智课网 GRE 备考资料
GRE 精确 完整 数学预测机经 151015 发布适用 2015 年 10 月考试 20150920 1. n is an integer. : (-1)n(-1)n+2 : 1 A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 答案 :C 解析 : 根据 A 的公式可以推导出 :(-1)n(-1)n+2=(-1)2(n+1)=1, 所以答案应选 C, 数 值 A 和 B 一样大 2. The population of Country X for 1980 was p. The population of Country X increased by 3.8 percent in each of the next two years. : The population of Country X for 1982. : 1.076p A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 答案 :B 解析 : 根据题干可知,1980 年时的人口数是 p, 每两年的增长率是 0.038, 那么到 1982 年 人口数应该是 1.038p, 显然比 1.076p 小, 所以选 B
3. x 0 : x2 : x(x+5) A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 答案 :D 解析 : 题干只说明 x 不为 0, 比较 X2 和 X2+5X 的大小, 因并未提及 X 的正负, 可带入不 同的数, 发现结果并不确定, 则答案为 D 4. x=2, y=3,z=5 : : x-1yz-2 ( xz y ) 2 A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 答案 :B 解析 : 将题干中已给信息 :x=2,y=3,z=5 带入公式, 数值 A 为 3/50; 数值 B 为 9/100, 比较 可得 B 比 A 大 5. x < y-2 : The average (arithmetic mean) of x and y : y-1 A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 答案 :B 解析 : 数值 A=x+y-2/2, 将 x<y-2 该条件带入数值 A 的公式, 可得出 A<y-1, 即 A<B, 所 以选 B 6. Each week a salesperson receives a commission that is equal to 12 percent of the first $500 of sales plus 20 percent of additional sales. If the salesperson received a commission of $380 last week, what was the total amount of the sales that the salesperson made last week? A. $1,600 B. $1,660 C. $1,860 D. $2,000 E. $2,100
答案 :E 解析 : 假设上周这位 salesperson 的 sales 总量为 X, 则根据题干信息可列出等式 : 380=500*12%+(X-500)*20%, 求出 X=2100, 选 E 7. In a class of 120 students, 60 percent can speak French and the rest can speak only English. If 25 percent of those in the class who can speak French can also speak English, how many of the students in the class can speak English? (A) 54 (B) 60 (C) 66 (D) 84 (E) 90 答案 :C 解析 : 题目给出信息 : 班里 120 个学生,60% 可讲法语,40% 只可讲英语 如果可讲法语的人里, 又有 25% 可讲英语 问这个班里有多少可讲英语的? 列出式子 : 60%*120*25%=18,40%*120=48, 则会说英语的总人数是 18+48=66 人 8. A time-study specialist has set the production rate for each worker on a certain job at 22 units every 3 hours. At this rate what is the minimum number of workers that should be put on the job if at least 90 units are to be produced per hour? (A) 5 (B) 8 (C) 12 (D) 13 (E) 30 答案 :D 解析 : 结合题干可知, 每个工人每小时可完成 22/3 units, 那么需要达到的目标是 90 units, 用 90 除 22/3 可得 12.2727 因为是人, 所以约成整数为 13 20150906 1 r=5 s=2 r-2s+2 rs/6 is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :A 解析 : 经计算, 显然 A 列结果是 3 而 B 列结果是 5/3,A 比 B 大
2 The area of the shaded region shown in Figure Ⅰ The area of the shaded region shown in Figure Ⅱ is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :C 解析 : 结合图中阴影, 不难看出其实面积是相同的, 所以选 C 3 Lila purchased a hat and a scarf for a total of $40. She received a 25 percent discount on the price of the scarf and a 15 percent discount on the price of the hat. The amount Lila saved on the scarf The amount Lila saved on the hat is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :D 解析 : 根据题干可列出等式 :75%*price of the scarf+85%*price of the hat=$40 然而在不知道另一个有关围巾和帽子价格的等式的前提下是无法获知 和 B 的大小的 4 (25% of 12)+8 25% of (12+8) is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :A 解析 : 计算可知, 显然 12*25%+8 的值大于 20*25%
