GRE Online Training

1. A large cube and a small cube are made of granite of uniform density- The large cube has

edges of length 1.2 meters and weighs 4.752 kilograms.

If the small cube has edges of length 10 centimeters, what is the weight, in grains, of the small cube?

2. For the 3 days shown with the greatest daily number of television viewers, approximately what was the average (arithmetic mean) daily number of television viewers who watched Show XI

3. In the at-plane, line k intersects the rectangle shown at points P and O.





Which of the following represents the slope of line k ?

A)





B)





C)





D)





E)

4. If one item is tobe randomly selected from the items whose manufacturing cost is greater than $140.

What is the probability that the item selected will be one whose manufacturing time is greater than 60 minutes?

A)





B)





C)





D)





E)

6. A candy retailer packs pieces of fudge either in boxes of 12 pieces each or in boxes of 15 pieces each. If the retailer uses only 12-piece boxes to pack a certain batch of fudge, then 1 piece will be left over. If the retailer uses only 15-piece boxes to pack the batch, then 10 pieces will be left over and the retailer will use 7 fewer boxes than when using the 12-piece boxes.

How many pieces of fudge are in the batch'1

7. All applicants for a certain job will take a skills test. An applicant who scores 80 percent or greater on the test has a probability of 0.65 of being hired.

8. The figure shows a semicircle intersected by a straight line in the rectangular coordinate system.





What is the area of the shaded region?

9.



A)





B)





C)





D)

10. A health club lias SOO members. 175 of whom exercised last Friday and 450 of whom exercised last Saturday. Of the members who exercised on at least one of the two days. 90 exercised both last Friday and last Saturday.

Which of the following statements are true?

11. A total of S72.000 was invested for one month in a new money market account that paid simple annual interest at the rate of r percent- If the investment earned $360 in interest for the month, what is the value of r?

12. Exhibit.





The 50 households are grouped according to the number of pets per household.

For the group with the greatest number of households having cats only, how many households have dogs only?

15.



A)





B)





C)





D)





E)

17. In triangle ABC, AB = 9 and BC = 12-

Which of the following values could be the perimeter of triangle ABC? Indicate all such values.

18. In each of the years after year A", the Alden family budgeted S200 more for savings than it budgeted for savings the previous year.





What is the total amount that the Alden family budgeted for savings over the 10 years beginning with year A"?

19. The right circular cylindrical tank above has inner dimensions of radius 4 feet and height 10 feet.





What is the greatest possible distance, in feet, between 2 points inside the tank?

A)





B)





C)





D)





E)

20. At a factory. 6 machines work independently at the same constant rate to produce certain parts.

If 5 of the machines, working simultaneously at this rate, produce a total of 200 such parts in 4 days, how many days will it take all 6 machines, working simultaneously at this rate, to produce a total of 300 such parts?

22. CORRECT TEXT

In a sequence of 300 numbers, the first number is 3. the second is 5. and each succeeding number is equal to the sum of the previous two numbers in the sequence.

If a number is to be randomly selected from the sequence, what is the probability that the number selected will be odd?

A)





B)





C)





D)





E)

24. Exhibit.





The variance of n numerical data x1, x2, x3, , , , , xn with the mean x is equal to







were S is the sum of the equal differences



for

For the shares of stock purchased and then sold by the investors shown, the mean of the 5 numbers for Stock Y is 50 and the corresponding mean for Stock X is 70.

The variance of the 5 numbers for Stock }' is what fraction of the corresponding variance for Stock X ?

A)





B)





C)





D)





E)

27.



If the area of triangle ABC shown is 120. what is the value of x?

29. If x < y, which of the following must be true?

A)





B)





C)





D)





E)

30. A continuous random variable R has a mean of 77 and a standard deviation of 8.

What is the value of R that is 2.5 standard deviations above the mean?

31. For which of the following values of v must x'-.x be divisible by 10?

Indicate all such values.

32. How many values of x are there such that x is an integer and |3x ― 2| < 8 ?

33. The cube root of which of the following integers is equal to

34. Exhibit.





Greg's income last year was $45,000. The graph above shows the distribution of his income, by income source.

Based on the information given, which of the following statements about his income last year are true?

Indicate all such statements.

36. Exhibit.





A group of 3 different investors is to be randomly selected from the 5 investors shown.

What is the probability that, for at least 2 of the 3 investors selected, the number of shares of Stock X purchased and then sold will be less than 1.5 times the corresponding number for stock Y?

A)





B)





C)





D)





E)

37. Exhibit.

38.



A)





B)





C)





D)





E)

39. Exhibit.

40. Exhibit.





What is the total number of cats and the total number of dogs in the households with 4 pets per household if 2 households have 3 cats and 1 dog per household and 2 households have 2 cats and 2 dogs per household?

41. Exhibit.





For selected minerals, the table shows the mineral content in an apple that weighs 100 grams and also shows the recommended daily allowance of the minerals.

For which of the following minerals is the total amount of the mineral contained in 5 such apples greater than 4 percent of the recommended dietary allowance of the mineral?

