海翔GMAT数学课程(陈文彬)

此讲义为海翔陈文彬老师的视频课程讲义具体课程地址：/xyzq_3.htmQ1:A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?A.0B.1/9C.2/9D.1/3E. 1Answer:-------------------------------------------------------------------------------------------------------Q2:In 1997 there were 300 female employees at Company C. If the number of female employees at Company C increased by 60 percent from 1977 to 1987, by what percent did the number of female employees at Company C increase from 1987 to 1997?(1) From 1977 to 1997 the number of female employees increased by 200 percent atCompany C.(2) In 1977 there were 100 female employees at Company C.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q3:A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?A.1/12B.1/6C.1/5D.1/3E.1/2Answer:-------------------------------------------------------------------------------------------------------Q4:If 1050– 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?A.424B.433C.440D.449E.467Answer:------------------------------------------------------------------------------------------------------------Q5:If w and c are integers, is w > 0?(1) w + c > 50(2) c > 48A. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q6:A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?A.5B. 6C.9D.24E.36Answer:------------------------------------------------------------------------------------------------------------Q7:Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?A.4B. 6C.8D.10E.12Answer:------------------------------------------------------------------------------------------------------------Q8:Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?(1) She bought $4.40 worth of stamps.(2) She bought an equal number of $0.15 stamps and $0.29 stamps.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q9:A positive integer n is said to be “prime-saturated” if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two-digitprime-saturated integer?A.99B.98C.97D.96E.95Answer:------------------------------------------------------------------------------------------------------------Q10:For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person?(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.(2) The daily cost per person for 2 people sharing the cost of a room equally is $25more than the corresponding cost for 4 people.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q11:What is the median number of employees assigned per project for the projects at Company Z?(1) 25 percent of the projects at Company Z have 4 or more employees assigned to eachproject.(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to eachproject.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q12:A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow. If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?A.3/64B.1/20C.1/16D.1/12E.1/8Answer:------------------------------------------------------------------------------------------------------------Q13:When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?A.96B.75C.48D.25E.12Answer:-------------------------------------------------------------------------------------------------------Q14:The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?A.5½ ftB.7½ ftC.8 ½ ftD.9½ ftE.10 ftAnswer:-------------------------------------------------------------------------------------------------------Q15:The operation ⊗ is defined for all nonzero numbers a and b by a ⊗ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?I.x ⊗ xy = x(1 ⊗ y)II.x ⊗ y = -(y ⊗ x)III.1/x ⊗ 1/y = y ⊗ xA. I onlyB. II onlyC. III onlyD. I and IIE. II and IIIAnswer:-------------------------------------------------------------------------------------------------------Q16:If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?(1) a = 2b(2) a + b > 1A. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q17:On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of th e ship’s passengers held round-trip tickets?A.33 1/3%B.40%C.50%D.60%E.66 2/3%Answer:-------------------------------------------------------------------------------------------------------Q18:A construction company was paid a total of $500,000 for a construction project. The company’s only costs for the project were for labor and materials. Was the company’s profit for the project greater than $150,000?(1) The company’s total cost was three times its cost for materials.(2) The company’s profit was greater than its cost for labor.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:Q19:There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this self include at least one paperback?A.40B.45C.50D.55E.60Answer:Q20:EA DIn the figure, each side of square ABCD has length 1, the length of line segment CE is 1, and the length of line segment BE is equal to the length of line segment DE. What is the area of the triangular region BCE?A.1/3B.(√2)/4C.1/2D.(√2)/2E.3/4Answer:Q21:There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?A.1/2B.2/3C.32/35D.11/12E.13/14Answer:-------------------------------------------------------------------------------------------------------Q22:What is the remainder when the two digit, positive integer x is divided by 3?(1) The sum of the digits of x is 5.(2) The remainder when x is divided by 9 is 5.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q23:If (y+3)(y-1) – (y-2)(y-1) = r(y-1), what is the value of y?(1) r2 = 25(2) r = 5A. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q24:If n and k are positive integers, is n/k an even integer?(1) n is divisible by 8.(2) k is divisible by 4.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q25:If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?(1) 2 is not a factor of n.(2) 3 is not a factor of n.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q26:Which of the following is equal to [1/(√3 - √2)]2?A.1B. 5C.√6D.5 - √6E. 5 + 2√6Answer:-------------------------------------------------------------------------------------------------------Q27:If S is a set of ten consecutive integers, is the integer 5 in S?(1) The integer –3 is in S.(2) The integer 4 is in S.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q28:If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?(1) k is parallel to the line with equation y = (1-m)x + b +1.(2) k intersects the line with equation y = 2x + 3 at the point (2, 7).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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q29:If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?A.600B.700C.900D.2,100E.4,900Answer:-------------------------------------------------------------------------------------------------------Q30:What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?