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博森 GWD 英吉管卫东GMAT阅读详解(下)9月12日更新

每月不定期更新，增加新的阅读讲解，敬请关注/mydoc-737508-1.html&folderId=4825 8GMAT题目讲解，2010-4-3In 1994, a team of scientists ledby David Mckay began studying themeteorite ALH84001, which had beenLine discovered in Antarctica in 1984.(5) Two years later, the McKay teamannounced that ALH84001, whichscientists generally agree originatedon Mars, contained compelling evidence that life once existed on Mars.(10) This evidence includes the discoveryof organic molecules in ALH84001,the first ever found in Martian rock.Organic molecules—complex, carbon-based compounds—form the basis for(15) terrestrial life. The organic moleculesfound in ALH84001 are polycyclic aromatic hydrocarbons, or PAH’s. When microbes die, their organic materialoften decays into PAH’s.(20) Skepticism about the McKay team’sclaim remains, however. For example,ALH84001 has been on earth for13,000 years, suggesting to somescientists that its PAH’s might have(25) resulted from terrestrial contamination.However, McKay’s team has demonstrated that the concentration of PAH’s increases as one looks deeper intoALH84001, contrary to what one would(30) expect from terrestrial contamination.The skeptic’s strongest argument,however, is that processes unrelatedto organic life can easily produce allthe evidence found by McKay’ steam,(35) including PAH’s. For example, starformation produces PAH’s. Moreover,PAH’s frequently appear in othermeteorites, and no one attributestheir presence to life processes.(40) Yet McKay’s team notes that theparticular combination of PAH’sin ALH84001 is more similar to thecombinations produced by decayingorganisms than to those originatingform no biological processes.5 The passage asserts which of the following about the claim that ALH84001 originated on Mars?It was initially proposed by the McKay team of scientists.It is not a matter of widespread scientific dispute.It has been questioned by some skeptics of the McKay team’s work.It has been undermined by recent work on PAH’s.It is incompatible with the face that ALH84001 has been on Earth for 13,000 years.6 The primary purpose of the passage is todescribe new ways of studying the possibility that life once existed on Mars revise 改进a theory regarding the existence of life on Mars in light of new evaluate a recently proposed argument concerning the origin of ALH84001 describe a controversy concerning the significance of evidence from ALH840017 The passage suggests that the fact that ALH84001 has been on earth for 13,000 years has been used by some scientists to support which of the following claims about ALH84001?ALH84001 may not have originated on Mars.ALH84001 contains PAH’s that are the result of nonbiological processes.ALH84001 may not have contained PAH’s when it landed on Earth.The organic molecules found in ALH84001 are not PAH’s.The organic molecules found in ALH84001 could not be the result of terrestrial contamination.文章分析：文章开头说一帮科学家研究ALH,说ALH里面包含的PAH能证明火星原来存在生命。

GMAT考试数学高分技巧解析

GMAT考试数学高分技巧解析GMAT考试数学高分技巧解析GMAT考试中对数学的复习很多考生都觉得没什么难度，因此只是看看基础的数学词汇知识，做做GMAT数学题就上考场。

这样的复习对拿GMAT数学高分远远不够。

在下面列举几点GMAT考试数学高分技巧的解析。

第一点：(数学单词)或者大家可以针对单词，单词是基础中的基础，你的GMAT数学单词要掌握，才可以知道这个题目要求的是什么，当中用到了什么数据，或者过程当中你需要考虑到哪些点，所以这是理解能力。

还有一点就是你对题目的问题，这样才可以直观了解到这道题要求什么。

第二点：接下来就是GMAT考试数学的术语，那还是单词和词组的问题，就是说这是针对数学里的数学术语，要去背一背，当然这个很快，没有多少东西;因为大家之前都学过，因为GMAT数学并不涉及到高数，只是初中、高中的数学，之前都学过，对比之前学过的东西，能知道它是考什么就OK了;第三点：它没有问到的，你以为这是常识，把它给代进去了，这是你自己对这道题目的'假设，也就是说你不能把场外信息带入进去，这就是GMAT考试，你所有的信息，只有针对这个题目出现的考点和题目给出你的信息对它进行解答，你不能进行主观假设，你不能把场外的信息带进去，也许对，这是你在常识过程中、在日常生活中的常识，但是不能带进去，因为有很多数学题，你如果用常识来想，它是很荒谬的，但是最终它要求你得到答案，而不是检测你的常识。

第四点：下面一个是逻辑错误，逻辑错误就是说之前你不要跳步骤，一步一步来解答它，时间肯定够，你首先要有一个正确的解答过程，也就是说你理解了这个点之后，你对它进行一个顺向的思维，这就是逻辑的问题。

第五点：接下来就是技巧和反应的问题，数学最基本的三个点，知识的掌握配合一定量的练习，你要有一定量的练习，考试的时候才会有足够快的反应时间，才可以节省你的时间。

然后这些技巧也是在你的平时做题，OG、prep、GWD之类的其他复习的材料上来提高的，或者说让你掌握的，你题目见得多了，它不管出什么题，你可以很明显地知道它用什么方法，就很好解决了。