Indicate all such minerals.

42. A rectangular floor will be completely covered with square tiles, each of which has sides of length 6 inches. If tiles are laid side by side with no space between them and no tiles are cut. then the number of tiles needed to cover the floor is 1.080.

Which of the following could be the dimensions of the floor? (Note: 12 inches- 1 foot.)

43. Exhibit.





Which of the following is closest to the average rate of change, in tonnes per year, for maize production from 2012 to 2017?

44. In a competition, a certain contestant scored either 2 points or 4 points in each round of the competition. This contestant's average (arithmetic mean) score for the entire competition was 3.8 points per round.

46. CORRECT TEXT

The list price of a certain snowblower is S600.0O. At Store At the sale price of the snowblower is 10 percent less than its list price, and there is no sales tax. At Store y the sale price of the snowblower is 15 percent less than its list price, plus there is a sales tax of 5 percent of the sale price.

If the cost of the snowblower is equal to its sale price plus any applicable sales tax. how much greater is the cost of the snowblower at Store X than at Store Y?

47. Exhibit.





In the figure above, the circle has center O, and AB and AD are tangent to the circle. If the degree measures of angles ABC and ADC are 20 and 40. respectively, what is the value of x + y.

48. CORRECT TEXT

The units digit of 7 is v. and the units digit of





What is the value of the product xy

50. For a certain type of can. the number of grams of aluminum per can decreased by 20 percent from 1994 to 1998. while the cost per gram of aluminum decreased by 60 percent. If the cost of the aluminum in y cans in 1994 was equal to the cost of aluminum in A v cans in 1998. then k =

51. CORRECT TEXT

How many positive integers less than or equal to 29 can be expressed as the product of two different integers greater than 1?

53. The lengths of the sides of triangle RST are 3. 4. and v.

Which of the following inequalities specifies those values of y for which each angle measure of mangle RST is less than 90°?

A)





B)





C)





D)





E)

54. For a list of k consecutive integers, the median is m and the range is r.

Which of the following must be equal to K?

57. CORRECT TEXT

If the ratio of positive integer x to positive integer y is 4 to 3, then x + y must be a multiple of integer k. where k >I.

What is the value of k?

58. Exhibit.

59. An investor purchased two properties. A and B. The investor later sold property A at a selling price that was 20 percent more than the purchase price of A. and the investor sold property B at a selling price that was 40 percent less than the purchase price of B. If the combined purchase price of properties A and B was S200.000 and the combined selling price was S210.000.

What was the selling price of property A?

61. Exhibit.





Which of the following statements are true about the end-of-month stock prices from January to December? Indicate all such statements.

62. If a set 5 has a total of 6 subsets that consist of 2 members each, then S consists of how many members?

64. The graph summarizes the responses from 4.500 respondents who rated their degree of confidence in each of eight United States institutions. Each respondent gave each institution one of five confidence ratings: high, moderate, little, none, or undecided.





If 20 percent of the respondents rated both their degree of confidence in the federal government and their degree of confidence in the news media high or moderate, what percent of the respondents gave neither of these institutions a confidence rating of high or moderate?

66. CORRECT TEXT

67. In the figure above, what is the length of AB?

68. Which of the following is greatest?

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B)





C)





D)





E)

69. The graph summarizes the responses from 4.500 respondents who rated their degree of confidence in each of eight United States institutions. Each respondent gave each institution one of five confidence ratings: high, moderate, little, none, or undecided.





Of the respondents who did not rate their degree of confidence in the federal government undecided, approximately what fraction rated their degree of confidence in that institution little or none?

A)





B)





C)





D)





E)

70. Exhibit

73. The sequence a1, a2, a3 ,,,,an is defined by

76. The number of employees at a certain company on January 1, 2007, was k. which was 15 percent greater than the number of employees at the company on January 1. 2006.

77. If set 5 consists of the squares of the integers from -5 to 5. inclusive, how many elements are in set S ?

78.



In the figure, quadrilateral ABCD is inscribed in the circle and line segment AC is a diameter of the circle. The measure of angle BCD is v degrees, and the measure of angle BAD is v degrees.

What is the value of y in terms of x?

79. CORRECT TEXT





In the figure shown, what is the length of line segment BD ?

80. In a set of polygons, 80 percent are hexagons. Of the hexagons. 20 percent are regular hexagons.

81. The perimeter of rectangle ABCD is 20. and the length of each side is an integer.

Which of the following values could be the length of diagonal AC? Indicate all such values.

A)





B)





C)





D)

82. Exhibit.





For what number of pets per household is the total number of households the least?

85. In the circle with center O, if the length of minor arc MP is 3, what is the area of square region MOPQ?

86. Stations A. M. and B are located along a certain train route, and Station M is between Stations A and B. At noon, a train engine passed Station A traveling at a constant speed of SO kilometers per hour toward Station B. Also at noon, another train engine passed Station B traveling at a constant speed of 60 kilometers per hour toward Station A. Botli train engines passed Station M at the same time.

What is the ratio of the distance along the route between Stations A and .1/ to the distance along the route between Stations A and B?

