013
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.[l3] If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase

164.    17177-!-item-!-187;#058&011044
A certain scholarship committee awarded scholarships in the amounts of $1,250, $2,500, and $4,000[l4] .  The committee awarded twice as many $2,500 scholarships as $4,000 scholarships, and it awarded three times as many $1,250 scholarships as $2,500 scholarships. [l5] If a total of $37,500 was awarded in $1,250 scholarships, how many $4,000 scholarships were awarded?

(A)  5
(B)  6
(C)  9
(D) 10
(E) 15

165. 16466-!-item-!-187;#058&010795
Of the 1,400 college teachers surveyed, 42 percent said that they considered engaging in research an essential goal. How many of the college teachers surveyed were women?
(1) In the survey, 36 percent of the men and 50 percent of the women said that they considered engaging in research an essential goal.[l6]
(2) In the survey, 288 men said that they considered engaging in research an essential goal.
【解】：A
1）破题：
A）理解的关键：见批注
B）破题：这是一个标准的二维表问题
2）思路：见下表
E E取非 T
F 50%x;700      X
M 36*(1400-x);288      1400-x
T *42%      1400
【NOTE】：黑色字为题干已知；绿色字为条件1已知；红色字为条件2已知。

作者: xiongbaobao 时间: 2010-11-8 11:38

179. 17750-!-item-!-187;#058&011285
A manufacturer conducted a survey to determine how many people buy products P and Q. [l7] What fraction of the people surveyed said that they buy neither product P nor product Q ?
(1)1/3 of the people surveyed said that they buy product P but not product Q.
(2) 1/2 of the people surveyed said that they buy product Q.

202. 19528-!-item-!-187;#058&012279
Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z[l8]  ?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half of the full-time employees of Company Z are employees of Division X[l9] , and more than half of the part-time employees of Company Z are employees of Division Y[l10] .

212. 20491-!-item-!-187;#058&012823
This morning, a certain sugar container was full. Since then some of the sugar from this container was used to make cookies. If no other sugar was removed from or added to the container, by what percent did the amount of sugar in the container decrease[l11] ?
(1) The amount of sugar in the container after making the cookies would need to be increased by 30 percent to fill the container.
(2) Six cups of sugar from the container were used to make the cookies.

85.    9649-!-item-!-187;#058&007038
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years.  If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent?[l12]

(A) 200
(B)  160
(C)  112
(D)  80
(E)  56

88.    9789-!-item-!-187;#058&007104
In May Mrs. Lee's earnings were 60 percent of the Lee family's total income.  In June Mrs. Lee earned 20 percent more than in May. [l13]  If the rest of the family's income was the same both months, then, in June, Mrs. Lee's earnings were approximately what percent of the Lee family's total income?

(A) 64%
(B) 68%
(C) 72%
(D) 76%
(E) 80%

176. 17259-!-item-!-187;#058&011402
In 1995 Division A of Company X had 4,850 customers. If there were 86 service errors in Division A that year, what was the service-error rate, in number of service errors per 100 customers[l14] , for Division B of Company X in 1995 ?
(1) In 1995 the overall service-error rate for Divisions A and B combined was 1.5 service errors per 100 customers.
(2) In 1995 Division B had 9,350 customers, none of whom were customers of Division A.

作者: xiongbaobao 时间: 2010-11-8 11:38

II．       工程问题
【怎么读】：读出模型的几个元素——
工程问题通用模型：
1/a + 1/b +1/c+…… = 1/t
原理：
ｔ×（va+vb+……）=T（工作总量）

105.    11075-!-item-!-187;#058&007490
Two water pumps, working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool.  If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?

(A) 5
(B)
(C)
(D) 6
(E)

5.       1353-!-item-!-187;#058&000886
Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours.  If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate[l15] ?

(A) 25%
(B)
(C) 50%
(D)
(E) 75%

179. 17563-!-item-!-187;#058&011544
Working independently at their respective constant rates, pumps X and Y took 48 minutes to fill an empty tank with water. What fraction of the water in the full tank came from pump X ? (1) Working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water.
(2) Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank with water.

作者: xiongbaobao 时间: 2010-11-8 11:38

III．    描述统计
【怎么读】：熟悉描述统计的相关术语及其公式的表达方式，找到各个统计指标的关系——
比如：average和SD

110.    11364-!-item-!-187;#058&007646
The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television.  The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours.  The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean.  Which of the following could be the number of hours that Pat watched television last week?