GMAT管卫东Math-第24套-智课网

智课网GMAT备考资料Math Section-24Q1If 25(5^x)=1 then x=A.–2B.–1C.0D.1E. 2Answer:-------------------------------------------------------------------------------------------------------Q2if p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?(1) p^3st=728(2) t=13●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q3in a certain game played with red chips and blue chips, each red chip has a point value of X and each blue chip has a point value of Y, where X>Y and X and Y are positive integers. If a player has 5 red chips and 3 blue chips, what is the average (arithmetic mean ) point value of the 8 chips that the player has?(1)The average point value of one red chip and one blue chip is 5.(2)The average point value of the 8 chips that the player has is an integer.-----------------------------------------------------------------------------------------------------●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q4A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?A.1/7B. ¼C. 5/14D. 11/28E. 13/26Answer:-------------------------------------------------------------------------------------------------------Q5The tens digit of positive integer X is 3. Is the units digit of X greater than 4?(1)The units digit of 2X is less than the units digit of X.(2)The tens digit of 2X is 7.----------------------------------------------------------------------------------------------------------●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q6|-4| (|-20|-|5|)=A.–100B. –60C. 60D. 75E. 100Answer-------------------------------------------------------------------------------------------------------Q7What is the maximum integer value of M for which 12!/2^M is an integer?A. 2B. 4C. 6D. 10E. 12Answer-------------------------------------------------------------------------------------------------------Q8Can a certain rectangular sheet of glass be positioned on a rectangular tabletop so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop?(1)The tabletop is 36 inches wide by 60 inches long.(2)The area of one side of the sheet of glass is 2400 square inches.●Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient●Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient●EACH statement ALONE is sufficient●Statements (1) and (2) TOGETHER are NOT sufficientAnswer-------------------------------------------------------------------------------------------------------Q9The operation* represents either addition, subtraction, or multiplication of integers, what is the value of 1*0?(1)0*2=2(2) 2*0=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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q10If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?A. 144B. 132C. 66D. 33E. 23Answer-------------------------------------------------------------------------------------------------------Q11An equilateral triangle that has an area of 9 3^1/2 is inscribed in a circle. What is the area of the circle?A . 6pi B. 9pi C. 12 pi D. 9pi 3^1/2 E. 18pi 3^1/2Answer-------------------------------------------------------------------------------------------------------Q12During a 10-week summer vacation, was the average (arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week?(1)Twice the average number of books that Carolyn read per week was greater than 5 less thantwice the average number of books that Jacob read per week.(2)During the last 5 weeks of the vacation, Carolyn read a total of 3 books more than Jacob.●Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient●Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient●EACH statement ALONE is sufficient●Statements (1) and (2) TOGETHER are NOT sufficientAnswer-------------------------------------------------------------------------------------------------------Q13If X, Y, and Z are positive integers, is Y>X?(1)Y^2=XZ(2)Z-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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q14Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a personal computer in 1998?A. 50%B. 52%C. 56%D. 70%E. 74%answer-------------------------------------------------------------------------------------------------------Q15Which of the following expressions can be written as an integer?(1)(82^1/2+82^1/2)^2(2)(82)(82^1/2)(3) (82^1/2)(82^1/2)82A.NoneB.(1) onlyC.(3) onlyD.(1)and(2)E.(1)and (3)answer-------------------------------------------------------------------------------------------------------Q16From May 1 to May 30 in the same year, the balance in a checking account increased. What was the balance in the checking account on May 30?(1)If, during this period of time, the increase in the balance in the checking account had been 12percent, then the balance in the account on May 30 would have been $504(2)During this period of time, the increase in the balance in the checking account was 8 percent.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q17If N is positive, which of the following is equal to1(n+1)^1/2-n^1/2A. 1B. (2n+1)^1/2C. (n+1)^1/2n^1/2D.(n+1)^1/2-n^1/2E. (n+1)^1/2+n^1/2Answer-------------------------------------------------------------------------------------------------------Q18The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 1 percent, what was the annual interest rate last year?A. 1%B. 1.1%C. 9.1%D. 10%E. 10.8%Answer-------------------------------------------------------------------------------------------------------Q19Color X ink is created by blending red, blue, green, and yellow inks in the ratio 6:5:2:2. what is the number of liters of green ink that was used to create a certain batch of color X ink?(1)The amount of red ink used to create the batch is 2 liters more than the amount of blue ink usedto create the batch.(2)The batch consists of 30 liters of color X ink.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q20Of the 32 students in a certain class, 15 are in a music club and 20 are in a dance club. If 10 of the students are not in either club, how many of the students are in only one of the two clubs?A. 5B. 9C.10D. 17E. 25Answer-------------------------------------------------------------------------------------------------------Q21If P and R are positive, is 25 percent of P equal to 10 percent of R?(1)R is 150 percent greater than P(2)P is 60 percent less than R.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q22If X^2+Y^2=1, is X+Y=1?(1)XY=0(2)Y=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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q23If A@B=A^2+B^2 for all real numbers A and B. then (A@B)@C=A. A^2+B^2+C^2B. 2A^2+2B^2+C^2C. A^4+B^4+C^2D. A^4+B^4+2A^2B^2+C^2Answer-------------------------------------------------------------------------------------------------------Q24Each week John earns X dollars per hour for the first 40 hours that he works that week and Y dollars for each additional hour. How much does John earn per hour for the first 40 hours?(1)Y=15X(2)If John works 45 hours in a week, he earns a total of $570 that week.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q25Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate ,produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate. Produces 500 feet of the same fiber in 5 hours. How many hours will it take machines A. B, and C, operating together at their respective constant rates, to produce 1000 feet of the fiber?A. 60/31B. 15/7C. 25/11D. 10/2E. 20/3Answer-------------------------------------------------------------------------------------------------------Q26Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?(1)P>Q(2)Q=8●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q27(1/2)^(-2)(2)^(-2)A. 16B. 8C. 4D. 1/8E. 1/16Answer-------------------------------------------------------------------------------------------------------Q28If k=-1, which of the following is (are) true?1.k^k=k2. | k| =-k.3.k^0=-kA. 1 onlyB. 1 and 2 onlyC. 1 and 3 onlyD. 2 and 3 onlyE. 1. 2. and 3.Answer-------------------------------------------------------------------------------------------------------Q29A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?A. 31B. 31.5C. 32D. 32.5E. 33Answer-------------------------------------------------------------------------------------------------------Q30A parent established a college fund for his daughter. Each year the parent made a contribution to the fund, and each year he increased his contribution by a constant amount. If he made a contribution of $800 in the first year, by what amount did the parent increase his contribution to the fund each year?(1)The parent’s contribution to the fund in the 18th year was $7600.(2)The parent’s contribution to the fund in the 7th year was twice what it was in the 3rd year.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q31Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18. which of the following is the measure of one of its angles?A. 30’B. 45’C. 60’D. 90’E.120’Answer-------------------------------------------------------------------------------------------------------Q32If ¼ of the larger of two numbers is greater than 5 times the smaller of the same two numbers, is the smaller number less than 4?(1)The larger number is greater than 70.(2)The larger number is less than 80.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q33Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?A. 95B. 115C. 125D. 160E. 180Answer-------------------------------------------------------------------------------------------------------Q34A certain carton holds fewer than 50 books. What is the number of books in the carton?(1)The books in the carton can be divided into 3 stacks of X books each, with 2 books left over.(2)The books in the carton can be divided into Y stacks of 7 books each, with 2 books left over.●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q35What is the value of x^2yz+xy^2z+xyz^2(1)x+y+z=18(2)xyz=10●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 sufficientAnswer-------------------------------------------------------------------------------------------------------Q36Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?A.30 minB.45 minC. 1 hrD.1 hr 15 minE. 1 hr 30 minanswer-------------------------------------------------------------------------------------------------------Q37If K is an integer and (0.0025)(0.025)(0.00025)*10^k is an integer, what is the least possible value of K?A.–12B.–6C.0D.6E.12Answer-------------------------------------------------------------------------------------------------------Answer:AACED,CDEAC,CACAE,AECDB,DEDCA,EAEDD,ABBEC,DE。

