INDEX – Drill Questions

Sr No Particulars Page No
1 Additional GRE Drill Questions 3-16
2 Drill Questions based on Charts and Graphs 17-24
3 Answer Key 25-26

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 1. Sadie distributes her collection of paintings, giving one -third of the paintings to friends and
selling half of the paintings. If she keeps the remaining paintings, what fraction of her
collection does Sadie keep?

2. The original price of an item at a store is 40% more than the price the retailer paid for it. To
encourage sales, the retailer reduces the price of the item by 15% from the original selling price.
If the retailer sells the item at the reduced cost, his profit is what percent of his cost?

3. On Sunday Belmond Public Library has 160 books, none of which have been checked out. On
Monday, 40 of the books are checked out. On Tuesday, 1/2 of the borrowed books are returned.
On Wednesday 1/2 of the books still checked out are returned and then 20 more are checked
out. On Thursday a wealthy patron donates 80 books, and 1/6 of the books still checked out are
returned. On Friday 30 more books are borrowed and on Saturday 35 are checked out. What is
the % change from the books in the library at the end of the day on Monday to the books in the
library at the end of the day the following Saturday?

4. In the wheel below, with center 0, the area of the entire wheel is 169 π . If the area of the
shaded hubcap is 144 π then t =
t

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5. For the final exam in a section diving certification course, Karl has to navigate underwater from
one point in a lake to another. Karl began the test at the boat and swam due south for 7 meters.
He then turned due east and swam for x meters. When he surfaced, he was 25 meters from the
boat. What is the value of x?

6. At a recent dog show, there were 5 finalists. One of the finalists was awarded Best in Show and
another finalist was awarded Honorable Mention. In how many ways the two awards be given
out?

7. Joe has $200. If he buys a CD player of $150, what is the greatest number of CDs he can buy with
the remaining money if CDs cost $12 each?

8. 20% of the sweaters in a store are white. Of the remaining sweaters 40% are brown, and the rest
are blue. If there are 200 sweaters in the store, then how many more blue sweaters than white
sweaters are in the store?

9. Oil is pumped from a well at a rate of 500 gallons per hour. How many gallons of oil are pumped
from the well in 3 hours and 15 minutes?
 10. At an office, 25% of the employees take the subway to work. Among those who ride the subway
42% transfer from one subway line to another during their commutes, and the rest do not
transfer. What percent of all employees transfer lines?

11. Y is a point on line segment XZ such that XY = 1/2 XZ. If length of YZ is 4a+6 and the length of XZ
is 68, then a =

12. The average arithmetic mean of a and b is 10 and the average arithmetic mean of c and d is 7. If
the average arithmetic mean of a, b and c is 8, what is the value of d?

13. One quarter of the cars that an automobile manufacturer produces is sports cars, and the rest
are sedans. If one fifth of the cars that the manufacturer produces are red and one third of the
sport cars are red, then what fractions of the sedans is red?

14. A palindrome is a number, such as 93539 that reads the same forward and backward. How many
palindromes are there between 100 and 1000?

15. In writing all of the integers from 1 to 300, how many times the digit 1 is used?

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16. Judy plans to visit the National Gallery once each month in 2012 except in July and August when
she plans to go three times each. A single admission costs $3.50, a pass valid for unlimited visits
in any 3 month period can be purchased for $18, and an annual pass costs $60.00. What is the
least amount in dollars that Judy can spend for her intended number of visits?

17. On a certain French American committee, 2/3 of the members are men and 3/8 of the men are
Americans. If 3/5 of the committee members are French what fraction of the members are
American women?

18. The Lirr River runs from Rosedale in the west to Oceanside in the east with the current moving
at an average of 10 miles per hour. Sasha is traveling by motorboat from Oceanside to Rosedale
and back. If the water were not moving, Sasha's motorboat would travel at an average speed of
20 miles per hour. Given the current, what was Sasha's actual average speed in miles per hour
for the round trip?

