Graduate Online Recruitment Test [grt4582]

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1. A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a twenty-day period.  What percent of the original amount of water evaporated during this period?  
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Graduate Online Recruitment Test [grt4582] - Quiz

This is a GMAT quantitative diagnostic test: Exam 1.

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2. A student's average (arithmetic mean) test score on 4 tests is 78.  What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?
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3. 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?  
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4. Theater M has 25 rows with 27 seats in each row.  How many of the seats were occupied during a certain show? (1)   During the show, there was an average (arithmetic mean) of 10 unoccupied seats per row for the front 20 rows.   (2)   During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row for the back 15 rows.  
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5.  In the xy-plane, line l and line k intersect at the point «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mfrac»«mn»16«/mn»«mn»5«/mn»«/mfrac»«mo»,«/mo»«mfrac»«mn»12«/mn»«mn»5«/mn»«/mfrac»«mo»)«/mo»«/math».  What is the slope of line l? (1)  The product of the slopes of line l and line k is –1.   (2)    Line k passes through the origin.  
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6. A certain candy manufacturer reduced the weight of candy bar M by 20 percent but left the price unchanged. What was the resulting percent increase in the price per ounce of the candy bar M?
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7. The tortoise and the hare are racing. The faster hare gives the tortoise a 1-hour head start. The tortoise runs the race at a constant speed of 2 kilometers per hour. The hare runs the race at a constant speed of 10 kilometers per hour. If the hare and the tortoise start from the same point and follow the same route, how long will it take the hare to overtake the tortoise ?  
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8. 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 126 centimeters.  
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9. Yesterday each of the 35 members of a certain task force spent some time working on project P.  The graph shows the number of hours and the number of members who spent that number of hours working on project P yesterday.  What was the median number of hours that the members of the task force spent working on project P yesterday?  
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10. The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions. What is the volume, in cubic centimeters of 1 gram of this substance under these condition (1 kilogram= 1000 grams and 1 cubic meter = 1,000,000 cubic centimeters. 
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11. In how many different ways can a chairperson and a secretary be selected from a committee of 9 people?  
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12.   For the cube shown above, what is the degree measure of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#8736;«/mo»«/math»PQR?  
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13. If «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mn»1«/mn»«/math», and «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»a«/mi»«mo»-«/mo»«mi»b«/mi»«/mrow»«mi»c«/mi»«/mfrac»«mo»=«/mo»«mn»1«/mn»«/math», which of the following is NOT a possible value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«/math» ?
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14. If f is the function defined for all k by «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»k«/mi»«mo»)«/mo»«/math» = «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»k«/mi»«mn»5«/mn»«/msup»«mn»16«/mn»«/mfrac»«/math», what is f(2k) in terms of f(k)?
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15. In the xy-plane, line k passes through the point (1,1) and line m passes through the point (1,-1).Are the lines k and m perpendicular to each other? (1)   Lines k and m intersect at the point (1,-1).   (2)   Line k intersects the x axis at the point (1,0).  
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16. There are 6 pairs of balls with each pair in a different color. If we select 2 from the 12 balls without replacement, what's the probability of selecting 2 balls with the same color?  
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17. If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2i3k5m7p, then i + k + m + p =
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18. In the figure above, O is the center of the circle.  If the area of the shaded region is 2π, what is the value of x?  
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19.   In the figure shown, the length of line segment QS is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math» . What is the perimeter of equilateral triangle PQR ?
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20. 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?