2024年1月GMAT试题MATH部分总结2篇

2024年1月GMAT试题MATH局部总结2024年1月GMAT试题MATH局部总结精选2篇〔一〕2024年1月GMAT试题MATH局部总结作为全球范围内广为认可的商学研究生入学考试，GMAT的数学局部一直都是考生们最为担忧的局部之一。

2024年1月GMAT数学局部继承了往期试题的难度，同时也在一定程度上有所变化。

通过对这一局部试题的总结和分析，可以帮助考生更好地理解和复习数学局部的内容和考点，为顺利通过GMAT考试打下坚实的根底。

本次GMAT数学局部试题共计37道，以整数、小数、分式、代数方程和几何等多种类型的题目为主。

整体难度中等偏上，局部试题具有出乎意料的难度，而有些试题那么相对简单。

但是与前面局部不同的是，数学局部时间相对较紧，考生需要尽快完成每道题目，否那么会降低正确率。

下面我们将从不同的角度，对一些常见的试题类型进展总结和分析。

1.整数与小数整数局部试题难度相对较小，在集合、排列组合等根本数学知识的根底上，通过简单的推算即可得出正确答案。

相对来说，小数局部题目的难度更大一些，需要对数字处理和计算有精准而灵敏的掌握，同时需要注意数据量级和单位的转换等问题。

需要注意将小数表示为分数，进展进一步的计算，以防止小数乘法和除法在计算机上产生的误差。

2.分数分数类型的题目是整个数学局部考试的核心，涵盖了相关的根本知识、比例、百分数、平均数、误差等内容。

分数的计算需要注意正确的约分、分母分子的转换、分数的分解等问题。

同时，考生还需要掌握求特定分数的过程，如1/7、1/9、1/11、1/13等，这些分数对一些直接计算问题非常有帮助。

3.代数方程代数方程是GMAT数学局部的难点和重点，也是考察考生对数学知识掌握程度的重要标志。

代数方程主要考察考生对方程的解法和操作的掌握程度，在解题的过程中需要注意切入点和思路的转换，同时需要注意精度的把控，防止连续计算产生的误差。

4.几何几何类型的题目在难度上介于中等和难之间，主要涉及到规那么图形、三角形、多边形等根底知识的运用。

GMAT管卫东31套第一套MATH.1

Math Section 3------------------------------------------------------------------------------------------------------------Q1:A family-size box of cereal contains more cereal and costs more than the regular-size box of cereal. What is the cost per ounce of the family-size box of cereal?(1) The family-size box of cereal contains 10 ounces more than the regular-size box of cereal.(2) The family-size box of cereal costs $5.40.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E------------------------------------------------------------------------------------------------------------Q2:A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?A.0B.1/9C.2/9D.1/3E. 1Answer: C------------------------------------------------------------------------------------------------------------Q3:If x and y are positive, is 4x > 3y?(1) x > y - x(2) x/y < 1A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E------------------------------------------------------------------------------------------------------------Q4:If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2k is a factor of n?A.10B.12C.15D.18E.20Answer: D------------------------------------------------------------------------------------------------------------Q5:Is x > k?(1) 2x • 2k = 4(2) 9x • 3k = 81A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: C------------------------------------------------------------------------------------------------------------Q6:If x and y are positive, what is the value of x – y?(1) (x2 – y2) / (x + y) = 4(2) x + y= 7A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: A------------------------------------------------------------------------------------------------------------Q7:A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?A.5/12B.2/5C.1/2D.3/4E.5/6Answer: D C------------------------------------------------------------------------------------------------------------Q8:In 1997 there were 300 female employees at Company C. If the number of female employees at Company C increased by 60 percent from 1977 to 1987, by what percent did the number of female employees at Company C increase from 1987 to 1997?(1) From 1977 to 1997 the number of female employees increased by 200 percent at CompanyC.(2) In 1977 there were 100 female employees at Company C.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: D------------------------------------------------------------------------------------------------------------Q9:A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2rosebushes in the middle of the row will be the red rosebushes?A.1/12B.1/6C.1/5D.1/3E.1/2Answer: B------------------------------------------------------------------------------------------------------------Q10:A set of numbers has the property that for any number t in the set, t + 2 is in the set. If –1 is in the set, which of the following must also be in the set?I.-3II. 1III. 5A. I onlyB. II onlyC. I and II onlyD. II and III onlyE. I, II, and IIIAnswer: D------------------------------------------------------------------------------------------------------------Q11:In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?A.3/5B.2/3C.3/4D.4/5E.5/6Answer: D------------------------------------------------------------------------------------------------------------Q12:If n is an integer and 2 < n < 6, what is the value of n?(1) n is a factor of 15.(2) n is a factor of 21.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: B------------------------------------------------------------------------------------------------------------Q13:If x and y are positive, is 3x > 7y?(1) x > y + 4(2) -5x < -14yA. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: B------------------------------------------------------------------------------------------------------------Q14:If 1050– 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?A.424B.433C.440D.449E.467Answer: C------------------------------------------------------------------------------------------------------------Q15:Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid 2/5 of the total amount, Carol paid $17, and Judy paid the rest, what fraction of the total amount did Judy pay?A.2/9B.14/45C.1/3D.2/5E.7/15Answer: A------------------------------------------------------------------------------------------------------------Q16:If J, S, and V are points on the number line, what is the distance between S and V?(1) The distance between J and S is 20.(2) The distance between J and V is 25.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E------------------------------------------------------------------------------------------------------------Q17:In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?A.16%B.25%C.32%D.40%E.52%Answer: B------------------------------------------------------------------------------------------------------------Q18:Note: Figure not drawn to scale.The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?A.56B.64C.68D.81E.100Answer: B------------------------------------------------------------------------------------------------------------Q19:A total of $60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?