GRE数学（易）错题

设参后还要注意参数求出来的值是不是和题目要求的值是同一个，有的时候求了参之后还要转换才能得到目标值；遇到长题干不要慌；看清题目问的是什么（number or proportion）；做之前、做之后都要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；考点就在题干中，题干没有废话；数值不确定就是要设参联立，不要嫌麻烦；填空题做完一定要把所求值代回到题干中看是否题干中的所有情况都满足；看清只存一次？还是每年持续存钱？；有些题的韦恩图是没有重叠部分的，要根据题干意思去斟酌；diameter是直径；注意#谁#是#谁#的几分之几，题干中的这两个对象会变来变去

（skip）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

（skip）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

(skip)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

（skip）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

（skip）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#

（skip）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。

（skip）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。

（skip）Let q be a prime number less than 100. When q is divided by 5, the remainder is 2. When q is divided by 7, the remainder is 6. What is the remainder when q is divided by 8?

正确：1

错误：3（q为27的情况，这时q不满足prime number）

（skip）Working continuously for a total of 120 hours, a machine first assembled x units of product A and then assembled y units of product B, where x and y are positive integers. It took the machine 3 hours to assemble each unit of product A and 5 hours to assemble each unit of product B. Which of the following could be the total number of units of product A and product B that the machine assembled in the 120 hours?

Indicate all such numbers.

A

22

B

33

C

38

#考点就在题干中，题干没有废话#

‘ where x and y are positive integers’推出考点为‘解每个选项的方程组，看有没有整数解。’

你的答案是：

BC（错误估计120/5 <= x+y <= 120/3，数值不确定就是要设参联立，不要嫌麻烦）

正确答案是 : C

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题目翻译；一台机器连续工作120小时，先组装x件产品a，再组装y件产品B，其中x和y为正整数。机器花了3个小时组装A件产品，花了5个小时组装B件产品，下面哪一个可以是机器在120小时内组装A件产品和B件产品的总数？标出所有这些数字。

解析：

设x个A和y个B，则3x+5y=120,那么我们看选项，第一个是x+y=22,第二个是x+y=33,第三个是x+y=38

分别解出x和y，只有第三个情况符合，x=35，y=3

选择第三个。

（skip）There are two overlapping circular regions on a level field, and the centers of the regions are 40 meters apart. One circular region has a radius of 25 meters, and within the region there is a marker located 5 meters away from its border. The other circular region has a radius of 30 meters, and within the region there is a marker located 7 meters away from its border. What is the greatest possible distance, in meters, between the two markers?

A

67

B

78

C

83

D

95

E

108

正确答案是 : C

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题目翻译：在一个平地上有两个重叠的圆形区域，区域中心相距40米。一个圆形区域的半径为25米，区域内距离边界5米处有一个标记。另一个圆形区域半径为30米，区域内距离其边界7米处有一个标记。两个标记之间可能的最大距离，以米为单位是多少？

解析：算两标记各自的定位半径：第一个标记距自身圆心 25-5=20 米，第二个距自身圆心 30-7=23 米，而因为两圆心固定相距 40 米已知，那么最大距离 = 两圆心距离 +两个定位半径之和，即 40+20+23=83 米

选第三个

（skip）The advertised size of a television is the length of the diagonal of the rectangular viewing screen. For a television advertised as 42-inch, if the ratio of the lengths of the sides of the viewing screen is 16 to 9, approximately what is the area, in square inches, of the viewing screen?

A

144

B

328

C

406

D

754

E

933

正确答案是 : D

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题目翻译：电视的广告尺寸是长方形屏幕对角线的长度。对于一台广告为42英寸的电视，如果屏幕的边长比是16:9，那么屏幕的面积（以平方英寸为单位）大约是多少？

解析：设长宽为x,y那么就是要求xy, 我们现在知道x/y=16/9,x²+y²=42**2,  解出x大约等于36.6，y大约等于20.6，面积大约等于754

选第四个

（skip）A certain town with a population of 50,000 uses an average of 5,000,000 gallons of water per day. If the average number of gallons of water used per person per day remained the same and the population of the town increased to 65,000, by how many gallons would the average amount of water used by the town per day increase?

