Each Data Sufficiency question has a math problem and two statements, labeled (1) and (2), which present data. Using this data with your knowledge of math and everyday facts (such as the number of days in July or what counter-clockwise means), decide whether the data in the statements are enough to solve the problem. Then pick one of these answer choices:

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.

Note: In Data Sufficiency questions that ask for a quantity’s value, the data given in the statements are sufficient only when they make it possible to find exactly one numerical value for the quantity.

Questions 1 to 31 - Difficulty: Easy

1. Each car at a certain dealership is either blue or white. What is the average (arithmetic mean) sticker price of all the cars at the dealership?

1. Of all the cars at the dealership, 1/3 are blue and have an average sticker price of $21,000.
2. Of all the cars at the dealership, 2/3 are white and have an average sticker price of $24,000. 

2. A box contains only white balls and black balls. What is the probability that a ball selected at random from the box is white?

1. There are 100 balls in the box.
2. There are 40 black balls in the box.  

3. Rita’s monthly salary is 2/3 Juanita’s monthly salary. What is their combined monthly salary?

1. Rita’s monthly salary is $4,000.
2. Either Rita’s monthly salary or Juanita’s monthly salary is $6,000.
    

4. Each of the 120 students in a certain dormitory is either a junior or a senior. How many of the juniors have credit cards? 

1. 2/3 of the 120 juniors and seniors have credit cards.
2. The number of seniors who have credit cards is 20 more than the number of juniors who have credit cards.

5. If the average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was $65, what was the cost of the cardigan sweater?

1. The average cost per sweater for the 3 pullover sweaters was $55.
2. The most expensive of the 3 pullover sweaters cost $30 more than the least expensive.

6. In each quarter of 1998, Company M earned more money than in the previous quarter. What was the range of Company M’s quarterly earnings in 1998?

1. In the 2nd and 3rd quarters of 1998, Company M earned $4.0 million and $4.6 million, respectively.
2. In the 1st and 4th quarters of 1998, Company M earned $3.8 million and $4.9 million, respectively.  

7. The range of the heights of a group of high school juniors and seniors is 20 centimeters. What is the average (arithmetic mean) of the height of the tallest senior in the group and the height of the shortest junior in the group?

1. The average of the heights of the juniors in the group is 165 centimeters.
2. The average of the heights of the seniors in the group is 179 centimeters.

8. In a certain factory, hours worked by each employee in excess of 40 hours per week are overtime hours and are paid for at 1 + 1/2 times the employee’s regular hourly pay rate. If an employee worked a total of 42 hours last week, how much was the employee’s gross pay for the hours worked last week?

1. The employee’s gross pay for overtime hours worked last week was $30.
2. The employee’s gross pay for all hours worked last week was $30 more than for the previous week.

9. Did Insurance Company K have more than $300 million in total net profits last year?

1. Last year Company K paid out $0.95 in claims for every dollar of premiums collected.
2. Last year Company K earned a total of $150 million in profits from the investment of accumulated surplus premiums from previous years. 

10. How many hours would it take Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full?

1. Working alone at its constant rate, Pump A would empty the full tank in 4 hours 20 minutes.
2. Working alone, Pump B would empty the full tank at its constant rate of 72 liters per minute.

11. Maria left home 1/4 hour after her husband and drove over the same route as he had in order to overtake him. From the time she left, how many hours did it take Maria to overtake her husband?

1. Maria drove 60 miles before overtaking her husband.
2. While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband’s average rate.  

12. In a school that had a total of 600 students enrolled in the junior and senior classes, the students contributed to a certain fund. If all of the juniors but only half of the seniors contributed, was the total amount contributed more than $740 ?

1. Each junior contributed $1 and each senior who contributed gave $3.
2. There were more juniors than seniors enrolled in the school. 

13. How much did credit-card fraud cost United States banks in year X to the nearest $10 million?

1. In year X, counterfeit cards and telephone and mail-order fraud accounted for 39 percent of the total amount that card fraud cost the banks.
2. In year X, stolen cards accounted for $158.4 million, or 16 percent, of the total amount that credit-card fraud cost the banks.   

14. Company X’s profits this year increased by 25% over last year’s profits. Was the dollar amount of Company X’s profits this year greater than the dollar amount of Company Y’s?

1. Last year, the ratio of Company Y’s profits to Company X’s profits was 5:2.
2. Company Y experienced a 40% drop in profits from last year to this year.  

15. A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

1. The average annual salary of the employees in Divisions A and B combined is $45,000.
2. The average annual salary of the employees in Division C is $55,000. 