5 M, N, P, and Q are midpoints of the sides of the rectangle. The sum of the areas of the shaded regions The area of the unshaded region MNPQ is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :C 解析 : 题目要求是比较连接了矩形四边中点组成的菱形面积与剩余部分面积 阴影部分和非阴影部分即菱形面积实际相同 6 38,205 200 is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :B 解析 : 去掉根号,A 列是 38205,B 列是 40000, 那么开根号得出的大小关系也一致, 一定比 B 小 7 The altitude of APQR from Q 6
is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :A 解析 : 根据勾股定理可以求出等腰三角形的高是 8, 显然比 中的 6 要大 8 Series x=21,23,24,21,22,23,21,25,23,26,21,22,27 The mode of x divided by the median of x 1
is greater. is greater. The two quantities are equal. The relationship cannot be determined from the information given. 答案 :A 解析 : 求出 应该是 23/21, 大于 1, 则 A 比 B 大 9 In the figure above, if x = 110 and y = 120, then z = 10 40 50 60 70 答案 :C 解析 : 此题中 x 由两部分组成, 我们分别用 a 和 b 表示 ; 同理,y 的部分可以有 c 和 d 表示, 而 d 的部分即为 z 我们知道 x 和 y 中的 c 可以一起组成 180, 即 :a+b+c=180, 由此可推知 c=70 由于 c+z=120, 所以 z=50, 正确答案为 C 10 What is the area of the triangular region above? 24 30 40 48 60
答案 :A 解析 : 求直角三角形面积, 可根据勾股定理得出另一条直角边长是 8, 那么面积就是 1/2*6*8=24 11 If n and k are positive integers, which of the following can prove that n divisible by 6? (A) n=k(k+2)(k-3) (B) n = k(k + 1)(k - 1) (C) 2n=3k (D) n/3=2k (E) 2n= 答案 :BD 解析 : 可代数进公式计算, 发现 BD 都对 12 A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount? (A) 2K (B) 6K (C) 7K (D) 8K (E) 12K 答案 :D 解析 : 两块矩形的地, 那么面积公式就是 K=smaller field s length*width, 然后又根据两块地的关系得出 larger field 的面积 =2*4*K=8K 20150829 1. x 2 + y x 2 y (A) is greater. (B) is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. 答案 :D 虽然已知 x 2 是正的, 但无法判定 y 的正负, 根据 y 的正负结果也会变化, 因此是不确定 2. The least positive integer that is divisible by both 14 and 21 The least positive integer that is divisible by both 14 and 28
(A) is greater. (B) is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. 答案 :C 通过计算可知, 能同时被 14 和 21 整除的最小整数是 1, 而能被 14 和 28 整除的最小整数也是 1, 所以显然 A 和 B 一样大 3. x y (A) is greater. (B) is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. 答案 :D 只从 PQ=RT 而不清楚 QR 的长度, 是无法判断 x 和 y 的度数大小的 4. Mrs. Jones sold two houses for $80,000 each. One house was sold at a 20 percent loss and the other at a 20 percent gain. The gain minus the loss 0 (A) is greater. (B) is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. 答案 :B 通过计算可知 :gain=80000-80000/1.2;loss=80000/0.8-80000, 显然损失的比赚的多, 所以用 gain-loss 也就小于 0 5.
x+y w+z