(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
这个题的重点理解题意：在the number of hours per week Pat watched TV was between 1 and 2 standard deviations below the mean.
one standard deviation below the mean = 21-6=15
two standard deviations below the mean = 21-6*2=9
所以Pat看电视的时间在9小时和15小时之间，只有答案D符合。
【小结】：标准差万变不离其宗的公式——
/Mean-某个element/=x*标准差【x为标准差的倍数或个数】
如果是above：mean+；反之：mean-

作者: xiongbaobao 时间: 2010-11-8 11:39

IV．    排列组合、概率
【怎么读】：从英文表述中识别出是求的排列组合三个基本类型的哪一类；概率问题准确判断分子和分母
117.    11706-!-item-!-187;#058&007820
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors:  blue, green, yellow, or pink.  The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. [l16]  If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

(A)  6
(B)  8
(C)  16
(D)  24
(E)  32

1.       246-!-item-!-187;#058&000117
Tanya prepared 4 different letters to be sent to 4 different addresses.  For each letter, she prepared an envelope with its correct address.  If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
排列问题

25.    3619-!-item-!-187;#058&003382
A fast-food company plans to build 4 new restaurants.  If there are 12 sites that satisfy the company's criteria for location of new restaurants, in how many different ways can the company select the 4 sites needed for the new restaurants if the order of selection does not matter?

(A)  48
(B)  288
(C)  495
(D)  990
(E)  11,880
组合问题

46.    5979-!-item-!-187;#058&004694
If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666
伯努利实验

74.    8516-!-item-!-187;#058&006446
There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field.  If 2 rocks are to be chosen at random and without replacement[l17] , what is the probability that both rocks will be slate rocks?

89.    9835-!-item-!-187;#058&007168——抛硬币两面概率不等的case！
For one toss of a certain coin, the probability that the outcome is heads is 0.6.  If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

(A) (0.6)^5
(B) 2(0.6)^4
(C) 3(0.6)^4(0.4)
(D) 4(0.6)^4(0.4) + (0.6)^5
(E) 5(0.6)^4(0.4) + (0.6)^5

152. 15540-!-item-!-187;#058&010751 20
A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?[l18]

作者: xiongbaobao 时间: 2010-11-8 11:39

V．       其他应用题
一．    路程问题: 注意单位换算！
178.    18885-!-item-!-187;#058&011972
Adam and Beth each drove from Smallville to Crown City by different routes.  Adam drove an an average speed of 40 miles per hour and completed the trip in 30 minutes.  Beth's route was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip.[l19] How many miles per hour was Beth's average speed on this trip?

(A) 24
(B) 30
(C) 48
(D) 54
(E) 75

155. 15462-!-item-!-187;#058&010358
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded to the nearest tenth[l20] .)
(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour.
(2) On average, it took Pei more than 9 minutes per kilometer to walk this distance.

163.    17463-!-item-!-187;#058&011464——读懂问题！
The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions.  What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions?  (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

(A)  0.80
(B) 1.25
(C) 8.00
(D) 12.50
(E) 80.00

作者: xiongbaobao 时间: 2010-11-8 11:39

二．    绩效工资模型
【提示】：基本模型——
A=B+C
找到底量B和增量C（“plus”）
135.    13701-!-item-!-187;#058&009670
For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 30 percent of the total amount of the sale in excess of $500[l21] .  If the total amount of one of her sales was $800, the saleswoman's commission was approximately what percent of the total amount of the sale?

(A) 22%
(B) 24%
(C) 25%
(D) 27%
(E) 28%

7.       1502-!-item-!-187;#058&001086
A certain telephone company offers two plans, A and B.  Under plan A, the company charges a total of $0.60 for the first 7 minutes of each call and $0.06 per minute thereafter. [l22]  Under plan B, the company charges $0.08 per minute of each call.  What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B ?

(A) 2
(B) 9
(C) 15
(D) 21
(E) 30

62.    7185-!-item-!-187;#058&005078
In a certain furniture store, each week Nancy earns a salary of $240 plus 5 percent of the amount of her total sales that exceeds $800 for the week[l23] .  If Nancy earned a total of $450 one week, what were her total sales that week?

(A) $2,200
(B) $3,450
(C) $4,200
(D) $4,250
(E) $5,000

65.    7385-!-item-!-187;#058&005343
A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100.[l24] If the sale price of each machine was $10,000 and the salesperson received a $36,000 commission, how many machines did she sell?

(A)  90
(B)  103
(C)  105
(D)  115
(E)  120

作者: xiongbaobao 时间: 2010-11-8 12:55

三．    其他
138. 14162-!-item-!-187;#058&009822
A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is $34,600. What was the theater's total revenue from ticket sales for last night's performance?
(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

182. 17963-!-item-!-187;#058&011379
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries.[l25]  If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.

