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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.

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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.

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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-

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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]

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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

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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

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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

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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

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（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

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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