(A) is greater. (B) is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. 答案 :C 四边形内角和为 360, 那么 360 -(x+y) 和 360 -(w+z) 是一样多的 6. x is 7 more than y x y (A) is greater. (B) is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. 答案 :A X 比 Y 大 7, 那么不论如何 A 都比 B 数字大 7. If 0 < st <1, then which of the following can be true? (A) s< 0 and t> 0 (B) s< -1 and t< -1 (C) s > -1 and t< -1 (D) s > 1 and t<-1 (E) s > 1 and t> 1 答案 :C st 比 0 大比 1 小, 则很有可能皆为负或者皆为正, 但是都不能同时大于 1 或者小于 -1, 则只有 C 符合要求 8. On segment WZ above, if WY=21, XZ =26, and YZ is twice WX, what is the value of X Y? (A) 5 (B) 10 (C) 11 (D) 16 (E) It cannot be determined from the in formation given 答案 :D 列出两个等式即可得出答案 :WX+XY=21; 2WX+XY=26, 最后计算可以得出,WX=5, XY=16 9. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values are more than 2.5 standard deviations from the mean? (A) 12.0 (B) 13.5
(C) 17.0 (D) 23.5 (E) 28.5 答案 :E 给出了平均数 20 和标准差 3, 那么要比 20+2.5*3 大的数, 只有 28.5 符合要求, 则答案为 E 10. Which of the following could be the equation of the graph in the xy-plane shown above? A. y = x 2 + x - 60 B. y = x 2 + x - 20 C. y = x 2 + 3x - 60 D. y = 3x 2 + x - 60 E. y = 3x 2 + 3x - 60 答案 :E 根据函数图像, 可将 X=0 时, y=-60; X=4 时, y=0; X=-5 时, y=0 三组数值带入选项中, 都符合条 件的只有 E, 则等式 E 为正确答案 20150821 1. Two librarians, Robert and Patricia, cataloged a combined total of 180 new books, each of which was cataloged by only one of the two librarians. Although they spent the same amount of time cataloging their books, Robert spent an average of 15 minutes per book whereas Patricia spent an average of 12 minutes per book. The number of books cataloged by Robert 60 A. is greater. B. is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. 参考答案 :A 假定 Robert 登记了 x 本书,Partricia 登记了 y 本书, 那么可以得到两个等式 x+y=180, 15x=12y 根据等式计算即可
2. One of the solutions of the equation x 2 +bx+c = 0 is -3. 3b c+9 A. is greater. B. is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. 参考答案 :C 将 -3 代入等式得到 :9-3b+c=0, 故 3b=c+9 3. For any x, 3 3 2 ( x 1) x 3x 3x 1 3 2 ( y 1) 3( y 1) 3( y 1) 1 3 y A. is greater. B. is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given 参考答案 :C 假设 x=y-1, 那么 y=x+1, 代入得出结果相同 4. x y 0 A. is greater. B. is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given 参考答案 :D 5. Parallelogram ABCD has adjacent sides of lengths 10 and 16. The area of region enclosed by ABCD 155 A. is greater. B. is greater. C. The two quantities are equal. xy y x D. The relationship cannot be determined from the information given 参考答案 :D 6. Jim exercised last Monday at 6:00 in the evening and then exercised every third day after that. For example, after last Monday, he exercised the following Thursday and
then the Sunday following that. How many days after last Monday will be the next Monday he exercises? 参考答案 :21 days 7. Which of the following is NOT the sum of a set of consecutive positive integers one of which is 1? 3 10 15 28 35 参考答案 :D 8. If 3k x and k 0, which of the following must be true? 5 20150710 1. 0 x k x k k x 2k x 2k x 2k 参考答案 :C The probability that event A will occur is 0.5 The probability that event B will occur is 0.4 The probability that event A or B will occur is 0.8 Column A Probability that A and B both occur Column B 0.1 A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given 参考答案 :C 通过题目条件可以得出 AB 同时发生的概率是 0.1.