29.    3873-!-item-!-187;#058&003594
If n denotes a number to the left of 0 on the number line such that the square of n is less than  1/100, then the reciprocal of n must be[l26]

(A) less than -10
(B) between -1 and
(C) between and 0
(D) between 0 and
(E) greater than 10

38.    5275-!-item-!-187;#058&004179
A certain business produced x rakes each month from November through February and shipped 0.5x rakes at the beginning of each month from March through October.[l27] The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped.  In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months from November through October?

(A) 0.40x
(B) 1.20x
(C) 1.40x
(D) 1.60x
(E) 3.20x

54.    6364-!-item-!-187;#058&004806
P, Q, and R are located in a flat region of a certain state.  Q is x miles due [l28] east of P and y miles due north of R.  Each pair of points is connected by a straight road.  What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y, and z ?  (Assume x, y, and z are positive.)

170.    18339-!-item-!-187;#058&011871(定义类)
For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (arithmetic mean) of the x-coordinates of the vertices of T and whose y-coordinate is the average of the y-coordinates of the vertices of T.[l29] If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?

(A) (3,4)
(B) (3,6)
(C) (4,9)
(D) (6,4)
(E) (9,6)

181.    19721-!-item-!-187;#058&012675
The distributor of cases of a certain beverage charges $60 per case for orders of 1 to 5 cases, $50 per case for orders of 6 to 20 cases, and $45 per case for orders of more than 20 cases.  [l30] If the distributor filled three orders, one for 3 cases of the beverage, one for 11 cases of the beverage, and one for 30 cases of the beverage, what was the total amount the distributor charged for the orders?

(A) $1,960
(B) $2,000
(C) $2,040
(D) $2,080
(E) $2,120

作者: xiongbaobao 时间: 2010-11-8 12:56

附件2：排列组合与概率问题专题

【推荐资料：博森数学书P75练习题。如下是对其进行的分类，可以参照练习】

（I）. 排列组合：
一．排列：计算绝对数
（一）一般情况：
1. 有序且不可重复：T5，T10（循环定位法）
2. 有序且可重复：T37

（二）其他：
1. 捆绑类：T8，T21
2. 插空：T42
3．定位问题：T7，T39，T41
T44：以上3种问题的综合——经典。
4. 正反1/2型：T4，T43
5. 内部元素相同，外部有序（需要消序）：T9
6. 其他：T38（循环赛），T47（结合集合的二维表），T49（握手），T48

二．组合：
（一）一般情况：T1，T2，T3，T45
（二）其他：T6

作者: xiongbaobao 时间: 2010-11-8 12:56

（II）. 概率：计算相对数
一．抽样：
（一）不可放回：sampling without replacement
1. 一次性抽取：T12，T17，T19，T22，T23，T24，T46
2. 依次抽取抽取：
（1）第k次抽到的概率：T36
（2）抽奖问题：
Eg：10张彩票，有一张奖票，人们依次抽出，则每个人中奖的概率相同。
1st：P=1/10
2nd: P=9/10 * 1/9
3rc: P=9/10 * 8/9 * 1/8

（3）几何概率（用面积或时间长度）：T14
（4）其他：T16，T17， T25，T26，T31（综合：体现分类抽取与一次性抽取的转换）

（二）可放回：sampling with replacement
Eg：10张彩票，2张奖票，重复抽样，一个人连续重复抽样3次，每次都中奖的概率？

（三）其他：T13，T15

作者: xiongbaobao 时间: 2010-11-8 12:56

二．伯努利概型：
【前提】：独立重复试验

三．涉及排列组合的：T20，T21（捆绑），T34，T35
四．其他：T28，T29（注意两个事件是否相互独立的判断），T30（条件概率），T18（条件概率），T50（容易忽略是2种情况）

附件3： GMAT数学概念和名词（转载）
Algebra & arithmetic terms:

Absolute value 绝对值
Add (addition) 加
Average value 算术平均值
Algebra 代数
Algebraic expression 代数式
Arithmetic mean 算术平均值
Arithmetic progression (sequence)等差数列
Approximate 近似
Abscissa 横坐标
Ordinate 纵坐标
Binomial 二项式
Common factor 公因子
Common multiple 公倍数
Common divisor 公约数
Simple fraction
Common fraction 简分数
Complex fraction 繁分数
Common logarithm 常用对数
Common ratio 公比
Complex number 复数
Complex conjugate 复共轭
Composite number 合数
Prime number 质数
Consecutive number 连续整数
Consecutive even(odd) integer 连续偶（奇）数
Cross multiply 交叉相乘
Coefficient 系数
Complete quadratic equation 完全二次方程
Complementary function 余函数
Constant 常数