16. A candle company determines that, for a certain specialty candle, the supply function is p = m₁x + b₁ and the demand function is p = m₂x + b₂, where p is the best price of each candle, x is the number of candles supplied or demanded, and m₁, m₂, b₁, and b₂ are constants. At what value of x do the graphs of the supply function and demand function intersect?

1. m₁ = -m₂ = 0.005
2. b₂ - b₁ = 6

17. A certain ski shop sold 125 pairs of skis and 100 pairs of ski boots for a total of $75,000. What was the average (arithmetic mean) selling price of a pair of the ski boots?

1. The average selling price of a pair of skis was $300.
2. The selling price of a pair of ski boots varied from $150 to $900.  

18. Last year Publisher X published 1,100 books, consisting of first editions, revised editions, and reprints. How many first editions did Publisher X publish last year?

1. The number of first editions published was 50 more than twice the number of reprints published.
2. The number of revised editions published was half the number of reprints published.  

19. How old is Jane?

1. Ten years ago she was one-third as old as she is now.
2. In 15 years, she will be twice as old as she is now.   

20. What was the population of City X in 2002 ?

1. X’s population in 2002 increased by 2 percent, or 20,000 people, over 2001.
2. In 2001, X’s population was 1,000,000.  

21. Yesterday Bookstore B sold twice as many softcover books as hardcover books. Was Bookstore B’s revenue from the sale of softcover books yesterday greater than its revenue from the sale of hardcover books yesterday?

1. The average (arithmetic mean) price of the hardcover books sold at the store yesterday was $10 more than the average price of the softcover books sold at the store yesterday.
2. The average price of the softcover and hardcover books sold at the store yesterday was greater than $14. 

22. A customer purchased 6 shirts priced at $10.99 each, excluding sales tax. How much sales tax did he pay on this purchase?

1. The customer paid a 5 percent sales tax on the total price of the shirts.
2. The customer paid a total of $11.54 for each shirt, including sales tax.   

23. The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

1. The lengths of the pieces of rope are in the ratio 8 : 5.
2. One piece of rope is 15 feet longer than the other piece. 

24. An initial investment of $10,000 was deposited in a bank account one year ago, and additional deposits were made during the year. If no withdrawals were made, what was the total amount of interest earned on this account during the year?

1. The additional deposits during the year totaled $5,000.
2. The account earned interest at the annual rate of 6 percent compounded quarterly.  

25. A poplar tree was 3 feet high when it was planted on January 1, 1970. During what year did it pass the height of 20 feet?

1. On January 1, 1973, it was 24 feet high.
2. It doubled its height during each year.  

26. Which weighs more, a cubic unit of water or a cubic unit of liquid X ?

1. A cubic unit of water weighs more than 1/3 cubic unit of liquid X.
2. A cubic unit of liquid X weighs less than 3 cubic units of water.

27. What were the individual prices of the vases that an antique dealer bought at store X ?

1. The antique dealer bought exactly 3 vases at store X.
2. The antique dealer’s total bill at store X was $225.  

28. Was the average (arithmetic mean) sale price of a new home in region R last month at least $100,000 ?

1. Last month the median sale price of a new home in region R was at least $100,000.
2. Last month the sale prices of new homes in region R ranged from $75,000 to $150,000. 

29. If the capacity of tank X is less than the capacity of tank Y and both tanks begin to fill at the same time, which tank will be filled first?

1. Tank X is filled at a constant rate of 1.5 liters per minute.
2. Tank Y is filled at a constant rate of 120 liters per hour.  

30. At a certain company, 30 percent of the employees live in City R. If 25 percent of the company’s employees live in apartments in City R, what is the number of the employees who live in apartments in City R ?

1. Of the employees who live in City R, 6 do not live in apartments.
2. Of the employees, 84 do not live in City R. 

 31. What was Mary’s average (arithmetic mean) score on 4 tests?

1. Her average (arithmetic mean) score on 3 of the tests was 97.
2. Her score on one of the tests was 96.

 Questions 32 to 59 - Difficulty: Medium

32. The table shows the number of people who responded “yes” or “no” or “don’t know” when asked whether their city council should implement environmental programs X and Y. If a total of 1,000 people responded to the question about both programs, what was the number of people who did not respond “yes” to implementing either of the two programs?

1. The number of people who responded “yes” to implementing only Program X was 300.
2. The number of people who responded “no” to implementing Program X and “no” to implementing Program Y was 100.