1. Yesterday, at a certain school, the ratio of boys to girls was 1 to 3. Today, an equal number of boys and girls joined the school. The number that joined was greater than zero and no students left. Column A Column B Ratio of boys to girls now 1/3 A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given 参考答案 :A. (1+x)/(3+x) > 1/3, 因为 x>0 3. x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x? 参考答案 :99 X 要满足两个条件,x-4 能被 5 整除,x-7 能被 23 整除 4. If k is an integer and 121 < k 2 < 225, then k can have at most how many values? A. 3 B. 4 C. 5 D. 6 E. 7 参考答案 :D. k 可以是 12,13,14,-12,-13,-14. 5. When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7? A. 1 B. 2 C. 3 D. 4 E. 5 参考答案 :C. 通过条件可以得出 k 为 17, 故 17/7, 余 3 6. In the quadrilateral shown here, a+b+c+d= 参考答案 :1080. 四边形内角和为 360. 故 360*4-360=1080
20150705 1. ABCE is a square, and BCDE is a parallelogram. : The area of square ABCE : The area of parallelogram BCDE A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案 :C. 正方形的面积是长乘以宽, 平行四边形的面积是长乘以高 一样大 2. n is an integer. : (-1) n (-1) n+2 : 1 A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案 :C 如果 n 是奇数, 则负负得正等于 1; 如果 n 是偶数, 依然是 1. 3. The population of Country X for 1980 was p. The population of Country X increased by 3.8 percent in each of the next two years. : The population of Country X for 1982. : 1.076p A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案 :A. p(1+3.8%) 2, 结果大于 B
4. x 0 : x 2 : x(x+5) A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案 :D. 如果 x>0, 则 B>A; 如果 x<0, 则 B<A; 如果 x=0, 则 A=B. 5. x=2, y=3,z=5 : x -1 yz -2 : xz -2 ( ) y A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案 :B A=1/2*3*1/25=3/50; B=9/100; B>A 6.Each week a salesperson receives a commission that is equal to 12 percent of the first $500 of sales plus 20 percent of additional sales. If the salesperson received a commission of $380 last week, what was the total amount of the sales that the salesperson made last week? A. $1,600 B. $1,660 C. $1,860 D. $2,000 E. $2,100 参考答案 :E $500*12%=$60; $380-$60=$320; $320/0.2=$1600; $1600+$500=$2100 7.If x < y, which of the following must be true? A. 2x < y B. 2x > y C. x 2 < y 2 D. 2x-y < y E. 2x-y < 2xy 参考答案 : D. D 项 2x<2y; x<y
8. 1/2 < r <1 : 2r : 1/r A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案 :D. 如果 r 为 1, 则 A>B, 如果 r 为 0.1, 则 A<B. 故选 D 201506 1. 箱子里装了 10 双鞋子 ( 总共 20 只 ) 任意取出两只, 是同一双鞋的概率是? 答案 :1/19 先取出一只, 剩下 19 只 再取出一只, 能够与第一只配对的概率是 1 /19. 2. A 发生的概率是 0.4,A 和 B 同时发生的概率是 0.25. A 或 B 发生的概率是 0.6. 请问 B 发生的概率是多少? 答案 :C 概率公式 :P(A B)=P(A)+P(B)-P(A B), 可通过集合来进一步理解 0.6 = 0.4 + B - 0.25 ; B = 0.45 3. 为了调制出一种灰色, 需要混合 2.016 升的黑墨与 1 升的白墨 现在有 350 升的黑墨, 要调制出这种灰色, 需要多少的白墨? 答案 :173.4 解题思路 :2.016:1 =350: x 4. 求解 :3x-6y=9; 2y-x-3=0 答案 :None. 无解 从等式一得出 x=3+2y, 代入等式二, 无解 5. 假设 x>0, 三角形两边边长分别为 2x+1 和 3x+4, 下面哪些可能是第三边的长度? 答案 :ACE 三角形任意两边之和大于第三边, 任意两边之差小于第三边, 所以假设第三边为 y, 则 x+3<y<5x+5. 所以 A,C,E 有可能 1. 能被九整除的数, 其各位和也能被九整除, 若由余数, 与原数除九余数一致 A/9=X.yu B/9=Y.yu (A-B)=X-Y 不同解法, 设 a,b,c,d,e 为小于 10 的正整数, 则题中所说五位数与其反数可表示为 ax10000+bx1000+cx100+dx10+e 与 ex10000+dx1000+cx100+bx10+a, 相减得 9999a+990b-990d-9999e, 不用说就看出来一定可以被 9 整除了吧 2. 55% 的 brown hair, 同群人中,80% 不是 red hair, 问 the fraction of those who do not have brown hair have red hair?? 答案是 4/9 没 brown hair 是 1-55%=45% 有 red hair 是 1-80%=20% 所以答案是 20%/45% = 4/9