(1) x = (3/4) y(2) The ratio of the amount that earned interest at the rate of x percent per year to the amountthat earned interest at the rate of y percent per year was 3 to 2.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: C------------------------------------------------------------------------------------------------------------Q20:If x > 0, t hen 1/[√(2x)+√x] =A.1/√(3x)B.1/[2√(2x)]C.1/(x√2)D.(√2-1)/√xE.(1+√2)/√xAnswer: D------------------------------------------------------------------------------------------------------------Q21:When Leo imported a certain item, he made a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what wasthe total value of the item?A.$1,600B.$1,850C.$2,250D.$2,400E.$2,750Answer: C------------------------------------------------------------------------------------------------------------Q22:In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?A.218B.3(217)C.7(216)D.3(216)E.7(215)Answer: E------------------------------------------------------------------------------------------------------------Q23:In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r2 + s2?(1) The circle has radius 2.(2) The point (√2, -√2) lies on the circle.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: D------------------------------------------------------------------------------------------------------------Q24:If w and c are integers, is w > 0?(1) w + c > 50(2) c > 48A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E------------------------------------------------------------------------------------------------------------Q25:A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?A. 5B. 6C.9D.24E.36Answer: D A------------------------------------------------------------------------------------------------------------Q26:Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?A. 4B. 6C.8D.10E.12Answer: E------------------------------------------------------------------------------------------------------------Q27:If n = 811– 8, what is the units digit of n?A.0B. 1C. 4D. 6E.8Answer: C------------------------------------------------------------------------------------------------------------Q28:For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2. What is the sum of all the even integers between 99 and 301?A.10,100B.20,200C.22,650D.40,200E.45,150Answer: B------------------------------------------------------------------------------------------------------------Q29:June 25, 1982, fell on a Friday. On which day of the week did June 25, 1987, fall? (Note: 1984 was a leap year.)A.SundayB.MondayC.TuesdayD.WednesdayE.ThursdayAnswer: E------------------------------------------------------------------------------------------------------------Q30:Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?(1) She bought $4.40 worth of stamps.(2) She bought an equal number of $0.15 stamps and $0.29 stamps.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: C------------------------------------------------------------------------------------------------------------Q31:A positive integer n is said to be “prime-saturated” if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two-digit prime-saturated integer?A.99B.98C.97D.96E.95Answer: D------------------------------------------------------------------------------------------------------------Q32:For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person?(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more thanthe corresponding cost for 4 people.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: A D------------------------------------------------------------------------------------------------------------Q33:Is xy > x/y?(1) xy > 0(2) y < 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E------------------------------------------------------------------------------------------------------------Q34:The function f is defined by f(x) = - 1/x for all nonzero numbers x. If f(a) = - 1/2 and f(ab) = 1/6, then b =A. 3B.1/3C.- 1/3D.-3E.–12Answer: A------------------------------------------------------------------------------------------------------------Q35:What is the median number of employees assigned per project for the projects at Company Z?(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to eachproject.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: C------------------------------------------------------------------------------------------------------------Q36:Each signal that a certain ship can make is comprised of 3 different flags hanging vertically in a particular order. How many unique signals can be made by using 4 different flags?A.10B.12C.20D.24E.36Answer: D------------------------------------------------------------------------------------------------------------Q37:A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow. If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?A.3/64B.1/20C.1/16D.1/12E.1/8Answer: B------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Answers:ECEDC, ACDBD, DBBCA, EBBCD, CEDEA, ECBED, DDEDC, DB。

gmat数学考试内容

gmat数学考试内容gmat数学考什么，关于很多计划如何准备gmat考试的人来说，首先必须要了解的就是各科的gmat都考哪些内容，好借此来准备复习计划。

下面就带大家了解gmat数学考试内容。

gmat数学考试内容由于gmat针对的是〔MBA〕的申请者，而MBA的学习必须要较强的数学推理能力，所以gmat数学考试难度相关于GRE General 而言较难。

ETS所给出的数学考试大纲要求掌握以下知识：Arithmetic 算术Elementary Algebra 基本代数Commonly Known Concepts of Geometry 一般的几何概念Data Analysis 数据分析gmat数学部分的所有题目都以两种方式数学背景和日常生活背景给出，考查考生所具有的basic mathematical skill(基本数学技巧)、understanding of elementary mathconcept(基本数学概念的理解)以及ability to reason quantitatively and solve problems in quantitative setting(在数学环境中的数字推理和解题的能力)。

关于中国考生而言，gmat数学部分的考查内容大部分是中国初中数学所涉及的内容，所以并不构成太大困难。

但因其也会涉及少量统计学中的简单概念，强调数学概念在日常生活中的运用，并且以英文出题，所以中国考生须了解其考查特点，熟悉英文概念，掌握应试方法和技巧。

gmat数学考试方法边做题边做笔记每次考完gmat考试，很多人都会埋怨数学时间太紧，根本没有做完，而在实际的观察过程中也发现了这样的问题，很少有同学能够在读完一遍后就开始答题，而是要读两遍，三遍，甚至更多遍才干进行答题，这大大的降低了答题的速度，那么怎么才干解决gmat数学速度问题呢?办法只有一个边做题边记笔记。

减少回读提升审题效率谈到回读和反复读，原因很简单，当一道题目里面的信息量过大且相对复杂时，只读题不记笔记的结果就是读着后面的，忘着前面的，读完最后一句觉得条件不完整，于是又回到前面去找条件，如此往复多次后才干找全条件，开始做题。