19. Points A and B are separated by 50 miles on a straight road. Cyclist A leaves point A, heading
toward point B at a constant speed of 15 miles per hour. At the same time, cyclist B leaves point
B, traveling toward point A, at a constant speed of 10 miles per hour. After how many minutes
have elapsed will the two meet?
 20. In triangle ABC, x < y + z. What is one possible value of x? C
0
z

0
x y
0

A B

21. At Pedantic Publishing Corporation, 1/5 of the employees take the bus to work and 1/3 drive to
work. Of the employees who do not take the bus or drive to work, 1/4 takes the subway and the
rest either walk or ride a bicycle. If 1/7 of the remaining employees ride a bicycle to work, what
fraction of the employees walks to work?

22. If x, y and z are consecutive even integers, such that x < y < z and xyz = 960, what is the value of
z?

23. Set X consists of all the even integers from 1 to 100, inclusive, and set Y consists of all the
integers divisible by 5 from 1 to 100, exclusive. How many members of set X are not members of
set Y?

24. In the equation xz/y = 420, x is an integer with 3 distinct prime factors and y is a positive integer
with no prime factors. If z is a positive, non-prime number, what is one possible value of z?

2102 * 213 * 491 2

25. = 7x , x =
304 * 3

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26. What is the tenths digit of the quotient when thirty five hundredths is divided by four
thousandths?

27. The price of Mabel's car not including interest is 12% more than the price of Rose's car.
Combined, Mabel and Rose's cars cost $53,000. If Mabel's car loan interest rate was $5.20%,
what was the total cost of Mabel's car, including interest?

28. Jenny's factory produces gear shafts at the rate of 250 gear shafts per hour. She finds that she is
short 3000 gear shafts on an order that must be completed in the next 10 hours. By what
percent must Jenny increase her rate of production in gear shafts per hour, in order to complete
the order on time?

29. What is the value of x2-1, when 9x+1 = 27 x-1 ?

30. If 3
x3 4
x 13 4
 
= (x1 4 * x 5 4 ) , then x =
2
 0
31. If angle ABC = 150 and triangle CED is isosceles, what is the value of angle CED in degrees?

A B
C

E D

32. A photographer is using a bipod to steady his camera while taking pictures, as shown in the
figure above. The legs of the biped are 5 feet long and are currently 6 feet apart. If he pulls the
legs another 2 feet apart, the top of the biped drops, x feet is?

33. In triangle ABD, AC =4 and is perpendicular to BD , which is equal to 125% the length of AC .
What is the area of triangle ABD?
B
C

A D

34. A parabola follows the function f(x) = x - 7x + 3. Point A lies on the parabola at (2, s) and point B
lies on the parabola at (6, t). What is the distance from A to B rounded to the nearest
hundredths place?

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35. If the diameter of circle A is eight times that of circle B, what is the ratio of the area of circle A to
the area of the circle B?

36. On a rectangular coordinate plane, a circle centered at (0,0) is inscribed within a square with

adjacent vertices at (0,-2 2 ) and (2 2 , 0). What is the area of the region, rounded to the
nearest tenth, that is inside the square but outside the circle?

37. Points A and B lie along the circumference with center O. A second circle with center M has a
radius one third as long as that of the circle with center O. If the area of sector AOB is equal to
the area of the circle with center M, then what is the measure in degrees of angle AOB?

38. An interior designer decides to accent a wall with an evenly spaced row of stenciled circles. The
wall is 31'6" long and the stencil has an area of 36π square inches. If the designer wants to leave
a space of x inches between each circle and at either end of the row, and x is an integer then
what is the greatest possible number of circles that the designer can use?
 39. A single slice cut from the center of a circular pizza has an edge length (from the center of the
pizza to the edge of the crust) of 5", has an arc length of 1.25π”, and weigh 4 ounces. If a serving
weighs 8 ounces, then to the nearest integer, what is the largest number of servings that 6"
diameter pizzas can yield? (Note that servings must weigh 8 ounces, but they do not need to be
equal in shape.)