3. acertain money market account that had a balance of $48000 during all of last month earned $360 in interest for the month.at what simple annual interst rate did the account earn interest last month?? 答案是 9% $48000 的月利息是 $360, 问年利率 360*12/48000 = 9% 4. 小于等于 16, 有时二倍的有 16,14,12,10 都不复合条件 那个数是 18 了, 当然大于 16 5. 意思是问如果 combined age 是指某一组中所有人年龄之和, 那么哪一个最大, 就这道题 来说就是年龄乘以该年龄人数谁最大了 很恶心的题, 我做得时候起码读了五遍题才看明 白 combined=age*population 60*1.2=72 6. 是问在 100 年中女性 1980 年多于 1986 年的占多大的比例, 也就是看阴影部分在实线之 外的大概是多少比例, 差不多 25% 吧 我也刚明白, 是这样, 大约 8-23, 和 50-60 这 25 个年龄段上 1980 的女性人口高于 1986, 所以在 0-100 年龄段中大约有 25% 的年龄段中 80 年女性人口数多于 86 年 7. 直线 y=ax+b, 在有相同的 X Y-intercept( 截距 ), 问直线的斜率与 -1 的大小相比哪个大 直线 y=ax+b, 在有相同的 X Y-intercept( 截距 ), 问直线的斜率与 -1 的大小相比哪个大 Let's get X-intercept first, According to the question, 0=ax+b b=-ax x=-b/a Let's get Y-intercept second, According to the question, y=b Because 有相同的 X Y-intercept( 截距 ) then -b/a = b a = -1 Conclusion, 直线的斜率与 -1 的大小相等 8. 500 代表中有 200 是共和党, 那么就有 300 人是民主党, 有 270 民主党人是非素食者, 也就是说有 300-270=30 民主党人是素食者, 素食者总共有 100 人, 另外 70 人就是共和党 人了 9. If one number is chosen at random from the first 1,000 positive integers,what is the probablity that the number chosen is a multiple of both 2 and 8? 答案 :1/8 1000/8)/1000 其中 1000/8 是 1000 以内的能被 2 和 8 整除的个数,8 是 2 和 8 的功倍数
10. 医生建议每人每天水的摄入量是 1/2( 盎司 / 磅体重 )--- 注意这里是总体重 ----- 再加上 ( 体重 - 标重体重 )X8/25, 如果医生给一个体重为 240 磅的人建议的每日水摄入量是 136 盎司, 那么这个人比理想体重重了多少? 列个一元一次方程就可以解出来了 240X1/2+8χ/25=136 11. x?y=x/3-1/y2 A 1/6?2/3 B 2/3?1/6? 是指一种未知的运算关系 A : x=1/6, y=2/3 -->x?y=1/18-1/(4/3) = 1/18-3/4 = -25/36 B : x=2/3, y=1/6 --> x?y=2/9-1/(1/3) = 2/9-3 = -25/9 所以,A>B 12. 标准差越接近 0 跟均值的偏差就越小 题是说下面哪个以标准差来衡量其分值范围最接近均数, 标准差和算法是每个样本值与均数之差的平方和除以样本数再开方得到的, 所以其值越小样本值波动范围越小, 比如所有样本值都相等, 标准差就等于零, 明白了这些我就不用说了吧, 选个标准差最小的一项就是了 13. 四位数, 首位为奇数, 末位为偶数, 多少个这样的四位数? 首位取 13579 中的一个, 末尾取 24680 中的一个中间两位各有 10 种可能, 所以有 5*10*10*5=2500 14. 根号下 79*80*81*82 与 6400 比, 哪个大? 答案 : 前者大 6400 的平方等于 80 的二次方 79*80*81*82=(80-1)*80*(80+1)(80+2)=80*(80+1)(80*80+80-2) 这个显然大于 80 的四次方 there are 7 possibilities for the begin of month X, from monday to sunday, then the fourth tuseday of this month also has 7 possible dates. 15. 就是 1 号是周三至周二 30 天第四个周二都会出现所以就 7 种 16.W,X,Y,Z 皆为整数 1<w<x<y<z WXYZ=210 比较 W+Z 和 10 的大小答案 :10 大 210=2 3 5 7 && 1<w<x<y<z so w=2 & z=7 w+z=9<10 Sara: 这道题是这样做的, 实际上 210=2*3*5*7, 所以 w=2;x=3;y=5;z=7; 所以 w+z=9<10; 就这么简单,Est 这道题容易把人的思路影响歧途, 其实很简单
17. 不用算吧, 两个 COLUMN 是等价的, 七个一圆钱账单三个人分, 怎么分都有一个人要不小于三个, 不是吗? 分法当然是相同了 18. 100,210*90,021 与 100,021*90,210 比大小咋看?? 100210*90021=100000*90000+210*21+100000*21+90000*210 100021*90210=100000*90000+210*21+100000*210+90000*21 就是比较后两项的大小两边同时减去 90000*210+90000*210 前一个数是 x+10000*21 后一个数是 x+10000*210 后一个数大 19. 13% 提供 compressed workweek,9% 提供 work at home, 所以两者都提供的最多 9%, 9%X300=27 300*18%=300*35%*(1/5)+300*(1/10)*40%+300*25%*? 就是 18=35/5+40/10+25/? 20. 要结合两张表, 列下来是这样 :35%X(1/5)+40%X(1/10)+25%X#=18% 算下来 #=7/25 21. The figure above shows the graph of a function f, defined by f(x)= 2x +4 for all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f? A g(x)=x 2 B g(x)=x+3 C g(x)=2x 2 D g(x)=2x+3 E g(x)=3x 2 这个题就是问两个函数图象相交的问题, 根据观察, 要与这个折线相交的直线的斜率满足的条件是要么是正斜率比 2 大, 要么是负斜率比 -2 小, 因此只能选 E 了