33. An estimate of an actual data value has an error of p percent if p = (100|e - a|)/a , where e is the estimated value and a is the actual value. Emma’s estimate for her total income last year had an error of less than 20 percent. Emma’s estimate of her income from tutoring last year also had an error of less than 20 percent. Was Emma’s actual income from tutoring last year at most 45 percent of her actual total income last year?

1. Emma’s estimated income last year from tutoring was 30 percent of her estimated total income last year.
2. Emma’s estimated total income last year was $40,000.

34. Was Store K’s profit last month at least 10 percent greater than its profit the previous month?

1. Store K’s expenses last month were 5 percent greater than its expenses the previous month.
2. Store K’s revenues last month were 10 percent greater than its revenues the previous month.

35. Gross profit is equal to selling price minus cost. A car dealer’s gross profit on the sale of a certain car was what percent of the cost of the car?

1. The selling price of the car was 11/10 of the cost of the car.
2. The cost of the car was $14,500. 

36. When the wind speed is 9 miles per hour, the wind-chill factor w is given by

w = −17.366 + 1.19t,

where t is the temperature in degrees Fahrenheit. If at noon yesterday the wind speed was 9 miles per hour, was the wind-chill factor greater than 0 ?

1. The temperature at noon yesterday was greater than 10 degrees Fahrenheit.
2. The temperature at noon yesterday was less than 20 degrees Fahrenheit.

37. How many members of a certain legislature voted against the measure to raise their salaries?

1. 1/4 of the members of the legislature did not vote on the measure.
2. If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3 .

38. During a certain bicycle ride, was Sherry’s average speed faster than 24 kilometers per hour? (1 kilometer = 1,000 meters)

1. Sherry’s average speed during the bicycle ride was faster than 7 meters per second.
2. Sherry’s average speed during the bicycle ride was slower than 8 meters per second. 

39. Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours. In how many hours can Rafael tabulate the data working alone?

1. Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.
2. Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.

40. Yesterday between 9:00 a.m. and 6:00 p.m. at Airport X, all flights to Atlanta departed at equally spaced times and all flights to New York City departed at equally spaced times. A flight to Atlanta and a flight to New York City both departed from Airport X at 1:00 p.m. yesterday. Between 1:00 p.m. and 3:00 p.m. yesterday, did another pair of flights to these 2 cities depart from Airport X at the same time?

1. Yesterday at Airport X, a flight to Atlanta and a flight to New York City both departed at 10:00 a.m.
2. Yesterday at Airport X, flights to New York City departed every 15 minutes between 9:00 a.m. and 6:00 p.m. 

41. Of the total number of copies of Magazine X sold last week, 40 percent were sold at full price. What was the total number of copies of the magazine sold last week?

1. Last week, full price for a copy of Magazine X was $1.50 and the total revenue from full price sales was $112,500.
2. The total number of copies of Magazine X sold last week at full price was $75,000. 

42. What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

1. If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.
2. The range of the 6 annual salaries is $31,500. 

43. In a certain order, the pretax price of each regular pencil was $0.03, the pretax price of each deluxe pencil was $0.05, and there were 50% more deluxe pencils than regular pencils. All taxes on the order are a fixed percent of the pretax prices. The sum of the total pretax price of the order and the tax on the order was $44.10. What was the amount, in dollars, of the tax on the order?

1. The tax on the order was 5% of the total pretax price of the order.
2. The order contained exactly 400 regular pencils.  

44. A total of 20 amounts are entered on a spreadsheet that has 5 rows and 4 columns; each of the 20 positions in the spreadsheet contains one amount. The average (arithmetic mean) of the amounts in row i is R_i (1 ≤ i ≤ 5). The average of the amounts in column j is C_j (1 ≤ j ≤ 4). What is the average of all 20 amounts on the spreadsheet?

1. R₁ + R₂ + R₃ + R₄ + R₅ = 550
2. C₁ + C₂ + C₃ + C₄ = 440  

45. Was the range of the amounts of money that Company Y budgeted for its projects last year equal to the range of the amounts of money that it budgeted for its projects this year?

1. Both last year and this year, Company Y budgeted money for 12 projects and the least amount of money that it budgeted for a project was $400
2. Both last year and this year, the average (arithmetic mean) amount of money that Company Y budgeted per project was $2,000. 

46. What is the probability that Lee will make exactly 5 errors on a certain typing test?

1. The probability that Lee will make 5 or more errors on the test is 0.27.
2. The probability that Lee will make 5 or fewer errors on the test is 0.85. 