40. A is the center of the top face of the right circular cylinder in the figure below. If the degree
measure of angle BAC is four times that of angle ACB, and the height of the cylinder is equal to
the diameter of its base, then the volume of the shaded region is what fraction of the volume of
the entire cylinder?

41. The Pranger metal company makes solid cylindrical steel rods by melting down blocks of steel
and pouring the melted steel into molds. Each cylindrical rod has a diameter of 14 inches and a
height of 8 inches, and the dimensions of each steel block are 2 feet by 12 feet by 15 feet. If no
steel is lost in the production process, how many complete cylinders can be made from a single
block of steel?

42. A cylindrical object has a volume of 332.75π cubic inches and its height is equal to its diameter.
What is the radius of the object?

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43. What is the product of the factors of twice the sum of the roots of the equation
2x2-4x-6=0?

44. All of the students in a certain class are either 7 or 8 years old. 80% of the students are boys and
25% of the girls are 8 years old. If there are an equal number of 7 years olds and 8 year olds,
what percent of the students in the class are boys who are 7 years old?

45. If -4 ≤ a ≤ 9 and -3 ≤ b ≤ 2, then what is the greatest possible value of a-b?

46. If x-2 - 2 = -1.96, y1/3 -5 = -2, and xy> 0, then what is the value of xy?

47. If x is positive and y is 1 more than the square of x, then what is the value of x in terms of y?

x 2 − 4x + 4 6x −12
48. If = 2 , then x =
x + x −6
2
x + 6x + 9
 49. Five numbers in a set are arranged from least to greatest. If the median of the first two numbers
is 13 and the average (arithmetic mean) of the remaining numbers is 23, what is the average
(arithmetic mean) of the entire set?

50. If the average (arithmetic mean) of 31, 41 and p is between 29 and 47, inclusive, what is the
least possible value of (p -7)2 =

51. A pair of dice is tossed twice. What is the probability that the first toss gives a total of either 7 or
11 and the second gives a total of 7?

52. In both rural and urban areas of country G, the average number of holidays taken by citizens is B
and the annual number of holidays follows a normal distribution. In rural areas, 2% of the
citizens take more than 12 holidays per year. In urban areas, 2% of the citizens take more than
16 holidays per year. How much greater is the standard deviation of the annual number of
holidays taken by urban citizens than that of rural citizens?

53. If x equals all prime numbers that satisfy the inequality:

1 5
 2
10 − x x

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 What is the average value of x?

54. Noah's contracting company builds road at the rate of 1 mile per week, except during the rainy
season, when the rate drops to 1/2 mile per week. If Noah is hired to build 11 miles of the road,
and his company begins construction 5 weeks before the start of the rainy season, how many
weeks will it take Noah's company to complete the contract? (Rainy season lasts 14 weeks.)

55. Mary is building a pyramid out of stacked rows of soup cans. When completed the top row of
pyramid contains a single soup can and each row below the top row contains 6 more cans than
the one above it. If the completed pyramid contains 16 rows, then how many soup cans did
Mary use to build it?

56. A certain password must contain 3 distinct digits followed by 2 distinct capital letters. Given 10
digits and 26 capital letters, how many different passwords are possible?

57. Six students compete in a table tennis tournament. Each student plays each of the other
students four times. What is the total number of games played in the tournament?
 58. Jess has nine different statues and chooses three to arrange in a display. How many
arrangements can she make?

59. Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other
members. How many different committees could be selected?

60. There are six cars in a motorcade. How many different arrangements of cars in the motorcade
are possible?

61. 12 runners enter a race to compete for first, second and third place. How many different
combinations of winners are possible?