22.Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and is $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees in the company? Indicate all such amounts. A $26,000 B $28,000 C $29,000 D $30,000 E $31,000 F $32,000 G $34,000 本题我们要注意到题目中的 more than twice 的字眼, 我们当做 twice 算的时候, 结果是 (25000*2+35000)/3 约等于 28333, 因为有 more than, 所以选的答案要么是比前面这个数大, 要么小, 又由于 more 的是 X 部门的, 那么肯定会将平均工资给拉低了, 因此, 选比前面那个数小的答案,AB 都可以了 23.Working alone at its constant rate, machine A produces k car parts in 10 minutes. Working alone at its constant rate, machine B produces k car parts in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k car parts? minutes 这类题目小学时候经常遇到, 相信很多人都是这种感受哈 1/(1/10+1/15)=6min 1)If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008? A $727,200 B $792,000 C $800,000 D $880,000 E $968,000 直接算,800000*(1+10%)*(1-10%)=792000, 即 B
2)At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1 percent. % 直接算,1/(1-8%)=108.7%( 约等于 ) 3)Which of the following statements must be true? Indicate all such statements. A For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores. B The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006. C The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006. 本题 A 选项一看到就可以排除了, 涉及到两个店的绝对量的比较, 这个不确定, 没有告诉绝对值 B 选项是把两个增长的比例简单地算术相加 肯定错了 所以 C 肯定是对的了 算一下也是的确是对的 24. A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy? A 9 B 10 C 11 D 12 E 20 这个题首先就可以想到单价越便宜的我就能买的越多, 因为它没有说两种笔一定要都买 25.A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a number in the list that is 2 standard deviations above the mean, what is the value of x? x=_8+2.5*2=13_ 这道题不知怎么的, 读题的时候度饶了, 感觉很费解, 什么是两个标准差, 以为是个什么特殊的东西, 后来问了同学才知道这就是个简单的计算题, 没啥特别的, 我的个汗啊, 考试的时候我碰到了, 我肯定错了 26.Frequency Distribution for List X Number 1 2 3 5 Frequency 10 20 18 12 Frequency Distribution for List Y Number 6 7 8 9 Frequency 24 17 10 9 List X and list Y each contain 60 numbers. Frequency distributions for each list are
given above. The average (arithmetic mean) of the numbers in list X is 2.7, and the average of the numbers in list Y is 7.1. List Z contains 120 numbers: the 60 numbers in list X and the 60 numbers in list Y. The average of the 120numbers in list Z The median of the 120 numbers in list Z A 中, 平均数肯定就是两组的平均数的和的一半, 也就是 (2.7+7.1)/2=4.9, 因为两组的人数相同, 而 B 中 median 就是 (5+6)/2=5.5, 所以就是 B 了 27.The figure above shows the graph of the function f in the xy-plane. What is the value of f ( f ( 1))? A 2 B 1 C 0 D 1 E 2 这个题就是读图题了, 一重重的往外算就好了,f ( 1)=2,f(2)=1, 即 D 28.By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution? A 10% B 13% C 15% D 19% E 26% 这个题小学也经常遇到,(3*8%+7+18%)/(7+3)=15% 29.Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?