A

150,000

B

650,000

C

1,500,000

D

3,500,000

E

6,500,000

正确答案是 : C

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题目翻译：某城镇有5万人口，平均每天使用500万加仑的水。如果每人每天的平均用水量保持不变，而小镇的人口增加到65,000，那么小镇每天的平均用水量会增加多少加仑？

解析：每人平均用水量就是500万/5万=100加仑，那么现在人口为65000，那么现在平均每天就是6500000加仑，增加了1500000

选第三个

（skip）If N is a positive integer, then the number of prime numbers between N+1 and N+6, inclusive, CANNOT be

A

0

B

1

C

2

D

3

E

6

正确答案是 : E

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题目翻译：本题问我们当N为正整数时，N+1与N+6之间的质数个数不可能为多少？（包含N+1和N+6）

解析：

首先我们知道N+1与N+6（包含）之间一共有6个数，又知道不存在连续的六个正整数都是质数，所以不可能为6. 所以答案选择6

（skip）b, c, and d are consecutive even integers such that 2 < b < c < d. What is the largest positive integer that must be a divisor of bcd?

正确答案是 : 48

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题目翻译：b, c，d是连续的偶数，使得2 < b < c < d.  一定是bcd正整数因子中最大的是多少？

题目问 must be a divisor（一定是因子），就是所有样本都共享的最大公因数。

（skip）m is a three-digit integer such that when it is divided by 5, the remainder is y, and when it is divided by 7, the remainder is also y. If y is a positive integer, what is the smallest possible value of m?

正确答案是 : 106

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题目翻译：m是一个三位数的整数，当它除以5时，余数是y，当它除以7时，余数也是y。如果y是一个正整数，m可能的最小值是多少？

解析：

找5和7在100以上的最小公倍数，是105.

此时y也取最小值，就是1。所以m最小就是105+1=106

（skip）等于？

is 72

not 36

（skip）If  x**2/4  is an integer greater than 50 and x is a positive integer, then what is the smallest possible value for x²?

正确答案：256

#填空题做完一定要把所求值代回到题干中看是否题干中的所有情况都满足#

错误答案：225（ x**2/4  is not an integer ）

正确答案：256

（skip）At the beginning of each year Jane puts $2,000 in an account that earns 6% interest, compounded annually. To the nearest dollar, how much money will Jane have in the account at the end of 4 years if she makes no withdrawals?

Round your answer to the nearest whole dollar:

#只存一次？还是每年持续存钱？#

正确答案是 : 9274

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题目翻译：每年年初，J都会存2000美元到一个账户，利息为6%，每年复利。4年后，如果J不提款，她的账户里还有多少钱？你的答案四舍五入到最接近的整数美元：

解析：

第一年后2000*1.06=2120，第二年后就是（2120+2000）*1.06=4367.2，第三年后就是（4367.2+2000）*1.06=6749.232，第四年后就是（6749.232+2000）*1.06=9274.18592约等于9274

填写9274。

(skip)A dealer buys a boat at auction and pays 10% below list price. He then sells the boat at a profit of 30% of his cost of the boat. At the same selling price, what would the dealer's percent profit over his cost have been if he had bought the boat at list price?

Round your answer to the nearest whole percentage point before entering:

正确答案是 : 17

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题目翻译：一个商人在拍卖会上买了一艘船，支付比标价低10%的价格。然后他以买价的30%为利润卖掉这艘船。在相同的售价下，如果经销商以标价买船，他的利润除以买价的百分比是多少？

解析：

设标价为x,那么买价为0.9x, 卖价为1.3*0.9x=1.17x,那么如果以x买，那么利润就是0.17x,除x为0.17，百分比即17%

填写17。

错解：27

0.3×0.9=0.27
虽然x是固定值但是前面的系数因为题目条件改变而改变了
有的时候不仅要注意参数变化还要注意参数前面的系数有没有变化

（skip）Of the vehicles in a parking lot, 38.75 percent are trucks and 52.5 percent are cars. What fraction of the vehicles in the parking lot are neither trucks nor cars?