(1) The average height of the students in class X is 120 centimeters.(2) The average height of the students in class X and class Y combined is 126centimeters.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q31:On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?A.0.008B.0.128C.0.488D.0.512E.0.640Answer:-------------------------------------------------------------------------------------------------------Q32If x < 0, then √(-x│x│) isA.-xB.-1C. 1D.xE.√xAnswer:------------------------------------------------------------------------------------------------------Q33:If x > 0.9, which of the following could be the value of x?A.√0.81B.√0.9C.(0.9)2D.(0.9)(0.99)E. 1 - √0.01Answer:-------------------------------------------------------------------------------------------------------Q34:If Antonio bought two half-gallon cartons of ice cream during a special sale, what percent of the total regular price of the two cartons did he save?(1) Antonio paid the regular price for the first carton and received the second carton forhalf the regular price.(2) The regular price of the ice cream Antonio bought was $4.00 per half-gallon carton.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q35:If n is a positive integer, which of the following is a possible value of |56 - 5n|?A.7B.9C.12D.15E.20Answer:-------------------------------------------------------------------------------------------------------Q36:If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?A.20B.40C.50D.80E.120Answer:-------------------------------------------------------------------------------------------------------Q37√[2√63 + 2/(8+3√7)] =A.8 + 3√7B. 4 + 3√7C.8D.4E.√7Answer:-------------------------------------------------------------------------------------------------------Q38:The infinite sequence a1, a2,…, a n,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and a n = a n-4 for n > 4. What is the sum of the first 97 terms of the sequence?A.72B.74C.75D.78E.80Answer:-------------------------------------------------------------------------------------------------------Q39:What is the value of │x+ 7│?(1) │x+ 3│= 14(2) (x + 2)2 = 169A. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q40:In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =A.6B. 5C. 4D.3E. 2Answer:------------------------------------------------------------------------------------------------------------Q41:A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)A.65 mphB.68 mphC.70 mphD.75 mphE.80 mphAnswer:------------------------------------------------------------------------------------------------------------Q42:Professor Vásquez gave a quiz to two classes. Was the range of scores for the first class equal to the range of scores for the second class?(1) In each class, the number of students taking the quiz was 26, and the lowest score ineach class was 70.(2) In each class, the average (arithmetic mean) score on the quiz was 85.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q43:Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. What percent of the families in City X owned a personal computer in 1998?A.50%B.52%C.56%D.70%E.74%Answer:------------------------------------------------------------------------------------------------------------Q44:If b, c, and d are constants and x2 + bx + c = (x + d)2 for all values of x, what is the value of c?(1) d = 3(2) b = 6A. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q45:If a, b, k, and m are positive integers, is a k a factor of b m?(1) a is a factor of b.(2) k≤ mA. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q46:If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?(1) None of the four numbers is greater than 60.(2) Two of the four numbers are 9 and 10, respectively.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q47:If n is the greatest positive integer for which 2n is a factor of 10!, then n =A.2B. 4C. 6D.8E.10Answer:-------------------------------------------------------------------------------------------------------Q48:Is │x - y│>│x - z│?(1) │y│>│z│(2) x < 0A. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q49:At a certain company, 25 percent of the employees are male and 50 percent of the employees are sales staff. What is the number of employees at this company?(1) Exactly 7 of the employees at the company are males who are sales staff.(2) There are 16 more female employees than male employees at the company.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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:-------------------------------------------------------------------------------------------------------Q50:If –4 < x < 7 and –6 < y < 3, which of the following specifies all the possible values of xy?A.–42 < xy < 21B.–42 < xy < 24C.–28 < xy < 18D.–24 < xy < 21E.–24 < xy < 24Answer:------------------------------------------------------------------------------------------------------------Q51:From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?1A.104B.91C.23D.52E.3Answer:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q52:For any integer k greater than 1, the symbol k * denotes the product of all the fractions of the form t1, where t is an integer between 1 and k , inclusive. What is the value of**45?A. 5B. 45C. 54D. 41E.51Answer:------------------------------------------------------------------------------------------------------------ Q53:Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month,32 were basic and the rest were deluxe. If it takes57 as manyhours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?A. 177B. 3114C. 157D. 3517E.21Answer:------------------------------------------------------------------------------------------------------------ Q54:On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J . Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?A. 6B. 13C. 18D. 20E. 24Answer:Q55:If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n (n + 1)(n + 2) will be divisible by 8?A. 41B. 83C. 21D. 85E.43Answer:------------------------------------------------------------------------------------------------------------ Q56:The annual rent collected by a corporation from a certain building was x percent more in1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?(1) x > y(2)100xy < x – yA. 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. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q57:。