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21. Pierre is driving 50 miles per hour for the first 20 miles of a 40-mile trip. What must be his average speed in the remaining 20 miles in order for his total average speed to be 60 miles per hour?  
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22. If an automobile averaged 22.5 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline did the automobile average?  (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest tenth.)  
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23. Joshua and Jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers will be randomly chosen to be interviewd. What is the probability that Joshua and Jose both will be chosen? 
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24. If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?  
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25. The points R, T, and U lie on a circle that has radius 4.  If the length of arc RTU is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»4«/mn»«mi»§#960;«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math», what is the length of line segment RU?  
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26. Which of the following fractions has a decimal equivalent that is a terminating decimal?
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27. At a garage sale, all of the prices of the items sold were different.  If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?
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28. When flipped, a certain coin has an equal chance of landing on either side.  If the coin is flipped 6 times, what is the probability that it will land heads up on the first 3 flips,  and not on the last 3 ?  
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29. What is the value of the integer n? (1)   n(n + 2) = 15   (2)   (n + 2)n = 125  
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30. The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively.  If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?     I.               3 II.              7 III.            12
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31. The number of books read by 7 students is 10,5, «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»,«/mo»«mi»q«/mi»«mo»,«/mo»«mi»r«/mi»«/math», 29 and 20. what was the range of books read by 7 students? (1)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«mo»§lt;«/mo»«mi»p«/mi»«mo»§lt;«/mo»«mi»q«/mi»«/math»   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»§lt;«/mo»«mi»r«/mi»«mo»§lt;«/mo»«mn»15«/mn»«/math»  
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32. If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
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33.   Lines m and n intersect, as shown in the figure above.  What is the value of u - w? (1)   u = 90   (2)   Lines m and n are perpendicular.  
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34. Is x2 + y2 > 6? (1)   (x + y)2 > 6 (2)    xy = 2  
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35. If s4v3x7 < 0, is svx < 0? (1)   v < 0 (2)   x > 0  
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36. If the length of a certain rectangle is 2 greater than the width of the rectangle, what is the perimeter of the rectangle?   (1)   The length of each diagonal of the rectangle is 10.   (2)   The area of the rectangular region is 48.  
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37. Of 500 people surveyed, 78 percent said they use their laptop computers at home, 65 percent said they use them in cafes, and 52 percent said they use them both at home and in cafes. How many of the people surveyed said they do NOT use their laptop computers either at home or in cafes?
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38. What is the total value of Company H's stock?     (1)   Investor P owns «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math» of the shares of Company H's total stock.   (2)   The total value of Investor Q's shares of Company H's stock is $16,000.  
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39. 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?
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40. One day Hotel Merinda rented 75 percent of its rooms, including «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«/math» of its luxury rooms. If 60 percent of Hotel Merinda's rooms are luxury rooms, what percent of the rooms that were NOT rented are luxury rooms?  
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41. 2x + y = 12                                     «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨|¨ open=¨|¨»«mi»y«/mi»«/mfenced»«/math» ≤ 12 For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?  
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42. Three thousand families live in a certain town. How many families who live in the town own neither a car nor a television set? (1)   Of the families who live in the town, 2,980 own a car.   (2)   Of the families who live in the town, 2,970 own both a car and a television set.   
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43. If x is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x+y ?