作者: xiongbaobao 时间: 2010-11-8 12:57

Coordinate system 坐标系
Decimal 小数
Decimal point 小数点
Decimal fraction 纯小数
Decimal arithmetic 十进制运算
Decimal system/decimal scale 十进制
Denominator 分母
Difference 差
Direct proportion 正比
Divide 除
Divided evenly 被整除
Differential 微分
Distinct 不同的
Dividend 被除数，红利
Division 除法
Division sign 除号
Divisor 因子，除数
Divisible 可被整除的
Equivalent fractions 等值分数
Equivalent equation 等价方程式
Equivalence relation 等价关系
Even integer/number 偶数
Exponent 指数，幂
Equation 方程
Equation of the first degree 一次方程
Endpoint 端点
Estimation 近似
Factor 因子
Factorable quadratic equation 可因式分解的二次方程
Incomplete quadratic equation 不完全二次方程
Factorial 阶乘
Factorization 因式分解
Geometric mean 几何平均数

作者: xiongbaobao 时间: 2010-11-8 12:57

Graph theory 图论
Inequality 不等式
Improper fraction 假分数
Infinite decimal 无穷小数
Inverse proportion 反比
Irrational number 无理数
Infinitesimal calculus 微积分
Infinity 无穷大
Infinitesimal 无穷小
Integerable 可积分的
Integral 积分
Integral domain 整域
Integrand 被积函数
Integrating factor 积分因子
Inverse function 反函数
Inverse/reciprocal 倒数
Least common denominator 最小公分母
Least common multiple 最小公倍数
Literal coefficient 字母系数
Like terms 同类项
Linear 线性的
Minuend 被减数
Subtrahend 被减数
Mixed decimal 混合小数
Mixed number 带分数

作者: xiongbaobao 时间: 2010-11-8 12:58

Minor 子行列式
Multiplicand 被乘数
Multiplication 乘法
Multiplier 乘数
Monomial 单项式
Mean 平均数
Mode 众数
Median 中数
Negative (positive) number 负（正）数
Numerator 分子
Null set (empty set) 空集
Number theory 数论
Number line 数轴
Numerical analysis 数值分析
Natural logarithm 自然对数
Natural number 自然数
Nonnegative 非负数
Original equation 原方程
Ordinary scale 十进制
Ordinal 序数
Percentage 百分比
Parentheses 括号
Polynomial 多项式
Power 乘方
Product 积

作者: xiongbaobao 时间: 2010-11-8 12:58

Proper fraction 真分数
Proportion 比例
Permutation 排列
Proper subset 真子集
Prime factor 质因子
Progression 数列
Quadrant 象限
Quadratic equation 二次方程
Quarter 四分之一
Ratio 比率
Real number 实数
Round off 四舍五入
Round to 四舍五入
Root 根
Radical sign 根号
Root sign 根号
Recurring decimal 循环小数
Sequence 数列
Similar terms 同类项
Tens 十位
Tenths 十分位
Trinomial 三相式

作者: xiongbaobao 时间: 2010-11-8 12:58

Units 个位
Unit 单位
Weighted average 加权平均值
Union 并集
Yard 码
Whole number 整数
Mutually exclusive 互相排斥
Independent events 相互独立事件
Probability 概率
Combination 组合
Standard deviation 标准方差
Range 值域
Frequency distribution 频率分布
Domain 定义域
Bar graph 柱图

Geometry terms:

Angle bisector 角平分线
Adjacent angle 邻角
Alternate angel 内错角
Acute angle 锐角
Obtuse angle 钝角
Bisect 角平分线
Adjacent vertices 相邻顶点
Arc 弧
Altitude 高

作者: xiongbaobao 时间: 2010-11-8 12:59

Arm 直角三角形的股
Complex plane 复平面
Convex (concave) polygon 凸（凹）多边形
Complementary angle 余角
Cube 立方体
Central angle 圆心角
Circle 圆
Clockwise 顺时钟方向
Counterclockwise 逆时钟方向
Chord 弦
Circular cylinder 圆柱体
Congruent 全等的
Corresponding angle 同位角
Circumference (perimeter) 周长
Concentric circles 同心圆
Circle graph 扇面图
Cone (V =pai * r^2 * h/3) 圆锥
Circumscribe 外切
Inscribe 内切
Diagonal 对角线
Decagon 十边形
Hexagon 六边形
Nonagon 九边形
Octagon 八边形
Pentagon 五边形
Quadrilateral 四边形
Polygon 多边形
Diameter 直径
Edge 棱
Equilateral triangle 等边三角形
Exterior (interior) angle 外角/内角
Extent 维数