A 0.5 B 0.6 C 0.7 D 0.8 E 0.9 这个就是组合的计算了,C 2 580 / C 2 700 =0.68( 约等于 ), 所以选 C 吧, 这个题可 以用下那个计算器了 30.Line k lies in the xy-plane. The x-intercept of line k is 4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k? Give your answer as a fraction. 3/4 这个题先求出那条线段的中点 (2,9/2), 然后斜率就是 (9/2)/(2-(-4)) =3/4 31. In the course of an experiment, 95 measurements were recorded, and all of the measurements were integers. The 95 measurements were then grouped into 7 measurement intervals. The graph above shows the frequency distribution of the 95 measurements by measurement interval. The average (arithmetic The median of the 95 mean) of the 95 measurements Measurements 这个题我觉得可以估计,median 应该在 6-10 这段, 而 average 呢, 根据图表判断, 左边的两段和右边的五段占总人数应该是差不多对半分, 那么平均数就应该是向高处拉了, 这个是经验估计 当然也可以通过算, 我觉得这个题去算的话, 量相对大些 答案为 A
32.The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively. The value at the 75 th 750 percentile of the distribution of X 这个题, 我做的时候是根据图像做的, 在正态分布的函数图象上,60% 90% 之间的这段是个下凸的, 所以当取 750 这个自变量的时候, 对应的函数值应该是比 650 和 850 对应函数值的平均值小的, 大家画个图就可以很直观的看出来了 所以 750 对应的白分比应该是比 75% 小, 选项是 B 33.If 1+x+x 2 +x 3 =60, then the average (arithmetic mean) of x, x 2, x 3, and x 4 is equal to which of the following? A 12x B 15x C 20x D 30x E 60x 这个题直接在等式的两边乘以 x 就好了, 然后除以 4, 答案就是 B 34. Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R? A (3, 2) B (3, 3) C (4, 4) D (5, 2) E (6, 2) 这个题直接读图, 应该有 Q 的坐标减去 P 的坐标等于 R 的坐标减去 O 的坐标, 其实也就是两个向量是相等的,O 又恰好是原点, 那么 R 的坐标就是 QP 的向量坐标了, 即 (6,2)E 选项
35.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. A 12 B 24 C 36 D 72 这个意思就是先求出 24 和 108 的最小公倍数, 然后通过加倍使其成为一个整数的平方, 这样就可以找出一系列的 n 了, 这些 n 的公公因数应该有哪些? 我找了前面的两个,36 和 72, 所以 AC 可以选出来了, 之后的所有数肯定包含了这两个选项, 而 BD 因为不满足前面这两数, 所以就排除了 36.The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4inches. Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class? Indicate all such statements. A The tallest male student in the class is 5.8 inches taller than the tallest female student in the class. B The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class. C The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class. 分析 : 在数轴上我们可以画出一段表示女生身高范围, 另一段表示男生身高范围, A 选项告诉我们的是男生最高的比女的最高的高 5.8inch, 那么我们就可以确定两段的相对位置了, 因此总的身高范围就可以确定了 选项 A 就是对的了 B 选项, 由于没有告诉我们男女生的人数, 所以这个是无法确定的 C 选项, 这个选项跟上面的 B 差不多, 没法确定 附上 OG 的解答, 以作参考 : 37.A random variable Y is normally distributed with a mean of 200 and a standard deviation of 10. The probability of the event 1/6 that the value of Y is greater than 220 这个可以复习下那个正态分布的图了,OG294 面 220 对应的就是 mean+ 两个标准差了, 那么 220 以下的比例是 (50+34+14)% 了, 在 220 以上的就是 1 减去前面这个数, 比 1/6 要小 B
38.In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry? 121 students 这个题我开始以为是那种集合性质的, 用 121+142-236, 算的, 但对答案发现错了, 细看题目才知道, 这两种考试并不是全集, 所以最多两种同时考的就是报的少的那个了 39.The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true? Indicate all such statements. A The price of the book was less than $9.50. B The price of the book was greater than $6.90. C The sales tax was less than $0.45. 如果设书的价格是 x, 那么总的支出是 1.04x, 根据题意有 (10-3)<1.04x<10, 解得 6.73<x<9.62, 由此判定 A B 不对,C 就对了, 税钱就是 0.04x<0.04*9.62=0.38 40.Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above? Indicate all such statements. A DBC is an equilateral triangle. B ABD is an isosceles triangle. C The length of BC is equal to the length of AD. D The length of BC is 10. E The length of AD is 10 只告诉了三角形是直角三角形和一条直角边, 要求我们补充条件可以求得三角形的面积 只能用排除法 A 说三角形 DBC 是等边的, 角 C 就是 60 度了, 其他的便也就可以求出来了, 面积就可以求 B 说 ABD 是等腰三角形, 这个没意义, 因为没说那两个边是等的, 比如如果 AB=AD, 是没法求的,C 说 BC=AD, 这个条件是没有意义的, 因为我们的 D 点可以移动, 当三角形的大小发生变化时, 我们总可以找到对应的 D 点使得 AD=BC,D 选项说 BC=10, 这就可以求了,E 说 AD 的长是 10, 这个同样没意义 所以选 AD