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44. The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers.  If 2 committee members are to be selected at random to write the committee's report, what is the probability that the two members selected will be an English teacher and a Mathematics teacher?  
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45. Two different pipes fill the same pool. Pipe A fills «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math» of the capacity of the pool in 3 hours while pipe B fills «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«/math» of it in 6 hours. If the two pipes fill the pool simultaneously with their respective rates, how long will it take for the pool to be filled to capacity?  
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46. In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?  
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47. What is the sum of a certain pair of consecutive odd integers? (1)   At least one of the integers is negative.   (2)   At least one of the integers is positive.  
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48. Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours.  S and T, working together at their respective constant rates, can do the same job in 5 hours.  How many hours would it take R, working alone at its constant rate, to do the same job?
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49. A certain list consist of several different integers. Is the product of all integers in the list positive? (1)   The product of the greatest and smallest of the integers in the list is positive.   (2)   There is an even number of integers in the list.  
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50. If r is a constant and an = r·n for all positive integers n, for how many values of n is an < 100?   (1)   a50 = 500     (2)   a100 + a105 = 2,050  
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51. In a survey of 200 college graduates, 30 percent said they had received student loans during their college careers, and 40 percent said they had received scholarships.  What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers? (1)   25 percent of those surveyed said that they had received scholarships but no loans. (2)   50 percent of those surveyed who said that they had received loans also said that they had received scholarships.  
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52. Mary walked from home to work in the morning at an average speed of 3 miles per hour. She returned in the evening taking the same route running an average speed of 6 miles per hour. What was her average speed, in miles per hour, for the whole journey to and from work?   
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53. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office.  In how many ways can the company assign 3 employees to 2 different offices?  
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54. Is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» an odd integer? (1)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/math» is an even integer.   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»x«/mi»«mn»3«/mn»«/mfrac»«/math» is an odd integer.  
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55. 70, 75, 80, 85, 90, 105, 105, 130,130,130    The list shown consists of the times, in seconds, that it took each of 10 students to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 sec, rounded to nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?  
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56. Plane A leaves San Francisco International Airport for New York's John F. Kennedy International Airport, a distance of 2500 miles. At the same time, Plane B, taking the same route in the opposite direction, leaves New York's John F. Kennedy International Airport for San Francisco International Airport. How long will it take Plane A and Plane B to cross, assuming the average speed of Plane A was 475 miles per hour and the average speed of Plane B was 525 miles per hour at the time the two planes passed?  
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57. Pat invested x dollars in a fund that paid 8 percent annual interest, compounded annually.  Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years?
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58. Of the fruit that arrives at a cannery, 20 percent by weight is rejected before processing.  Of the fruit that is processed, 15 percent by weight is rejected before canning.  Of the fruit that arrives at the cannery, what percent by weight is canned?
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59. The operation ○ is defined by the equation «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8728;«/mo»«mi»y«/mi»«/math» = «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«/mrow»«/mfrac»«/math», where y ≠ -x.  If  «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§#8728;«/mo»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«mo»§#8728;«/mo»«mn»4«/mn»«/math», then «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math» =
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60. If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
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61.   In the parallelogram shown, what is the value of x? (1)   y = 2x   (2)   x + z = 120  