#有些题的韦恩图是没有重叠部分的，要根据题干意思去斟酌#

正确答案是 :

7/80

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题目翻译：停车场的车辆中，38.75%是卡车，52.5%是轿车。停车场的车辆中有多少既不是卡车也不是小汽车？

解析：

1-38.75%-52.5%=8.75%=8.75/100=17.5/200=35/400=7/80

填写7/80。

（skip）diameter什么意思

直径

（skip）On a construction map of a college campus,  1/3  of the area of the campus is marked for landscaping. Of the part of the campus that is not marked for landscaping,  1/8  of the area is marked for gym buildings. What fraction of the area of the campus is not marked for either landscaping or gym buildings?

错误答案：13/24（注意#谁#是#谁#的几分之几，题干中的这两个对象会变来变去）

正确答案是 :

7/12

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题目翻译：一所大学校园的建筑地图上，校园面积的1/3被标记为景观美化。校园中没有被标记为景观美化的部分，这一地区的1/8被标记为健身房。校园中有多少区域没有被标记为景观美化或健身房？

解析：

标记为其中之一的有1/3+2/3 * 1/8=5/12，那么反过来没有被标记为任何之一的就是7/12

填写7/12。

x and y are integers and x > y.

x2**+y**2=25

Quantity A

x

Quantity B

4

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the information given.

那么这个等式可以看出，x=5,y=0与x=4,y=3都满足，但这么一来x与4的大小比较就不能确定唯一，无法判断。

正确答案为D。

Which of the following is closest to the percent of the students enrolled in college who were female students in their junior year and in the age-group 20 to 24?

A

3%

B

7%

C

16%

D

22%

E

41%

正确答案是 : B

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题目翻译：以下哪一项最接近在大学就读的学生中，处于大三且年龄在20至24岁之间的女生所占百分比？

解析：

读图得20至24岁年龄组的大三女生人数为913000人，而大学入学人数为13000000人，所以比例为913000/13000000=0.07=7%

正确答案为B。

#不要漏看表标题下面的‘(thousand)’，看懂题干的句型结构#

Which of the following is closest to the percent of 【college‑enrolled students】【who are female, juniors, aged 20‑24】.

答案=A / B

（直接看解析）Jeremy bicycled a distance of 16 miles in x minutes. He averaged 15 miles per hour for the first 8 miles he bicycled.

Quantity A

The number of minutes he took to bicycle the last 8 miles

Quantity B

x - 32

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the information given.

#一定要设参严谨计算，不要凭感觉#

正确答案是 : C

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题目翻译：Jeremy在10分钟内骑了16英里。他骑自行车的前8英里平均每小时15英里。

解析：A选项就=x- 60*(8/15)=x-32，相等

选第三个

x≤50

y≤4

Quantity A

xy

Quantity B

300

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the information given.

正确答案是 : D

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解析：

比如x,y可以分别等于负的100，就乘积就大于300；而当各自取0时，乘积又小于300，因此答案不唯一无法判断。

条件不足，正确答案为D。

Quantity A

a

Quantity B

-1

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the information given.

【公众号：A加GRE】

解析：

因为a小于0，所以第二个式子的分母a-1一定小于0，又因为这个分数大于0，就需要分子a+1也小于0，即a一定小于-1。

所以正确答案为B。

又看错题了，题目问的是a的大小

Near the equator, a boat traveled 17 kilometers along a straight route from point A to point B, which is 15 kilometers north and a certain distance east of point A. The boat then traveled 12 kilometers due east from point B to point C. The boat then traveled along a straight route from point C back to point A. What was the total distance, in kilometers, that the boat traveled from A to B to C and then back to A?

