GMAT强化数学一.ppt

1、GMAT强化数学,s,中国考生平均分600 数学平均分 中国50 / 美国29 语文平均分 中国24 / 美国35 思维,GMAT,210min Writing 1 hour Maths 75 min Verbal 75 min 每个part之间休息5min 加上一些考前考后的流程 约四小时,GMAT数学题型介绍,75min 37题 Problem solving 21-22 Data sufficiency 16-17,Problem Solving & Data Sufficiency,PS：五选一,1.录取范围少于5人，x(30-5)=25 2.x27,25x27,*. If 4x-2y

2、=8,what is the value of 2x-y? (A) 3 (B) 4 (C) 5 (D) 6 (E) 8,* If the product of three consecutive integers is equal to the middle integer, what is the LEAST of the three integers? (A) 2 (B) 1 (C) 0 (D) -1 (E) -2,1. 从选项推断,乘积,连续数,整数,* If k is an integer and ,what is the greatest possible value of k? (

3、A) 6 (B) 7 (C) 8 (D) 9 (E) 10,2. 一般挑选中间选项先验算,A,B,C,m, n, k are positive integers. Which of the following numbers belongs in the set represented by the shaded region? (A) 2 (B) 4 (C) 10 (D) 25 (E) 100,3. 用排除法,Problem Solving & Data Sufficiency,DS：logic,A ONLY(1) B ONLY(2) C TOGETHER D EACH E TOGETHER

4、 NOT,单独（1）：a=3 or a=-4 单独（2）：a=2 or a=-2 结合起来仍然不行,Tips： 强调的是给出的信息是否足够回答问题，不需要花大把时间去解题！,Eg：求x值 60+40+2x=180 知道能求出x即可,设 the number of hours budgeted for the job 为 x, the actual number of hours used for the job 为 y： （1）x + y = 140 （2）y x = 8,c,答案唯一性原则,官方说法： In data sufficiency problems that ask for the

5、 value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.,1. x = 1 or x = -1,1. x = 1 or x = -2,结合（1）和（2）得出 x = 1,C,1. t2 + 8t = -8 x 2,( t + 4)2 = 0,2. t2 = 4,t = -4,t = 2 or t = -2,A,答案充分性原则,回答yes是回答，回答

6、no也是回答 E.g.: Is x equal to 1? (1) x2=1 (2) x2 x 2 = 0,1. x = 1 or x = -1,1. x = 2 or x = -1,1 不一定等于一，根据答案的唯一性原则，不能够回答问题,2 一定不等于答案是no也可以,B,条件独立性原则,Answer the question not solve the problem 前例： （1）x = 1 or -1 （2）x = -1 or 2 综合可得 x = -1 则选C,在考虑一个条件时不应受另一个条件的影响，如果一个条件已经能够独立回答问题，就不必再联合起来求解 选C之前应该仔细考虑是否可以

7、选择A或B。,If the units digit of integer n is greater than 2, what is the units digit of n ? (1) The units digit of n is the same as the units digit of n2. (2) The units digit of n is the same as the units digit of n3. E,What is the value of the integer p ? (1) Each of the integers 2, 3, and 5 is a fact

8、or of p. (2) Each of the integers 2, 5, and 7 is a factor of p. E,How old is Jim? (1)Eight years ago Jim was half as old as he is now. (2)Four years from now Jim will be twice as old as he was six years ago. D,Is the positive integer n equal to the square of an integer? (1)For every prime number p .

9、If p is a divisor of n, then so is p2. (2)n(1/2) is an integer. B,If x and y are positive integers and x is a multiple of y, is y=2? (1)y1 (2)x+2 is a multiple of y. E,If x and y are integers between 10 and 99.inclusive,is (x-y)/9 an integer? (1)x and y have the same two digits, but in reverse order

10、. (2)The tens digit of x is 2 more than the units digit, and tens digit of y is 2 less than the units digit.,A,Pam and Ed are in a line to purchase tickets. How many people are in the line? (1)There are 20 people behind Pam and 20 people in front of Ed. (2)There are 5 people between Pam and Ed.,E,In

11、 City X last April, was the average (arithmetic mean) daily high temperature greater than the median daily high temperature? (1) In City X last April, the sum of the 30 daily high temperatures was 2,160. (2) In City X last April, 60 percent of the daily high temperatures were less than the average d

12、aily high temperature. B,Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January? (1) More of the people in the auditorium have their birthday in February than in March. (2) Five of

13、the people have their birthday in March D,arithmetic,一、 基本数论和运算 二、 分数（小数，百分数）相关问题 三、 集合相关问题 四、 幂次运算,arithmetic,一 整数相关问题 重点词汇 Integer Odd number Even number Prime number Composite number Positive number Negative number Multiple Factor/divisor,arithmetic 算术,Perfect square Perfect cube Remainder Consec