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62. On line segment AD shown, AB = «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math»CD and BC = 10.  If AD = 100, then CD =  
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63. Is xy > x2y2? (1)   14x2 = 3 (2)    y2 = 1  
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64. If r, s, and t are positive integers, is r + s + t even?   (1)   r + s is even.   (2)   s + t is even.  
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65. Company S produces two kinds of stereos:  basic and deluxe.  Of the stereos produced by Company S last month, «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«/math» were basic and the rest were deluxe.  If it takes «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»7«/mn»«mn»5«/mn»«/mfrac»«/math» as many hours 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?
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66. Over a certain time period, did the number of shares of stock in Ruth's portfolio increase?  (1)   Over the time period, the ratio of the number of shares of stock to the total number of shares of stocks and bonds in        Ruth's portfolio increased.    (2)  Over the time period, the total number of shares of stock and bonds in Ruth's portfolio increased.   
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67. 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.  
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68. In June 1989, what was the ratio of the number of sales transactions made by Salesperson X to the number of sales transactions made by Salesperson Y? (1)   In June 1989, Salesperson X made 50 percent more sales transactions than Salesperson Y did in May 1989. (2)   In June 1989, Salesperson Y made 25 percent more sales transactions than in May 1989.  
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69. Which of the following is equal to «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mn»2«/mn»«mn»12«/mn»«/msup»«mo»-«/mo»«msup»«mn»2«/mn»«mn»6«/mn»«/msup»«/mrow»«mrow»«msup»«mn»2«/mn»«mn»6«/mn»«/msup»«mo»-«/mo»«msup»«mn»2«/mn»«mn»3«/mn»«/msup»«/mrow»«/mfrac»«/math» ?
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70. What is the value of │x + 7│? (1)  │x + 3│= 14   (2)    (x + 2)2 = 169  
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71. Lines k and m are parallel to each other.  Is the slope of line k positive? (1)   Line k passes through the point (3, 2).   (2)   Line m passes through the point (-3, 2).  
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72. Is n divisible by 12?   (1)  «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»n«/mi»«mn»6«/mn»«/mfrac»«/math» is an integer.   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»n«/mi»«mn»4«/mn»«/mfrac»«/math» is an integer.  
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73. If «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«msup»«mn»2«/mn»«mi»x«/mi»«/msup»«mo»)«/mo»«mo»(«/mo»«msup»«mn»3«/mn»«mi»y«/mi»«/msup»«mo»)«/mo»«mo»=«/mo»«mn»288«/mn»«/math», where «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» and «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math» are positive integers, then «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«msup»«mn»2«/mn»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»)«/mo»«mo»(«/mo»«msup»«mn»3«/mn»«mrow»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»)«/mo»«mo»=«/mo»«/math»
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74. For a recent play performance, the ticket prices were $25 per adult and $15 per child.  A total of 500 tickets were sold for the performance.  How many of the tickets sold were for adults? (1)   Revenue from ticket sales for this performance totaled $10,500.   (2)   The average (arithmetic mean) price per ticket sold was $21.  
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75. (n-x) + (n-y) + (n-c) + (n-k) What is the value of the expression above? (1)   The average (arithmetic mean) of x, y, c, and k is n. (2)   x, y, c, and k are consecutive integers.  
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76. What is the ratio of the number of cups of flour to the number of cups of sugar required in a certain cake recipe?   (1)  The number of cups of flour required in the recipe is 250% of the number of cups of sugar required in the recipe.   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math» more cups of flour than cups of sugar are required in the recipe.  
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77. What is the remainder when the positive integer n is divided by 3?   (1)   The remainder when n is divided by 2 is 1.   (2)   The remainder when n + 1 is divided by 3 is 2.  
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78.  In the figure shown, what is the area of the circular region with center O and diameter BC? (1)  «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»B«/mi»«mi»C«/mi»«/mrow»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math»    (2)    «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mi»D«/mi»«mo»=«/mo»«mn»25«/mn»«/math»  
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79. When tossed, a certain coin has an equal chance of landing on either side.  If the coin is tossed 4 times, what is the probability that it will land on the same side each time?