(整理)新题型变更--GWD课堂笔记

GMAT语文听课笔记一、GMAT考试总论GMAT考试是美国商科研究生的入学考试，其目的是为了挑选符合商科入学标准的人才，所以GMAT考试不是一个英语语言能力的测试，而是一种逻辑思维方法的测试。

具体的来说，GMAT考试是在模拟商业环境，检验考生解决商业问题的能力。

商科是一门实践科学，商业的很多问题都是新的，因此解决新问题的能力是解决商业问题的最重要能力。

管老师提到，在商业中我们都不会追求完美而是做到必须要做的，不会追求充分而是用不充分性思维解决问题，不会问为什么(Why)而是着重于怎么做（How），不会追求复杂而是追求简单（把复杂问题简单化）。

二、GMAT考试的原则和套路原则是指根据考试规律总结出来的做题方法，套路是指根据某种出题形式总结出来的出题方法。

由于出题风格总是变化的，因此根据套路做题犯错的风险很大，近期从2008年4月以来，GMAC的出题风格变化非常大，可以说套路做题已经很难取得GMAT考试的成功了。

三、GMAT考试的原则总论1、做题的原则我们做题的过程就如同经理选择一个战略的过程，因此我们应该：步骤一、把肯定不对的选项去掉。

就像经理会有一些无法不遵守的原则，违背这些原则的方案一定不能选。

步骤二、比较剩下的选项，就算心中有答案的方向也要记住“答案是比出来的”。

2、接受信息的选择我们对信息要客观接受，可以归纳信息，可以客观的推理，但是一定不能主观推理。

比如，题目说“有个人他一拿着斧头上街就像杀人，他一杀人就会被枪毙，他一被枪毙他老婆就会改嫁。

”我们可以推理“他一拿斧头上街他老婆就会改嫁”，这是客观的，因为我们没有添加任何新的信息。

但是我们绝对不对推理为“他脑子进水了才拿斧头上街的吧”（你添加了新的题目没告诉的信息就成了主观推理）。

另外，题目告诉的信息是字面意思以及其前提的总和。

比如题目说“老管在喝水”，那么除了告诉我们“老管在喝水”这件事以外，我们还知道“老管是存在的”“水是存在的”“老管具有喝水的能力”。

GWD MATH错题集

GWD MA TH错题集1The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?A.56B.64C.68D.81E.100Answer: B2A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?A. 5B. 6C.9D.24E.36Answer: A3 If w and c are integers, is w > 0?(1) w + c > 50(2) c > 48A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E4 If n = 811– 8, what is the units digit of n?A. 0B. 1C. 4D. 6E. 8Answer: C5 Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?(1) She bought $4.40 worth of stamps.(2) She bought an equal number of $0.15 stamps and $0.29 stamps.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.AnswerA6 A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?A. 0B. 1/9C. 2/9D. 1/3E. 1Answer:C 3X2X1/3X3X37The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?A. 5½ ftB. 7½ ftC. 8 ½ ftD. 9½ ftE. 10 ftAnswer: B8 The operation ⊗ is defined for all nonzero numbers a and b by a ⊗ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?I. x ⊗ xy = x(1 ⊗ y)II. x ⊗ y = -(y ⊗ x)III. 1/x ⊗ 1/y = y ⊗ xA. I onlyB. II onlyC. III onlyD. I and IIE. II and IIIAnswer: E9 Is the sum of the integers x and y a prime number?(1) x is an even prime number.(2) y is a prime number between 10 and 20.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: E10 AMOUNT OF BACTERIA PRESENTData for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?A. 12.0B. 12.1C. 12.2D. 12.3E. 12.4Answer:A11 What is the remainder when the two digit, positive integer x is divided by 3?(1) The sum of the digits of x is 5.(2) The remainder when x is divided by 9 is 5.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer: D12In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?A. 16%B. 25%C. 32%D. 40%E. 52%Answer:B 0.64是E, 0.48是男&E,0.16是女&E,0.16/0.64是女&E在所有E的比例13How many seconds will it take for a car that is traveling at a constant rate of 45 miles per hour to travel a distance of 22 yards? (1 mile = 1,160 yards)A. 8B. 9C. 10D. 11E. 12Answer: C14Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?A. k/m %B. (k-m) %C. [100(k-m)]/(100+k) %D. [100(k-m)]/(100+m) %E. [100(k-m)]/(100+k+m) %Answer: D假设前年Price per share =x, 前年earning per share =y 那么去年的price per share 为（1＋k％）x，去年的earning per share 为（1＋m％）y 求去年的price per share 与earningper share的比率比前年的比率增加了多少。

GMAT一战760分经验分享

GMAT一战760分经历分享GMAT一战760分经历分享1. GMAT是什么(针对初学者)刚接触GMAT的时候我其实很懵，不知道CR, RC, SC, IR, AWA这些都是啥，看着这些简写真的挺手足无措。

于是我想先来科普一下，GMAT大概是个啥玩意。

GMAT总分值800，考试的流程是：首先是两个不计入总分的局部：先一篇AWA(作文)时间为30分钟，总分值6分;再是Integrated Reasoning (IR) 12道题目30分钟，总分值8分IR局部完毕后，你可以选择进入8分钟(还是7分钟来着)的休息，当然也可以不休息，直接进入计分局部的考试。

计分局部：先是数学(Q)37题75分钟，题型两种：DS(data suficiency)和PS(problem solving)数学完毕后又是一个可选的休息时间。

然后是语文(Verbal)41题75分钟，题型有三种：阅读(Reading Comprehension), 逻辑(Critical reasoning)，语法(sentence correction)需要注意的是，数学和语文的题目都是分题型，但是考试的时候不同类型的题目是随机交替出现的，理论上是不会有做完一种题型再考第二种题型这样的情况。

