新GRE数学电子讲义 2.docxVIP

第一章算术integer (whole number): 整数* positive integer：正整数，从1开始，不包括0。odd even number 奇数与偶数奇+奇=偶，奇+偶=奇…若干个整数相乘，除非都是奇数，其乘积才会是奇数…例：若a2+b2=c2,其中a,b,c为整数，下面哪个不能是a+b+c的值？(A)2 (B)1 (C)－2 (D) 4 (E) 6例：若a-b是偶数，a/b是偶数，下面那一个选项一定是奇数？(A) a/2 (B) (a-b)/2 (C) (a+b)/2 (D) (a+2)/2 (E) b/23.prime number composite number 质数与合数*A prime number is a positive integer that has exactly two different positive divisors,1 and itself. A composite number is a positive integer greater than 1 that has more than two divisors. * The numbers 1 is neither prime nor composite, 2 is the only even prime number.factor(divisor) prime factor因子和质因子* 一个数能被哪些数整除，这些数就叫它的因子（因数、约数）。* 因子里的质数叫质因子（数）。例1： If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?2 (B) 3 (C) 4 (D) 6 (E) 8例2： 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例3：What is the greatest prime factor of 2100 - 296? (A) 2 (B) 3 (C) 5 (D) 7 (E) 11例4：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) 99 (B) 98 (C) 97 (D) 96 (E) 95the greatest common divisor (GCD) the least common multiple(LCM) 最大公约数和最小公倍数例：If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M? 600 (B)700 (C) 900 (D) 2,100 (E) 4,900例：下面选项中哪一个是最小的能被1~7都整除的正整数？420 (B)210 (C) 840 (D)630 (E) 700decimals fractions 小数和分数*相关词汇：reaccuring decimal ; terminating decimal ; numerator ; denominator ; improper fracion ; mixed number *整数位与分位：后面加s的是整数位（小数点前面的某位），加th或ths的是分位（小数点后面的某位），如tens是十位数，而tenth是十分位*What is the fractional part of ….这样的表达法意为“谁的几分之几”*小数和分数的互相转换：例1： 0．373737…=? (将其转换成一个分数)例2：Which of the following fractions has a decimal equivalent that