Explanation


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80. Each week a certain salesman is made a fixed amount equal to $300 plus a commission equal to 5 percent of the amount of these sales that week over $1,000.  What is the total amount the salesman was paid last week?   (1)   The total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week.   (2)   The salesman's sales last week total $5,000.  
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81. Theater M has 25 rows with 27 seats in each row.  How many of the seats were occupied during a certain show? (1)   During the show, there was an average (arithmetic mean) of 10 unoccupied seats per row for the front 20 rows.   (2)   During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row for the back 15 rows.  
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82. If «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» and «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«/math» are integers, is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»§gt;«/mo»«mn»0«/mn»«/math» ? (1)  «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»+«/mo»«mn»1«/mn»«mo»§gt;«/mo»«mn»0«/mn»«/math»   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mi»p«/mi»«mo»§gt;«/mo»«mn»0«/mn»«/math»   
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83. If x and y are integers and x > 0, is y > 0?   (1)   7x – 2y > 0   (2)   -y < x  
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84. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mrow»«mo»[«/mo»«mn»2«/mn»«msqrt»«mn»63«/mn»«/msqrt»«mo»+«/mo»«mfrac»«mn»2«/mn»«mrow»«mo»(«/mo»«mn»8«/mn»«mo»+«/mo»«mn»3«/mn»«msqrt»«mrow»«mn»7«/mn»«mo»)«/mo»«/mrow»«/msqrt»«/mrow»«/mfrac»«mo»)«/mo»«mo»]«/mo»«/mrow»«/msqrt»«mo»=«/mo»«/math»
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85. The figure above shows two entries, indicated by m and n, in an addition table.  What is the value of n + m? (1)   d + y = -3   (2)   e + z = 12  
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86. Each of the numbers w, x, y, and z is equal to either 0 or 1. What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»w«/mi»«mo»+«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»?«/mo»«/math» (1)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»w«/mi»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mi»x«/mi»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mi»y«/mi»«mn»8«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mi»z«/mi»«mn»16«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mn»11«/mn»«mn»16«/mn»«/mfrac»«/math»   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»w«/mi»«mn»3«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mi»x«/mi»«mn»9«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mi»y«/mi»«mn»27«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mi»z«/mi»«mn»81«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mn»31«/mn»«mn»81«/mn»«/mfrac»«/math»  
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87. Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much to the project as Kate and «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/math» as much time as Mark, how many more hours did Mark charge to the project than Kate? 
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88. Is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨|¨ open=¨|¨»«mi»x«/mi»«/mfenced»«/math»+«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨|¨ open=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»= 1 ? (1)   x «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 0 (2)   x «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#8804;«/mo»«/math» 1  
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89. Is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«mo»=«/mo»«mi»z«/mi»«/math», is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨|¨ open=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«/mrow»«/mfenced»«/math» > 0 ? (1)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mn»0«/mn»«/math» (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«/math»  
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90. If x and y are integers, is x + y greater than 0?   (1)   x is greater than 0.   (2)   y is less than 1.  
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91. If the symbol ▼ represents either addition, subtraction, multiplication, or division, what is the value of 6 ▼ 2?   (1)   10 ▼ 5 = 2   (2)    4 ▼ 2 = 2  
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92. In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«/math».  What is the value of b? (1)   a = 4   (2)   c = −6  
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93. If «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» is a positive integer and «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«/math» is the remainder when «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msup»«mi»n«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/math» is divided by 8, what is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«/math»?  (1)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» is odd.   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» is not divisible by 8.  
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94. Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K.  What is the median weight of the 89 boxes on these shelves? (1)   The heaviest box on shelf J weighs 15 pounds. (2)    The lightest box on shelf K weighs 20 pounds.  
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95. If n and k are positive integers, is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»n«/mi»«mi»k«/mi»«/mfrac»«/math» an even integer?   (1)   n is divisible by 8.   (2)   k is divisible by 4.  
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96. The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4.  What is the sum of the first 97 terms of the sequence?
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97. If «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»y«/mi»«mo»+«/mo»«mn»3«/mn»«mo»)«/mo»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»-«/mo»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»2«/mn»«mo»)«/mo»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»=«/mo»«mi»r«/mi»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/math»,  what is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math»?   (1)     «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»25«/mn»«/math»   (2)     «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»=«/mo»«mo»-«/mo»«mn»5«/mn»«/math»  
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98. 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).  

Explanation

When 2 lines are parallel, their slopes are equal.

(1) Since the slope of K is m and the slope of the line y = (1-m)x + b +1 is m-1, we have m = 1-m, which gives  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math».

(1) is sufficient.

(2) Line k intersecting the line with equation y = 2x + 3 at the point (2,3) is useless to find the slope of k because we know only one point of k, (2,3). We need another point of k to find the slope of K.

(2) is not sufficient.

So the correct is (A).


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99. Working independently at their respective constant rates, pumps X and Y took 48 minutes to fill an empty tank with water. What fraction of the water in the full tank came from pump X?    (1)   Working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water.    (2)   Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank with water.    
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100. A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective contant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour? (1)   Working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water.    (2)   Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank with water.    
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101. In a poll involving two yes- or no-questions, all the people who were asked the two questions answered "yes" or "no". If 75 percent of these people answered "yes" to the first question, 55 percent of the people answered "yes" to the second question, and 20 percent of the people answered "no" to both questions, what percentage of the people answered "yes" to both questions?   
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102. What is the value of  «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mn»3«/mn»«mrow»«mo»-«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«/mrow»«/msup»«msup»«mn»3«/mn»«mrow»«mo»-«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»)«/mo»«/mrow»«/msup»«/mfrac»«/math» ?   (1)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mn»2«/mn»«/math»   (2)   «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«/math»  
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103.  Material A costs $3 per kilogram, and material B costs $5 per kilogram.  If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x > y? (1)  y > 4   (2)   The cost of the 10 kilograms of material K is less than $40.  
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