GRE数学

看清题目问的是什么（number or proportion）；检查一下题目有什么条件没用上；积累数学语境下的词汇；有的是因为题干是英文，有些条件没读懂或者遗漏；不要凭直觉做题，一定要有依据

According to a survey of 300 college students, 40 percent had student loans and 25 percent had scholarships. If 55 percent of the students surveyed had neither student loans nor scholarships, how many of the students had both student loans and scholarships?

选项： 20 30 45 60 75

错误：20

正确：60

#看清题目问的是什么（number or proportion）#

还有要检查一下题目有什么条件没用上，例如如果选‘20’，那题目条件‘300 college students’就没有用上

In order to adequately heat or cool a house, a contractor must determine the number of cubic meters of space inside the house. A floor plan of a house with two sections, A and B, is shown above. Each section of the house has a rectangular floor and is shaped like a rectangular solid. Section A is 1 story high, section B is 2 stories high, and the distance from the floor to the ceiling for each story is 2.7 meters. Disregarding the dimensions of interior walls and structures, approximately how many cubic meters of space are inside the house?

正确：1,555

错误：1,123

错因：A 区域为 1 层高，B 区域为 2 层高（story为楼层），当时写的时候以为是A is 10 meters,B is 20 meters，但是几米在图中已经给出，没必要再文字说一遍

x and y are integers, x ≤ 6, and y > 3 - 2x.

Quantity A

The least possible value of y

Quantity B

-8

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

正确：C

错误：D（不是比较x和y的大小）

题目翻译：x和y为整数，x≤6 , y>3-2x .

解析：那么y最小也＞-9，整数的话就是-8为最小可能值，相等

选第三个

Quantity A

The sum of the areas of the three shaded regions

Quantity B

4π

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

#不要凭直觉做题，一定要有依据#

三角形外角和为180

正确：C

错误：A

The product of nine consecutive integers is 0.

Quantity A

The sum of the nine integers

Quantity B

30

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

正确：D

错误：A

#要考虑负数情况，并且该情况用笔算出结果，不要心算，你不知道你会犯多离谱的错误#

Quantity A

The number of possible integers x for which x, 2, and 6 are the respective lengths of three sides of a triangle

Quantity B

4

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

#看清题目问的是什么#

问的是整数可能值的个数，不是可能值和4的大小关系

已知x，2，6分别为某个三角形的三条边，那么根据两边之差小于第三边，所以x＞6-2=4，再根据两边之和大于第三边，6+2＞x，也就是x<8，得到4<x<8，又因为x是整数，所以x可以取5、6、7，一共有3种取值，所以A小于B。

The average (arithmetic mean) of a set of 10 positive integers is 7.5.

Quantity A

The probability that the value of one randomly chosen integer from the set will be greater than 7

Quantity B

½

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

正确：D

题目翻译：已知十个正整数的均值为7.5。

解析：

这里光知道均值，并无法判断有几个数是大于7的，所以无法判断A的概率，也就无法比较AB的值。

正确答案为D。

A jar contains only red marbles and black marbles. The jar contains more than one red marble and 5 times as many black marbles as red marbles. Five marbles are to be selected from the jar without replacement.

Quantity A

Of the marbles selected, the number that will be red

Quantity B

Of the marbles selected, the number that will be black

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

错误：B

正确：D

#陷阱题！！！问的是数量不是概率。因为不知道具体的红黑球的数量，所以无从知晓#

题目翻译：一个罐子只包含红色弹珠和黑色弹珠。罐子里有不止一颗红色弹珠，黑色弹珠的数量是红色弹珠的 5 倍。要从罐子中选择五颗弹珠，不放回。

解析：

让我们比较从罐子里选出的红色弹珠和黑色弹珠的数量。

这里我们不知道红色弹珠的数量，也就无法知道黑色弹珠的数量，所以能从罐子里选出多少个我们也无法判断。

正确答案为D。