41.The fabric needed to make 3 curtains sells for $8.00 per yard and can be purchased only by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains? A $40.00 B $38.40 C $24.00 D $16.00 E $12.80 一共三个窗帘, 每个 1.6m, 那么一共要 4.8m, 由于不能零卖, 只能整数的卖, 所以买 5m, 一共是 5*8=40 了 42.In the xy-plane, the point with coordinates ( 6, 7) is the center of circle C. The point with coordinates ( 6, 5) lies inside C, and the point with coordinates (8, 7) lies outside C. If m is the radius of C and m is an integer, what is the value of m? m = 这个题大家可以画个坐标图, 标出那几个点,(-6,5) 在圆内, 那么半径 m >5-(-7)=12( 之所以能这么算, 是因为圆心坐标跟这个点的横坐标相同 ), 而点 (8,-7) 在圆外, 那么 m<8-(-6)=14, 又因为 m 是整数, 因而 m=13 了 43.What is the least positive integer that is not a factor of 25! and is not a prime number? A 26 B 28 C 36 D 56 E 58 这个题, 你看 25! 里面包括了 2 到 25 的所有 factor 了, 所以你看 26=2*13,28=2*14,36=2*18,56=7*8, 而只有 58=2*29,29 不在里面, 所以就选这个了 44. If 1 is expressed as a terminating decimal, how many nonzero digits 1/[(2 11 )(5 17 )] will the decimal have? A One B Two C Four D Six E Eleven 将分子转化下, 使之成为以 10 为底数的指数, 由此可以判断小数点的位数了, (2 11 )(5 17 )=10 11 *5 6 =(1/64)*10 17, 由此可知, 倒过来后, 非零数位有两位, 6 和 4.
45.Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below. (a) What are the range, the three quartiles, and the interquartile range of the measurements? (b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams? a. 这个范围就是 146-105=41 了, 四分之一分位点在 114 这儿, 四分之二分位点在 118 这儿, 四分之三分位点在 126 这儿, 四分位差为 126-114=12, b.. 在 80% 这儿是 130, 在 75% 这儿是 126, 那么 126 至 130 之间是 5% 了, 对应的 measurements 是 800*4%=40; 46.The figure shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown. Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters. (a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall? (b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin s height will be less than 60 centimeters? Give your answer to the nearest 0.05 a.65 和 75 之间, 刚好是 2 个的标准差, 因此对应的就是 34%+14%=48% 了, 对应的企鹅是 3000*48%=1440 了 B. 算的结果应该是 2%+14%=16%, 最经的 0.05 应嘎是 0.15 了
42. (51!-50!)/ (50!-49!)=? (50*50/49) 43. 确定是多选题 (select all that apply): 有一个半径为 50 的圆, 问以下哪些点在圆上 (go through)? 选项有 (25,25),(-30,40) 等等 44. A 数列是 21 个连续整数构成的,B 数列是 15 个连续整数构成的 A 数列的中位数与 B 数列的中位数一样,A 数列的平均数与 B 数列的平均数比大小 45. 有 a kg 的某东西, 每一 kg 的 a 里面有 x kg 茶原料 b kg 的另外一样东西, 每一个单位的 b 有 y kg 的茶原料 最后有 c kg 的某东西, 每一个单位的 c 有 z kg 的茶原料. 问大混合之后茶原料的比例 =(ax+by+cz)/(a+b+c) 46. 有一个数是 1234567891011 499500. 问这个数一共有几位? 分类后解决, 不难 47. 某小树, 第 2 年比第 1 年增高 20%, 第 3 年比第 1 年增高 38%, 问第 3 年比第 2 年增高多少比率? (1.38-1.2)/1.2 48. 有个 survey 调查了 248 个 company, 其中 120 个 company 有一个 central switchboard, 这 120 个 company 里面有 90 个有给 employee 提供一个 service, 问多少个公司没有该 service, 和 26 还是 28 比较 49.Set S 包含了 100-226 之间是 4 的倍数的 positive integer,set Q 包含了 perfect square number, 问 both in S and Q 的 number 有多少个? 50. 两个圆柱体都装着某种液体, 一个的 base 是 5pai, 另一个 base 是 10pai, 第一个液体的高度是 6, 第二个液体高度是 2, 把第一个的部分液体倒进第二个, 使两个圆柱体里液体高度相同, 问倒了之后它们的液体高度是多少