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GMAT数学题型分享：
Information required (Introduction or Background)
Question
Two statements labeled (1) and (2)
Option:
(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) Statement (1) and (2) TOGETHER are NOT sufficient.
【答题步骤】
1.分析问句类型
数值计算——特殊疑问句 (Special Question).
判断是非——一般疑问句 (General Question).
2.分析什么是充分与不充分
特殊疑问句——答案：唯一确定实数解.
例 1 What is the value of x ?
(1) 3x = 15
(2) 5x < 30
例 2 Tom and Jack are in a line to purchase tickets. How many people are in the line?
(1) There are 20 people behind Tom and 20 people in front of Jack.
(2) There are 5 people between Tom and Jack.
一般疑问句——答案：明确回答”YES”或者”NO”.
充分：完全符合或者完全不符合 Question提出的内容，即能理直气壮回
答”YES”或者”NO”，不留任何余地的 Statement.
不充分：不完全符合 Question提出的内容，即只能心虚回答”Yes, but…”或
者”No, but…”，及其它一切无法判断结果的 Statement.
例 3 Is x equal to 1 ?
(1) x2
(2) x2
= 1
= 4
1
例 4 体会下列两个 Question的区别.
There are eight balls in the pocket. (已知袋中有 8个球.)
Question 1: Are all the balls in the pocket red? (袋中所有的球都是红色的吗?)
充分：”YES”:
”NO”:
Question 2: Are there any red balls in the pocket? (袋中有红色的的球吗?)
充分：”YES”:
”NO”:
Statement 1: Three balls are removed; whose colors are brown, green, and red, respectively.
Statement 2: Three balls are removed; whose colors are brown, green, and yellow, respectively.
Statement 3: Three balls are removed; whose colors are red, red, and red, respectively.
3. 按照 Problem Solving常规题型继续思考
牢记：当分析 Statement (1) 时，不要预测 Statement (2);
当分析 Statement (2) 时，确信忘记 Statement (1).
2
GMAT数学重点解析
第一章 基本数论
I. 奇数与偶数 (Odd and Even Numbers)
1. 奇数 + 奇数 = 偶数
偶数 + 偶数 = 偶数
奇数 + 偶数 = 奇数
奇数 奇数 = 奇数
奇数 偶数 = 偶数
偶数 偶数 = 偶数
2. 多个整数之和为奇数——其中包含奇数个奇数.
多个整数之和为偶数——其中包含偶数个奇数.
多个整数之积为奇数——全部都是奇数.
多个整数之积为偶数——其中包含至少一个偶数.
任何一个大于 2的偶数都能够表示成为两个质数的和(哥德巴赫猜想)
例1.1 If x and y are integers and xy2
is a positive odd integer, which of the following must
be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
例1.2 Is x an even integer?
(1) x is the square of an integer.
(2) x is the cube of an integer.
II. 因数与质因数 (Factors and Prime Factors)
分解质因数：将一个大的合数写成质数相乘的形式，是极其重要的基本数学技能.
方法：(1) 将大合数写成显而易见的若干小合数相乘的形式，例如 4500 = 45 100;
(2) 反复用 2 除这个小合数，直至不能被 2 整除，再反复用 3 除，以此类推，
直至被完全分解，写成完全由质数相乘的形式.
例1.3 If y is the smallest positive integer such that 3,150 multiplied by y is the square of
an integer, then y must be
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
例1.4 How many factors does 360 have?
(A) 24
(B) 36
(C) 48
(D) 120
(E) 360
III. 最大公约数与最小公倍数
(Greatest Common Divisors and Least Common Multiples)
两个数的最大公约数与最小公倍数的求解方法：
(1) 将两个数分别各自分解质因数;
(2) 每一个质数，取较小的指数(含 0)，相乘得到最大公约数;
每一个质数，取较大的指数，相乘得到最小公倍数.
例1.5 The greatest common divisor of a and b is 21, and the least common multiple of a
and b is 126, where a and b are positive integers, what is the sum of a and b ?
(A) 105
(B) 147
(C) 150
(D) 105 or 147
(E) 105 or 150
例1.6 Is the integer n a multiple of 140?
(1) n is a multiple of 10.
(c59)
(2) n is a multiple of 14.
IV. 余数 (Remainders)
牢记：y kx b ，表示 y 除以 x，商是 k，余数是 b.
例1.7 If x and y are integers, is xy+1 divisible by 3?
(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.
(c52)
例1.8 If n is a positive integer, what is the remainder when 38n+3
+ 2 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4....
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