GRE 数学满分攻略

Arithmetic
If n is an odd integer, then n2-1 must be (A) a prime number (B) an odd integer (C) divisible by 8 (D) a multiple of 2n (E) a positive integer
• 计算错误
课程结构
Arithmetic
• Integers, whole number • Positive/ negative • A multiple of • Even integer = integers that are multiples of 2 • Odd integer • Consecutive integers • composite • Prime
5602?d6250?e652024x能被24整除能被4整除自然数n次幂的尾数特征?尾数为2的数的幂的个位数以2468循环?尾数为3的数的幂的个位数以3971循环?尾数为4的数的幂的个位数以46循环?尾数为7的数的幂的个位数以7931循环?尾数为8的数的幂的个位数以8426循环?尾数为9的数的幂的个位数以91循环arithmeticifnisanoddintegerthenn21mustbeaaprimenumberbanoddintegercdivisibleby8damultipleof2neapositiveinteger设n2k1则n214kk1kamp
(最小)公分母 四分之一 无穷小数 有限小数 循环小数 四舍五入 数字 近似
6 5选1
4
4或更多选2或更 多
2 无选项
Quantitative Comparison Questions 比较大小题
• Column A X>Z,Y>Z
X+Y
Column B Z
(A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined
Arithmetic
If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M ?
(A) 600 (B) 700 (C) 900 (D) 2,100 (E) 4,900
A 26
26=132
B 28
28=142
C 36
36=182
D 56
5 6 = 2 82 = 1 44
E 58
余数 remainder
Arithmetic
牢记：
，表示 y 除以 x，商是 k，余数是 b.
Arithmetic
n=7*a + 3 n为偶数 a 是奇数 a=2b+1 其中b为任意整数 n=7*(2b+1)+3 = 14*b+10
B
-7
C
6
D
8
Numeric Entry Questions-填空题
1. A merchant made a profit of ＄5 on the sale of a coat that cost the merchant ＄15.What is the profit expressed as a percent of the merchant’s cost? Give your answer to the nearest whole percent. ％
• Odd and Even (奇偶性) • （1）n 为整数，则2n 为偶数，2n+1为奇数 • （2）奇数个奇数相加减，结果为奇数 • （3）偶数个奇数相加减，结果为偶数 • （4）奇数和偶数相加减，结果为奇数 • （5）任意多个偶数相加减，结果为偶数 • 求最小公倍数和最大公约数：分解质因数 • 会表示连续的整数，奇数，偶数
设n=2k+1 则n2-1= 4k*（k+1） k&k+1是一对连续数，一定是2的倍数
Arithmetic
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be
C
Arithmetic
2. The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 21st of September 1990?
A. Monday B. Tuesday C. Wednesday D. Thursday E. Friday
2. Rectangle R has length 30 and width 10, and square S has length 5. The perimeter of S is what fraction of the perimeter of R?
4. 常见错误
• 英文理解能力差 -专业词汇
真分数 假分数 带分数 普通分数 简分数 繁分数 分子 分母
(least)common denominator quarter infinite decimal terminating decimal recurring decimal round to the nearest digital approximate
if S equals N times P and S is a
A
B
C
digit?
D
E
0.0000S 0.000S
0.00S
0.0S
0.S
Multiple-choice Questions 多项选择题（3~12个选项）
• Which two of the following numbers have a product that is greater than 60? -A9
• digit
positive
• integer
negative
• odd even factor
• prime
decimal
• fraction divisible
• multiple successive
常见数学表达
in terms of X : 用X表示 the ratio of a to b ：a：b Twice as many A as B : A=2B 运算中“is”代表“等于”，“of”代表“乘以” 2/3 of 1/2 of what number is 4?
除:1264 能被9整除的数：各位数字和能被9整除
• Each of the following numbers has two digits blotted out. Which of the number could be the numbers of hours in x days, where x is an integer?
1987.9.19 Saturday
365/7余1, 366/7余2
ordinary year : 365 Leap year: 366
1990.9.21 ?
1987----1990： 87-88 2 days 88-89 1 day 89-90 1 day
19-----21： 2 days
6 days shift
Fraction & Decimal
proper fraction improper fraction mixed number common/vulgar fraction simple fraction complex fraction numerator denominator
Arithmetic
A 12
B 24 C 36
24=23 3
D 72
108=22 33
Answer: A,C
n2=2434 n=22 32
What is the least positive integer that is not a factor of 25! and is not a prime number?
from the information given.
Multiple-choice Questions — 单选
1 = 0.0 N x
题
1 = 0 .0 0 P
y
The fractions can be written as
decimals as shown above, where N
and P represent different 1 digits. Which of the following isx ey qual to
Arithmetic
3. If s and t are positive integers such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(A) 2 (B) 4 (C) 8 (D) 20 (E) 45
• A. 23■,■06
• B. 50■,■26 • C. 56■,■02 • D.62■,■50
24x
能被24整除
• E.65■,■20
能被4整除
自然数n次幂的尾数特征
• 尾数为2的数的幂的个位数以2，4，6，8循环 • 尾数为3的数的幂的个位数以3，9，7，1循环 • 尾数为4的数的幂的个位数以4，6循环 • 尾数为7的数的幂的个位数以7，9，3，1循环 • 尾数为8的数的幂的个位数以8，4，2，6循环 • 尾数为9的数的幂的个位数以9，1循环
GRE 数学
1.GRE数学考试形式： 2 sections (不考虑加试) 35 minutes for each section 20 questions for each section
分数区间: 130 — 170
2.GRE数学题型及分布
题型
数值比较大小 单选
多选
计算填空
题量 选项设置
8 4选1
14
3 1 5 03 2 5 2 2 7
Arithmetic
How many factors does 360 have?
(A) 24 (B) 36 (C) 48 (D) 120 (E) 360
36023325
因子数公式
ax by cz (x 1)( y 1)(z1)
10000a+1000b+100c+10d+e 10000e+1000d+100c+10b+a 9999a+990b-990d-9999e
Vertex (pl. vertices) Quadrilateral/ Pentagon/ Hexagon/ Heptagon/ Octagon/ Nonagon/Decagon - 数学表达 The ratio of A to B A is twice as much as B/ There is twice as much A as B
连续的整数：a，a+1，a+2….
3 6 22,32
9 0 2,32,5
GCD,最大取最小 232 18 LCM,最小取最大 22325180
• 整除特性： 能被2整除的数：末位是0，2，4，6，8的 能被3整除的数：各位数字和能被3整除 能被4整除的数：末尾的两位数能被4整除：
232 能被5整除的数：末位是0或5 能被6整除的数：能被2和3整除的 能被8整除的数：末尾的三位数能被8整
90 2 32 5 196 22 72 300 22 3 52
L C M ( 9 0 ,1 9 6 ,3 0 0 ) 2 2 3 2 5 2 7 2
去 掉 1 0 （ 02 2,5 2),则 剩 下 3 ,3 ,7 ,7 选 项 分 别 为 6,7,9,21 ,49
Let S be the set of all positive integers n such that n2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ? Indicate all such integers.
On a certain number line, if -7 is a distance 4 from n and 7 is a distance of 18 from n, then n=?
a distance 4=a distance of 4
• 思维不严谨 -The probability of the occurrence of matter A is 0.6 while that of matter B is 0.7, what ‘s the probability of the coincidence of A and B? -小于100的整数中有多少可被6整除?