47. A small factory that produces only upholstered chairs and sofas uses 1 cushion for each chair and 4 cushions for each sofa. If the factory used a total of 300 cushions on the furniture it produced last week, how many sofas did it produce last week?

1. Last week the factory produced more chairs than sofas.
2. Last week the factory produced a total of 150 chairs and sofas. 

48. In year X were there more female salespersons in the securities sector than in the insurance sector?

1. There were more male salespersons in the insurance sector than in the securities sector.
2. The total number of salespersons was greater in the securities sector than in the insurance sector.

49. If a club made a gross profit of $0.25 for each candy bar it sold, how many candy bars did the club sell?

1. The total revenue from the sale of the candy bars was $300.
2. If the club had sold 80 more candy bars, its gross profits would have increased by 20 percent.

50. In one year 2,100 malpractice claims were filed with insurance company X and of these 1/4 resulted in a financial settlement. Of those resulting in a financial settlement of less than $400,000, what was the average payment per claim?

1. Company X paid a total of 24.5 million dollars to the claimants.
2. Only 5 claims resulted in payments of $400,000 or more. 

51. If there are 13 boys in club X, what is the average age of these boys?

1. The oldest boy is 13 years old and the youngest boy is 9 years old.
2. Eleven of the boys are either 10 years old or 11 years old. 

52. If all the employees of a company fall into one and only one of 3 groups, X, Y, or Z, with 250, 100, and 20 members in each group, respectively, what is the average (arithmetic mean) weekly salary of all the employees of this company, if all employees are paid every week of the year?

1. The average (arithmetic mean) annual salary of the employees in Group X is $10,000, in Group Y $15,000 and in Group Z $20,000.
2. The total annual payroll is $4,400,000. 

53. According to the graph above, the sale of fruits and vegetables in Store S last week accounted for what percent of the total sales income for the week?

1. Last week the total income from the sale of fruits and vegetables in Store S was $16,000.
2. x = 2y

54. Larry saves x dollars per month. Will Larry’s total savings one year from now exceed his present savings by at least $500 ? (Assume that there is no interest.)

1. In 6 months Larry’s total savings will be $900.
2. In 3 months Larry’s total savings will exceed his present savings by $150. 

55. If Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice, what is the combined number of coins that all three of them have?

1. Alice has 4 fewer coins than Randy.
2. Maria has 20 more coins than Randy. 

56. A line of people waiting to enter a theater consists of seven separate and successive groups. The first person in each group purchases one ticket for each person in the group and for no one else. If n is the total number of tickets sold for the first six groups, is n an even number?

1. There are no more than 4 people in each group.
2. The 19th person in line purchases the tickets for the seventh group.

57. If John has exactly 10 coins each of which was minted in 1910 or 1920 or 1930, how many of his coins were minted in 1920 ?

1. Exactly 6 of his coins were minted in 1910 or 1920.
2. Exactly 7 of his coins were minted in 1920 or 1930. 

58. The total profit of corporation K was $3,400,000 in year X. What was the total profit in year Y ?

1. Income in year Y was 30 percent more than in year X.
2. Costs in year Y were 40 percent more than in year X. 

59. Zelma scored 90, 88, and 92 on 3 of the 6 mathematics tests that she took. What was her average (arithmetic mean) score on the 6 tests?

1. Her average (arithmetic mean) score on 5 of the tests was 90.
2. Her score on one of the tests was 91. 

Questions 60 to 83 - Difficulty: Hard 

60. What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

1. 28 percent of the students at University X are enrolled in a biology course.
2. 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.

61. Each Type A machine fills 400 cans per minute, each Type B machine fills 600 cans per minute, and each Type C machine installs 2,400 lids per minute. A lid is installed on each can that is filled and on no can that is not filled. For a particular minute, what is the total number of machines working?

1. A total of 4,800 cans are filled that minute.
2. For that minute, there are 2 Type B machines working for every Type C machine working.

62. In a two-month survey of shoppers, each shopper bought one of two brands of detergent, X or Y, in the first month and again bought one of these brands in the second month. In the survey, 90 percent of the shoppers who bought Brand X in the first month bought Brand X again in the second month, while 60 percent of the shoppers who bought Brand Y in the first month bought Brand Y again in the second month. What percent of the shoppers bought Brand Y in the second month?

1. In the first month, 50 percent of the shoppers bought Brand X.
2. The total number of shoppers surveyed was 5,000.

63. If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?

1. If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.
2. If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.

64. In Year X, 8.7 percent of the men in the labor force were unemployed in June compared with 8.4 percent in May. If the number of men in the labor force was the same for both months, how many men were unemployed in June of that year?