14、utive integers A plus B/the sum of A and B A minus B/the difference of A and B A multiplied by B/the product of A and B A divided by B/the quotient of A and B,Symbols,= is equal to is not equal to is less than is less than or equal to is greater than Is greater than or equal to is parallel to Is app

15、roximately equal to is approximately Is perpendicular to I I Absolute value Square root % Percent a/b Ratio of a to b or,Addition Positive + Positive = Positive Negative + Negative = Negative Negative + Positive = either positive or negative Subtraction The definition of subtraction is: A - B = A +

16、(-B) A minus B is the same as A plus (the opposite of B) Multiplication and division Positive x Positive = Positive Negative x Negative = Positive Negative x Positive = Negative,real number 实数 rational number 有理数 Irrational number 无理数 Integer 整数 fraction 分数,composite number合数e.g.4,6,8,9,10,12,14,15

17、prime number质数e.g.2,3,5,7,11,13,15 NOTE: 1 is not a prime number, and both the smallest and the only even prime number is 2 Round off 四舍五入 Expression: Rounding off xxx to the nearest x,consecutive integers x, x+1, x+2, Consecutive even integers Consecutive odd integers E.g.: find two consecutive int

18、egers whose sum is 71.,the rules of divisibility,1. Numbers divisible by 2 end in even numbers. 2. Numbers divisible by 3 can be determined by adding the sum of their digits and checking if that number is divisible by 3 (for example the number 123: 1+2+3=6, 6 is divisible by 3 with no remainder). 3.

19、 The number a（10） is divisible by both x（5） and y（2）.a can be divided by both of these integers without leaving a remainder.,4. Numbers divisible by 4 can be identified if their last two digits will divide by 4 without a remainder (for example, the number 624: the last two digits are 24, which are d

20、ivisible by 4 with no remainder). 5. Numbers divisible by 9 occur when the sum of its their digits are divisible by 9 (for example, the number 639: 6+3+9 = 18, which is divisible by 9). 6. A number is only divisible by 10 if it ends in 0. Numbers divisible by 5 end only in 5 or 0.,If x is an even in

21、teger, which of the following is an odd integer? A 3x+2 B 7x C 8x+5 D x2 E x3,Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two? (A) 90 (B) 82 (C) 80 (D) 45 (E) 36,What is the greatest prime factor

22、 of 2100296? (A) 2 (B) 3 (C) 5 (D) 7 (E) 11,Three consecutive integers are listed in increasing order. If their sum is 102,what is the second integer is the list? A 28 B 29 C 33 D 34 E 35,If y is not 3 and 3x/y is a prime integer greater than 2,which of the following must be true? I x=y II y=1 III x

23、 and y are prime integers. A None B I only C II only D III only E I and III,n=795 The number of distinct positive factors of n,Since n=7(32)5 Then (1+1)(10+1)=2214,If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n? （A） 2 (B) 3 (C) 4

24、 (D) 6 (E) 8,If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n2 have? (A) 4 (B) 5 (C) 6 (D) 8 (E) 9,If n is an integer greater than 6, which of the following must be divisible by 3? A n(n+1)(n-4) B n(n+2)(n-1) C n(n+3)(n-5) D n(n+4)(n-2) E n(n

25、+5)(n-6),If n and k are integers whose products is 400. which of the following statements must be true? A n+k 0 B n=/=k C either n or k is a multiple of 10 D if n is even, then k is odd E if n is off, then k is even,If （a+3/5）is an integer, what is the remainder when a is divided by 5 ? 1 (B) 2 (C)

26、3 (D) 4 (E) It cannot be determined from the information given.,In the correctly worked out addition problem at the right, each letter represents a different digit. What is the value of C? (A) 5 (B) 6 (C) 7 （D) 8 (E) 9,A positive integer n is said to be “prime-saturated” if the product of all the di

27、fferent positive prime factors of n is less than the square root of n. What is the greatest two-digit prime-saturated integer? (A) 99 (B) 98 (C) 97 (D) 96 (E) 95,最佳饱和数,Each of the following numbers has two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an

28、 integer?(A)25,06(B)50,26(C)56,02(D)62,50(E)65,20,能被4整除的数，后两位一定能被4整除 24*X然后再看后结果两位数，太麻烦,One month Mary used 1/6 of her monthly salary for a car payment and more than the car payment for rent. What fraction of her monthly salary did Mary use that month for the car payment and rent combined? A 5/24 B 3/8 C 5/12 D E 7/12,If United States imports increased 20 percent and exports decreased 10 percent during a certain year, the ratio of imports to exports at the end of the year was how many times the ratio at the be