另外，GMAT考试是CAT形式也就是自适应性质的.，所以不存在托福考试那样提交一道题之后还可以回头更改答案的做法，并且前一题的正确与否会影响到你下一道题的难度。

2.我的背景简介(学生党，两个半月)2023年2月开场准备，4月中旬考试。

大概是两个半月的准备时间，3月开学之后除了上课之外都在复习GMAT。

托福100+之前在论坛上看过一些帖子有说过，要看那些条件和你差不多的人是怎么备考的。

很赞同。

比方我并没有方法全职复习，所以全职复习且复习时间很久的牛牛们的时间安排啊什么的对我而言就没有太大的参考价值。

同样的，建议各位看经历尤其是复习进度安排的时候，要考虑对方的方法对你到底是否适用。

GMATGWD数学部分考试复习资料

Math Section------------------------------------------------------------------------------------------------------------ Q1:If x2 = 4 and y2 =7, then x6–y4 =A.33B.25C.15D.-3E.-33Answer:------------------------------------------------------------------------------------------------------------ Q2:There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?A. 120B. 720C.1,060D.1,520E.1,980Answer:------------------------------------------------------------------------------------------------------------ Q3:If p, s, and t are positive prime numbers, what is the value of p3s3t3 ?(1) p3st = 728(2) t = 13A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q4:If x and y are integers, what is the value of 2x6y- 4 ?(1) x2y = 16(2) xy = 4A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q5:A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department ?(1) The numbers of pens, pencils, and pads that each staff member received were inthe ratio 2 : 3 : 4, respectively.(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q6:The function f is defined for each positive three-digit integer n by f (n ) = 2x 3y 5z , where x , y and z are the hundreds, tens, and units digits of n , respectively. If m and v are three-digit positive integers such that f (m ) = 9 f (v ), then m - v =A. 8B. 9C. 18D. 20E. 80Answer:------------------------------------------------------------------------------------------------------------ Q7:If N = 31 + 231 + 331, then N is betweenA. 0 and 91B. 91 and 31C. 31 and 98D. 98 and 34E. 34and 2Answer:------------------------------------------------------------------------------------------------------------ Q8:A cash register in a certain clothing store is the same distance from two dressing rooms in the store. If the distance between the two dressing rooms is 16 feet, which of the following could be the distance between the cash register and either dressing room?I. 6 feetII. 12 feetIII. 24 feetA. I onlyB. II onlyC. III onlyD. I and IIE. II and IIIAnswer:------------------------------------------------------------------------------------------------------------ Q9:Is x < 0 ?(1) x3 < x2(2) x3 < x4A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q10:A rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $12 apiece, what is the total cost for the number of carpet squares needed to cover the floor?A.$200B.$240C.$480D.$960E.$1,920Answer:------------------------------------------------------------------------------------------------------------ Q11:In the sequence 1, 2, 4, 8, 16, 32, …, each t erm after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence ?A.218B.3(217)C.7(216)D.3(216)E.7(215)Answer:------------------------------------------------------------------------------------------------------------ Q12:Some computers at a certain company are Brand X and the rest are Brand Y. If the ratio of the number of Brand Y computers to the number of Brand X computers at the company is 5 to 6, how many of the computers are Brand Y ?(1) There are 80 more Brand X computers than Brand Y computers at the company. (2) There is a total of 880 computers at the company.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q13:Each of 20 parents chose one of five days from Monday through Friday to attend parent-teacher conferences. If more parents chose Monday than Tuesday, did at least one of the parents choose Friday?(1) None of the five days was chosen by more than 5 parents. (2) More parents chose Monday than Wednesday.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q14:A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 250 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?A. 280B. 290C. 300D. 310E. 320Answer:------------------------------------------------------------------------------------------------------------ Q15:If R = QP, is R ≤ P ?(1) P > 50 (2) 0 < Q ≤ 20A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q16:If 2, x, y, and z are different positive integers whose average (arithmetic mean) is 10, what is the greatest possible value of z ?A.10B.24C.34D.36E.40Answer:QX:If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?A.8B.10C.20D.28E.30Answer:------------------------------------------------------------------------------------------------------------ Q17:Which of the following is closest to 10180– 1030 ?A.10210B.10180C.10150D.1090E.106Answer:------------------------------------------------------------------------------------------------------------ Q18:A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m +d ?A.16%B.32%C.48%D.84%E.92%Answer:------------------------------------------------------------------------------------------------------------ Q19:If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?A.141B.200C.318D.391E.412Answer:------------------------------------------------------------------------------------------------------------ Q20:Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?(1) Last year 12 of the 30 businesses reported a net profit and had investments inforeign markets.(2) Last year 24 of the 30 businesses reported a net profit or invested in foreignmarkets, or both.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q21:y––––●xO–P–––In the figure shown, the circle has center O and radius 50, and point P has coordinates (50,0). If point Q (not shown) is on the circle, what is the length of line segment PQ ?(1) The x-coordinate of point Q is – 30.(2) The y-coordinate of point Q is – 40.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q22:If –2x > 3y, is x negative?(1) y > 0(2) 2x + 5y– 20 = 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q23:The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?A.14B.15C.16D.28E.29Answer:------------------------------------------------------------------------------------------------------------ Q24:The positive numbers w, x, y, and z are such that x is 20 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?A.15.2%B.16.0%C.20.0%D.23.2%E.24.8%Answer:------------------------------------------------------------------------------------------------------------ Q25:Machine M processes a certain chemical product at a constant rate. Does machine M process the product at a rate that is greater than 25 grams per second? (1 kilogram =1,000 grams)(1) Machine M processes the product at a rate that is greater than 92 kilograms perhour.(2) Machine M processes the product at a rate that is less than 95 kilograms per hour.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q26:Is –7 < y < 10 ?(1) y > -6 (2) y < 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q27:If k is an integer and (0.0025)(0.025)(0.00025) × 10k is an integer, what is the least possible value of k ?A. -12B. -6C. 0D. 6E. 12Answer:------------------------------------------------------------------------------------------------------------ Q28:Jacob purchased 100 boxes of oranges at $8.00 per box. He sold 8 of the boxes at $4.00 per box to Company A , and he sold the rest of the boxes at x dollars per box to Company B . If Jacob’s profit from the purchase and sale of the 100 boxes of oranges was $336.00, at what price per box did he sell the boxes to Company B ?A. $11.36B. $11.60C. $12.00D. $12.35E. $12.90Answer:------------------------------------------------------------------------------------------------------------ Q29:A sum of money was divided between John and Anne such that the ratio of John’s shareto Ann e’s share was 5 to 3. If John’s share exceeded 95of the sum of money by $50,what was Anne’s share?A. $180B. $270C. $340D. $450Answer:------------------------------------------------------------------------------------------------------------ Q30:From May 1 to May 30 in the same year, the balance in a checking account increased. What was the balance in the checking account on May 30 ?