1. In May of Year X, the number of unemployed men in the labor force was 3.36 million.
2. In Year X, 120,000 more men in the labor force were unemployed in June than in May. 

65. On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning?

1. The machine began filling the order at 9:30 a.m.
2. The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 of the order by 11:10 a.m. 

66. After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?

1. Team A played 25 games altogether.
2. Team A won 60 percent of all the games it played.

67. Michael arranged all his books in a bookcase with 10 books on each shelf and no books left over. After Michael acquired 10 additional books, he arranged all his books in a new bookcase with 12 books on each shelf and no books left over. How many books did Michael have before he acquired the 10 additional books?

1. Before Michael acquired the 10 additional books, he had fewer than 96 books.
2. Before Michael acquired the 10 additional books, he had more than 24 books.

68. Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

1. Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
2. Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

69. For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2r dollars for each additional hour or fraction of an hour, where r > 100. Did a particular landscaping job take more than 10 hours?

1. The contractor charged a total of $288 for the job.
2. The contractor charged a total of 2.4r dollars for the job.

70. If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1. 60 percent of the guests who ordered dessert also ordered coffee.
2. 90 percent of the guests who ordered coffee also ordered dessert.

71. A tank containing water started to leak. Did the tank contain more than 30 gallons of water when it started to leak? (Note: 1 gallon = 128 ounces)

1. The water leaked from the tank at a constant rate of 6.4 ounces per minute.
2. The tank became empty less than 12 hours after it started to leak.   

72. Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a paperback written in Spanish?

1. Of the books on the shelf, 30 are paperbacks.
2. Of the books on the shelf, 15 are written in Spanish.  

73. A small school has three foreign language classes, one in French, one in Spanish, and one in German. How many of the 34 students enrolled in the Spanish class are also enrolled in the French class?

1. There are 27 students enrolled in the French class, and 49 students enrolled in either the French class, the Spanish class, or both of these classes.
2. One-half of the students enrolled in the Spanish class are enrolled in more than one foreign language class. 

74. Last year 3/5 of the members of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?

1. More than half of the new members are male.
2. The number of members of the club this year is 6/5 the number of members last year.  

75. Machines K, M, and N, each working alone at its constant rate, produce 1 widget in x, y, and 2 minutes, respectively. If Machines K, M, and N work simultaneously at their respective constant rates, does it take them less than 1 hour to produce a total of 50 widgets?

1. x < 1.5
2. y < 1.2  

76. Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

1. At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
2. Train Q averaged a speed of 55 miles per hour for the entire trip. 

77. In a two-story apartment complex, each apartment on the upper floor rents for 75 percent as much as each apartment on the lower floor. If the total monthly rent is $15,300 when rent is collected on all of the apartments, what is the monthly rent on each apartment on the lower floor?

1. An apartment on the lower floor rents for $150 more per month than an apartment on the upper floor.
2. There are 6 more apartments on the upper floor than on the lower floor.

78. A motorboat, which is set to travel at k kilometers per hour in still water, travels directly up and down the center of a straight river so that the change in the boat’s speed relative to the shore depends only on the speed and direction of the current. What is the value of k ?

1. It takes the same amount of time for the boat to travel 4 kilometers directly downstream as it takes for it to travel 3 kilometers directly upstream.
2. The current flows directly downstream at a constant rate of 2.5 kilometers per hour.  

79. If the book value of a certain piece of equipment was $5,000 exactly 5 years ago, what is its present book value?

1. From the time the piece of equipment was purchased, its book value decreased by 10 percent of its purchase price each year of its life.
2. The present book value of another piece of equipment is $2,000. 

80. The total cost to charter a bus was shared equally by the people who went on a certain trip. If the total cost to charter the bus was $360, how many people went on the trip?

1. Each person who went on the trip paid $9 to charter the bus.
2. If 4 fewer people had gone on the trip, each person’s share of the total cost to charter the bus would have increased by $1.  

81. If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought at least one of each denomination, what is the number of 25-cent stamps that she bought?

1. She spent a total of $1.45 for stamps.
2. She bought exactly 6 stamps.

82. A car traveled a distance of d miles in t minutes at an average rate of r miles per minute. What is the ratio of d to r ?

1. t = 30
2. d = 25 

83. Pat is reading a book that has a total of 15 chapters. Has Pat read at least 1/3 of the pages in the book?

1. Pat has just finished reading the first 5 chapters.
2. Each of the first 3 chapters has more pages than each of the other 12 chapters in the book.