A

50

B

52

C

54

D

58

E

60

题目解析

船从 A 到 B 直线 17km；B 在 A 正北 15km，东边若干 km。 再从 B 向正东走 12km 到 C；再 C 直线返回 A。 求总路程：A→B→C→A 的全部距离。

第一步：求 A 到 B 的东向距离

A‑B 是斜边 17，向北直角边 = 15

\(\text{东向距离} = \sqrt{17^2-15^2}=\sqrt{289‑225}=\sqrt{64}=8\) 👉B 在 A 东边 8 km。

第二步：C 相对于 A 的坐标

• 南北：C 和 B 一样，在 A 正北 15 km

• 东西：B 已经东 8km，B 再向东 12km 到 C

\(A到C的东向 = 8+12 = 20\ \text{km}\)

第三步：求 C 回到 A 的直线距离 CA

直角三角形：南北 15，东西 20

\(CA=\sqrt{15^2+20^2}=\sqrt{225+400}=\sqrt{625}=25\)

第四步：全部路程相加

A→B =17； B→C=12； C→A=25

\(\text{总路程}=17+12+25=\boldsymbol{54}\)

✅答案 C 54

If an integer is chosen at random from the integers between 101 and 550, inclusive, what is the probability that the chosen integer will begin with the digit 1, 2, or 3, and end with the digit 4, 5, or 6?

A

0.02

B

0.05

C

0.10

D

0.15

E

0.20

正确答案是 : E

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题目翻译：如果从101到550（包括在内）之间的整数中随机选择一个整数，所选整数以数字1、2或3开始，以数字4、5或6结束的概率是多少？

解析：

一共有450个整数，个位限定这三个，然后十位从0到9一共10个，百位也是限定了这三个，就一共有3*10*3=90种情况符合，所以90/450=1/5=0.2，所以答案是0.20

An investor invested x dollars into each of two certificates of deposit. One certificate of deposit earned 3 percent interest compounded annually for k years. The other certificate of deposit earned 2.4 percent interest compounded annually for n years. Which of the following expressions represents the total amount of interest, in dollars, earned by the two certificates of deposit?

你的答案是：

C

正确答案是 : D

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解析：

第一份存单利息：本金x，利率3%，年数k，所以x（1.03）k−x=x[（1.03）k−1]

第二份存单利息：本金x，利率2.4%，年数n，所以x（1.024）n−x=x[（1.024）n−1]

总利息：x[（1.03）k−1]+x[（1.024）n−1]=x[(1.03)k+(1.024)n−2]

A group of n people is standing in line to purchase theater tickets. The line is a straight line with more than 10 people. Meg is the 4th person behind the person at the front of the line, and Cory is the 4th person in front of the person at the back of the line.

Quantity A

The number of people in the line between Meg and Cory

Quantity B

N-10

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the information given.

#是个数，不是百分位数#

你的答案是：

D

正确答案是 : C

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题目翻译：n个人在排队买戏票。超过10人的队伍排成一条直线。Meg是排在队首的人后面的第4个人。Cory是排在队尾前面的第4个人。

解析：

统一都从前往后数，M是第5个人，C就是第n-4个人，他们两个人中间的人数就为n-4-5-1=n-10，相等。

正确答案C。

For Maine, which of the following most closely approximates the average annual growth in forest area from 1907 to 1992?

A

28,000

B

31,000

C

34,000

D

37,000

E

40,000

正确答案是 : B

【公众号：A加GRE】

题目翻译：对于缅因州，下列哪项最接近1907年至1992年森林面积的年平均增长？

解析：

读图，Maine的1907年到1992年为14.9到17.53，那么就是增长了2.63milloin就是2630000，那么年平均增长就是2630000/85=30941，大约为31000

正确答案为B。