(1) If, during this period of time, the increase in the balance in the checking accounthad been 12 percent, then the balance in the account on May 30 would have been $504.(2) During this period of time, the increase in the balance in the checking accountwas 8 percent.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q31:In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?A.4B. 3C. 2Answer:------------------------------------------------------------------------------------------------------------ Q32:What is the probability that event E or event F or both will occur?(1) The probability that event E will occur is 0.6.(2) The probability that event F will occur is 0.4.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:QX:If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?0.22A.0.32B.0.37D. 0.63Answer:------------------------------------------------------------------------------------------------------------ Q33:If Diana’s stamp collection, 54 of the stamps are Canadian, and 73of the Canadianstamps were issued before 1940. If 192 stamps in Diana’s collection are Canadian stamps that were issued in 1940 or later, how many stamps in her collection are not Canadian?A. 84B. 88C. 96D. 104E. 112Answer:------------------------------------------------------------------------------------------------------------ Q34:If a rectangular room measures 10 meters by 6 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter = 100 centimeters)A. 24,000B. 240,000C. 2,400,000D. 24,000,000E. 240,000,000Answer:------------------------------------------------------------------------------------------------------------ Q35:For a certain car repair, the total charge consisted of a charge for parts, a charge for labor, and a 6 percent sales tax on both the charge for parts and the charge for labor. If thecharge for parts, excluding sales tax, was $50.00, what was the total charge for the repair?(1) The sales tax on the charge for labor was $9.60. (2) The total sales tax was $12.60.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q36:If x and y are integers, is y an even integer?(1) 2y – x = x 2 – y 2 (2) x is an odd integer.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q37:For any number x , ⎣⎦x denotes the greatest integer less than or equal to x . What is thevalue of ⎥⎦⎥⎢⎣⎢-410?A. 0B. –1C. –2D. –3E. –4Answer:------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ Answers:CEAAE, DCECB, EDABE, C(D )BDCD, ADBAA, CECBC, CE(B )AED, ADF. MATH---------------------------------------------------------------------------------------------------------------------- Q1:If Henry were to add 5 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?A. 25B. 40C. 64D. 80E. 96Answer:---------------------------------------------------------------------------------------------------------------------- Q2:The function f is defined for each positive three-digit integer n by f(n) = 2x 3y 5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m) = 9f(v), then m-v = ?A. 8B. 9C. 18D. 20E. 80Answer:----------------------------------------------------------------------------------------------------------------------Q3:At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52?A. 1B. 2C. 3D. 4E. 5Answer:----------------------------------------------------------------------------------------------------------------------Q4:Professor Vasquez gave a quiz to two classes. Was the range of scores for the first class equal to the range of scores for the second class?(1) In each class, the number of students taking the quiz was 26, and the lowestscore in each class was 70.(2) In each class, the average (arithmetic mean) score on the quiz was 85.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:----------------------------------------------------------------------------------------------------------------------Q5:If x and y are positive integers, what is the value of x?(1) 3x5y = 1,125(2) y = 3A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:----------------------------------------------------------------------------------------------------------------------Q6:If ∣d - 9∣ = 2d, then d =A. -9B. -3C. 1D. 3E. 9Answer:----------------------------------------------------------------------------------------------------------------------Q7:There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?A. 120B. 720C. 1,060D. 1,520E. 1,980Answer:----------------------------------------------------------------------------------------------------------------------Q8:In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18√2, then what is the perimeter of each square?A. 8√2B. 12C. 12√2D. 16E. 18Answer:----------------------------------------------------------------------------------------------------------------------Q9:Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?(1) T wo of the interior angles of ABCD are right angles.(2) The degree measure of angle ABC is twice the degree measure of angleBCD.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:----------------------------------------------------------------------------------------------------------------------Q10:$10,000 is deposited in a certain account that pays r percent annual interest compounded annually, the amount D(t), in dollars, that the deposit will grow to in t years is given by D(t) = 10,000 {1+(r/100)}t . What amount will the deposit grow to in 3 years?(1) D (t) = 11,000 (2) r =10A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer:---------------------------------------------------------------------------------------------------------------------- Q11:If a and b are integers, is b even?(1) 3a + 4b is even. (2) 3a + 5b is even.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer:---------------------------------------------------------------------------------------------------------------------- Q12:Working alone at its constant rate, machine K took 3 hours to produce 41of the unitsproduced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M , working alone at its constant rate, to produce all of the units produced last Friday?A. 8B. 12C. 16D. 24E. 30Answer:------------------------------------------------------------------------------------------------------------ Q13:If x + y is an integer, is y an integer?(1) x–y is an integer.(2) x + 2y is an integer.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q14:A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and a k = a k-1 + 2a k-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?A. 32B. 43C. 64D. 100E. 128Answer:----------------------------------------------------------------------------------------------------------------------Q15:At a certain bookstore, the regular price of each book is 20 percent less than its list price. If during a sale the price of each book at the store was 15 percent less than its regular price, then the price of a book during the sale was what percent less than its list price?A. 30%B. 32%C. 35%D. 38%E. 40%Answer:----------------------------------------------------------------------------------------------------------------------Q16:What is the value of the ratio of x to y2?(1) T he ratio of x2 to y is 5/3.(2) The ratio of x to 1 is 5/3.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:。