作者: xiongbaobao 时间: 2010-11-8 12:59

Exterior angles on the same side of the transversal同旁外角
Hypotenuse 三角形的斜边
Intercept 截距
Included angle 夹角
Intersect 相交
Inscribed triangle 内接三角形
Isosceles triangle 等腰三角形
Midpoint 中点
Minor axis 短轴
Origin 原点
Oblique 斜三角形
Plane geometry 平面几何
Oblateness (ellipse) 椭圆
Parallelogram 平行四边形
Parallel lines 平行线
Perpendicular 垂直的
Pythagorean theorem 勾股定理
Pie chart 扇图
Quadrihedron 三角锥
Radius 半径
Rectangle 长方形
Regular polygon 正多边形
Rhombus 菱形
Right circular cylinder 直圆柱体

作者: xiongbaobao 时间: 2010-11-8 13:00

Right triangle 直角三角形
Right angle 直角
Rectangular solid 正多面体
Regular prism 正棱柱
Regular pyramid 正棱锥
Regular solid/polyhedron 正多面体
Slope 斜率
Sphere ( surface area=4 pai r^2, V=4 pai r^3 / 3)
Side 边长
Segment of a circle 弧形
Semicircle 半圆
Solid 立体
Square 正方形，平方
Straight angle 平角（180度）
Supplementary angle 补角
Scalene cylinder 斜柱体
Scalene triangle 不等边三角形
Trapezoid 梯形
Volume 体积
Width 宽
Vertical angle 对顶角

作者: xiongbaobao 时间: 2010-11-8 13:00

Word problem terms:

Apiece 每人
Per capita 每人
Decrease to 减少到
Decrease by 减少了
Brace 双
Cardinal 基数
Cent 美分
Nickel 五美分
Dime 一角
Penny 一美分
Down payment 定金，预付金
Simple interest 单利
Compounded interest 复利
Foot 英尺
Dozen 打
Gross = 12 dozen 罗
Gallon = 4 quart 加仑
Fahrenheit 华氏温度
Depth 深度
Discount 折扣
Cumulative graph 累计图
Interest 利息
Margin 利润
Profit 利润
Retail price 零售价
Pint 品脱
Score 二十
Common year 平年
Intercalary year(leap year) 闰年

作者: xiongbaobao 时间: 2010-11-8 13:00

[l1]浓缩液：水=1：3（单位：can）
[l2]有如下2个关系：
1）1con：3water （单位：can；12 ounce/can）
2）浓缩液的量+水的量=juice的量（单位：ounce。因为can的规格不同，不能用“can”直接相加！
[l3]转化为数学模型：
C=K*(A^2/B)
[l4]奖学金的规格（单位价值量）：三种
[l5]
1）2500的个数=4000的个数*2
2）1250的个数=2500的个数*3
[l6]数学模型：
男人*36%+女人*50%=总considering人数
[l7]全集=只有P+只有Q+P∩Q+两者都没有。
或：
全集=P+只有Q+两者都没有。
[l8]Xf/xp>总f/总p=zf/zp？
[l9]分母：z中所有f；
分子：x中的f！
[l10]分母：z中所有p；
分子：y中所有p！
[l11]移出的sugar/原来总糖量=？

作者: xiongbaobao 时间: 2010-11-8 13:00

[l12]T*70%-y=60%*（T-y）
[l13]May: T*60%=Lee
June: T*60%*(1+20%)=Lee’
Key: Lee6/T6= T*60%*(1+20%)/[ T*60%*(1+20%)+ T*40%]
[l14]定义！
[l15]分子：faster的c
分母：总数
  [l16]两种规格：
1）  同size的3个：相同颜色
2）  同size的3个：不同颜色
[l17]组合+无放回
[l18]比较对象：红色的概率>白色的概率！
[l19]比较类：把握比较对象！
[l20]精确到十分位
[l21]数学模型：
Commission=20%*500+30%*（T-500）
[l22]T=0.6+0.06*（t-7）
[l23]一定要注意有没有这句话：如果没有，就可能分母是总数！
[l24]T=3%*100*P+4%*P*（N-100）
[l25]倍数关系：
（M-J）=2（M-K）
  [l26]条件：n<0 且 n^2<1/100;
问题：1/n？
  [l27]11-2月：每月生产x；
3-10月：每月运出0.5x
  [l28]in exactly the direction mentioned
  [l29]中心的x=三个顶点的x的average
中心的y=3个顶点的y的average
[l30]注意是三种规格，而非连续相加——与“绩效工资模型”区分开！

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