A)





B)





C)





D)





E)

87. The probability that event R will occur is 0.65. The probability that event T will occur is 0.47.

89.



For each integer ;; greater than

I. the sum of the first » positive integers is given by the formula shown.

If the average (arithmetic mean) of the first // positive integers is k. what is the sum of the first n positive integers in terms of k?

A)





B)





C)





D)





E)

91. In a survey of 150 computer owners, 98 owned a primer. 72 owned a digital camera, and all of them owned either a printer or a digital camera or both.

92. CORRECT TEXT

The following appeared as a letter to the editor from the owner of a skate shop in Central Plaza.

"Two years ago the city council voted to prohibit skateboarding in Central Plaza. They claimed that skateboard users were responsible for litter and vandalism that were keeping other visitors from coming to the plaza. In the past two years, however, there has been only a small increase in the number of visitors to Central Plaza. and litter and vandalism are still problematic. Skateboarding is permitted in Monroe Park, however, and there is no problem with litter or vandalism there. In order to restore Central Plaza to its former glory, then, we recommend that the city lift its prohibition on skateboarding in the plaza."

Write a response in which you discuss what questions would need to be answered in order to decide whether the recommendation and the argument on which it is based are reasonable. Be sure to explain how the answers to these questions would help to evaluate the recommendation.

93. CORRECT TEXT

No act is done purely for the benefit of Claim: others

All actions―even those that seem to be done for other people―are based on self-interest.

Reason-Write a response in which you discuss the extent to which you agree or disagree with the claim and the reason on which that claim is based.

94. CORRECT TEXT

Colleges and universities should require their students to spend at least one semester studying in a foreign country.

Write a response in which you discuss the extent to which you agree or disagree with (lie claim. In developing and supporting your position- be sure to address the most compelling reasons and or examples that could be used to challenge your position.

95. CORRECT TEXT

The following appeared in a letter to the editor of a Batavia newspaper

"The department of agriculture in Batavia reports that the number of dairy farms throughout the country is now 25 percent greater than it was 10 years ago. During this same time period, however, the price of milk at the local Excello Food Market has increased from SI.50 to over $3.00 per gallon. To prevent farmers from continuing to receive excessive profits on an apparently increased supply of milk, the Batavia government should begin to regulate retail milk prices Such regulation is necessary to ensure fair prices for consumers."

Write a response in which you discuss what questions would need to be answered in order to decide whether the recommendation is likely to have the predicted result Be sure to explain how the answers to these questions would help to evaluate the recommendation

96. CORRECT TEXT

The following appeared in a memo from the president of Bower Builders, a company that constructs new homes.

"A nationwide survey reveals that the two most-desired home features are a large family room and a large, well-appointed kitchen. A number of homes in our area built by our competitor Domus Construction have such features and have sold much faster and at significantly higher prices than the national average. To boost sales and profits, we should increase the size of the family rooms and kitchens in all the homes we build and should make state-of-the-art kitchens a standard feature. Moreover, our larger family rooms and kitchens can come at the expense of the dining room, since many of our recent buyers say they do not need a separate dining room for family meals."

Write a response in which you examine the stated and or unstated assumptions of the argument. Be sure to explain how the argument depends on these assumptions and what the implications are for the argument if the assumptions prove unwarranted.

97. CORRECT TEXT

The following appeared in a letter to the editor of a Batavia newspaper

"The department of agriculture in Batavia reports that the number of dairy farms throughout the country is now 25 percent greater than it was 10 years ago. Dunne this same time period, however, the price of milk at the local Excello Food Market has increased from SI.50 to over S3.00 per gallon. To prevent farmers from continuing to receive excessive profits on an apparently increased supply of milk, the Batavia government should begin to regulate retail milk prices Such regulation is necessary to ensure fair prices for consumers."

Write a response in which you discuss what questions would need to be answered in order to decide whether the recommendation is likely to have the predicted result Be sure to explain how the answers to these questions would help to evaluate the recommendation

98. CORRECT TEXT

Claim: Governments must ensure that their major cities receive the financial support they need in order to thrive.

Reason: It is primarily in cities that a nation's cultural traditions are preserved and generated.

Write a response in which you discuss the extent to which you agree or disagree with the claim and the reason on which that claim is based.

99. CORRECT TEXT

The following appeared in a letter from the owner of the Sunnyside Towers apartment complex to its manager.

"Last week, all the showerheads in the first three buildings of the Sunnyside Towers complex were modified to restrict maximum water flow to one-third of what it used to be. Although actual readings of water usage before and after the adjustment are not yet available, the change will obviously result in a considerable savings for Sunnyside Corporation, since the corporation must pay for water each month. Except for a few complaints about low water pressure, no problems with showers have been reported since the adjustment. Clearly, modifying showerheads to restrict water flow throughout all twelve buildings in the Sunnyside Towers complex will increase our profits further."

Write a response in which you examine the stated and or unstated assumptions of the argument. Be sure to explain how the argument depends on these assumptions and what the implications are for the argument if the assumptions prove unwarranted.