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Math Section------------------------------------------------------------------------------------------------------------Q1:A family-size box of cereal contains more cereal and costs more than the regular-size box of cereal. What is the cost per ounce of the family-size box of cereal?(1) The family-size box of cereal contains 10 ounces more than the regular-size box ofcereal.(2) The family-size box of cereal costs $5.40.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q2:A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?A. 0B. 1/9C. 2/9D. 1/3E. 1Answer:------------------------------------------------------------------------------------------------------------Q3:If x and y are positive, is 4x > 3y?(1) x > y - x(2) x/y < 1A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q4:If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2k is a factor of n?A. 10B. 12C. 15D. 18E. 20Answer:------------------------------------------------------------------------------------------------------------Q5:Is x > k?(1) 2x • 2k = 4(2) 9x • 3k = 81A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q6:If x and y are positive, what is the value of x – y?(1) (x2 – y2) / (x + y) = 4(2) x + y= 7A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q7:A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?A. 5/12B. 2/5C. 1/2D. 3/4E. 5/6Answer:------------------------------------------------------------------------------------------------------------Q8:In 1997 there were 300 female employ ees at Company C. If the number of female employees at Company C increased by 60 percent from 1977 to 1987, by what percent did the number of female employees at Company C increase from 1987 to 1997?(1) From 1977 to 1997 the number of female employees increased by 200 percent atCompany C.(2) In 1977 there were 100 female employees at Company C.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q9:A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?A. 1/12B. 1/6C. 1/5D. 1/3E. 1/2Answer:------------------------------------------------------------------------------------------------------------Q10:A set of numbers has the property that for any number t in the set, t + 2 is in the set. If –1 is in the set, which of the following must also be in the set?I. -3II. 1III. 5A. I onlyB. II onlyC. I and II onlyD. II and III onlyE. I, II, and IIIAnswer:------------------------------------------------------------------------------------------------------------Q11:In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fract ion of the employees in the corporation are females?A. 3/5B. 2/3C. 3/4D. 4/5E. 5/6Answer:------------------------------------------------------------------------------------------------------------Q12:If n is an integer and 2 < n < 6, what is the value of n?(1) n is a factor of 15.(2) n is a factor of 21.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q13:If x and y are positive, is 3x > 7y?(1) x > y + 4(2) -5x < -14yA. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q14:If 1050– 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?A. 424B. 433C. 440D. 449E. 467Answer:------------------------------------------------------------------------------------------------------------Q15:Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid 2/5 of the total amount, Carol paid $17, and Judy paid the rest, what fraction of the total amount did Judy pay?A. 2/9B. 14/45C. 1/3D. 2/5E. 7/15Answer:------------------------------------------------------------------------------------------------------------Q16:If J, S, and V are points on the number line, what is the distance between S and V?(1) The distance between J and S is 20.(2) The distance between J and V is 25.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q17:In T own X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?A. 16%B. 25%C. 32%D. 40%E. 52%Answer:------------------------------------------------------------------------------------------------------------Q18:The figure shows a square patio surrounded by a walkway of width x meters. If the area of thewalkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?A. 56B. 64C. 68D. 81E. 100Answer:------------------------------------------------------------------------------------------------------------Q19:A total of $60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?(1) x = (3/4) y(2) The ratio of the amount that earned interest at the rate of x percent per year to theamount that earned interest at the rate of y percent per year was 3 to 2.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q20:If x > 0, t hen 1/[√(2x)+√x] =A. 1/√(3x)B. 1/[2√(2x)]C. 1/(x√2)D. (√2-1)/√xE. (1+√2)/√xAnswer:------------------------------------------------------------------------------------------------------------Q21:When Leo imported a certain item, he made a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?A. $1,600B. $1,850C. $2,250D. $2,400E. $2,750Answer:------------------------------------------------------------------------------------------------------------Q22:In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?A. 218B. 3(217)C. 7(216)D. 3(216)E. 7(215)Answer:------------------------------------------------------------------------------------------------------------Q23:In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r2 + s2?(1) The circle has radius 2.(2) The point (√2, -√2) lies on the circle.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q24:If w and c are integers, is w > 0?(1) w + c > 50(2) c > 48A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q25:A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?A. 5B. 6C. 9D. 24E. 36Answer:------------------------------------------------------------------------------------------------------------Q26:Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?A. 4B. 6C. 8D. 10E. 12Answer:------------------------------------------------------------------------------------------------------------Q27:If n = 811– 8, what is the units digit of n?A. 0B. 1C. 4D. 6E. 8Answer:------------------------------------------------------------------------------------------------------------Q28:For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2. What is the sum of all the even integers between 99 and 301?A. 10,100B. 20,200C. 22,650D. 40,200E. 45,150Answer:------------------------------------------------------------------------------------------------------------Q29:June 25, 1982, fell on a Friday. On which day of the week did June 25, 1987, f all? (Note: 1984 was a leap year.)A. SundayB. MondayC. TuesdayD. WednesdayE. ThursdayAnswer:------------------------------------------------------------------------------------------------------------Q30:Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?(1) She bought $4.40 worth of stamps.(2) She bought an equal number of $0.15 stamps and $0.29 stamps.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q31:A positive integer n is said to be “prime-saturated” if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two-digit prime-saturated integer?A. 99B. 98C. 97D. 96E. 95Answer:------------------------------------------------------------------------------------------------------------Q32:For a convention, a hotel charges a daily room rate of $120 for 1 pers on and x dollars for each additional person. What is the charge for each additional person?(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 morethan the corresponding cost for 4 people.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q33:Is xy > x/y?(1) xy > 0(2) y < 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q34:The function f is defined by f(x) = - 1/x for all nonzero numbers x. If f(a) = - 1/2 and f(ab) = 1/6, then b =A. 3B. 1/3C. - 1/3D. -3E. –12Answer:------------------------------------------------------------------------------------------------------------Q35:What is the median number of employees assigned per project for the projects at Company Z?(1) 25 percent of the projects at Company Z have 4 or more employees assigned to eachproject.(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to eachproject.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q36:Each signal that a certain ship can make is comprised of 3 different flags hanging vertically in a particular order. How many unique signals can be made by using 4 different flags?A. 10B. 12C. 20D. 24E. 36Answer:------------------------------------------------------------------------------------------------------------Q37:A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow. If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?A. 3/64B. 1/20C. 1/16D. 1/12E. 1/8Answer:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------。