62. Paul and Allen are choosing ties out of a selection of three distinct red ties, five distinct green
ties and six distinct blue ties. If Paul and Allen each wear one tie, how many different ways could
they wear ties of the same color?

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63. If the x-coordinates of the two x-intercepts of a parabola are 3 - 2 and 5 + 2 , then what is
the distance between them?

64. The circle's circumference includes points (0, 3) and (3,0) and the base of the inscribed isosceles
triangle passes through the center of the circle. What is the area of the triangle?

65. If point A is at (0,8), point C is at (6, 0) and the distance from point B to point C is x, what is x/

7?

66. In the figure, circumference of the circle is equal to 8π and arc PQR is equal to 1/4 of the total
circumference. What is the approximate area of the shaded region? (Round your answer to the
nearest whole number)
 DRILL QUESTIONS BASED ON CHARTS & GRAPHS

A
REFER TO THE FOLLOWING DATA
Membership of the North County Auto Mechanics and Auto Sales Associations in 1998

Auto Mechanics Association Auto Sales Association

Gender
345 Male 500
464 Female 400
809 Total 900
Age
23 Youngest 25
68 Oldest 72
34 Average 44
Number of Children
125 0 209
223 1 126
204 2 98
117 3 85
54 4 132
52 5 128
34 6 or more 122
Highest Education
Level
129 Some High School 185
286 High School Graduate 419
307 College Graduate 202
87 Advanced Degrees 94

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Question A1
If 50 of the male members of the Auto Sale Association were replaced by 50 female members, what
would be the ratio of male to female members in the Auto-Sales Association ?

Question A2

If 92 members of the Auto Sales Association were females with 5 children, how many members of the
Auto Sales Association were males who did not have 5 children ?

Question A3
If all the members of the Auto Mechanics Association who held advanced degrees and all the members
of the Auto Mechanics Association who had at least 5 children voted for a measure, how many more
votes were needed to gain a majority ?

Question A4
Technology books have become an increasingly important subcategory of science/nature books. If
technology books represent 30% of new adult science/nature books half of used adult science/nature
books and 1/10 of children's science nature books, how many technology books were sold in 2005.
 B
REFER TO THE FOLLOWING DATA

AIRLINE DEPARTURES BY COUNTRY IN 1990 AND 2001

COUNTRY 1990 PERCENT 2001 PERCENT

United States 24.2 31.1
United Kingdom 10.8 9.5
France 9.1 5.0
Germany 5.5 6.2
Japan 4.3 3.1
Brazil 3.1 4.0
China 2.0 7.7
Spain 1.2 0.3
Australia 0.8 0.6
All Others 39.0 32.5
Total Number of Departures 12,050,205 18,205,301

Question B1

If the nine individually listed countries (excluding those characterize as “All Others”) are ranked for
highest to lowest by number of departures in 1990, how many countries ranked lower in 2001 than in
1990?

Question B2

To the nearest percent, what was the percentage increase for the country that experienced the greatest
percent increase in the number of departures between 1990 to 2001?

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 C
REFER TO THE FOLLOWING DATA

Question C1

If Happy Puppy Pet Depot saw the same percentage increase in total number of animals sold from 2003
to 2004 as it did from 2002 to 2003 how many animals, to the nearest integer, did the store sell in 2004
?

Question C2

In 2003, how many categories of animals individually accounted for more than 20% of the depot’s
annual sales?
 D

REFER TO THE FOLLOWING DATA

Tree Number of Number of Trees Standard Deviation of
Individuals Diameter
Oak 64 58 11.2
Maple 50 42 7.4
Hickory 12 17 9.6
Ash 8 39 14.5
Birch 7 25 12.0

Question D

How many maple trees had a diameter greater than 49.4 cm ?

REFER TO THE FOLLOWING DATA

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Question E

In which year was the change from the prior year of the combined GDP of the two countries the least?

F
HONEY PRODUCTION IN REGION Z: 1980 TO 1986

30
Pounds of Honey Produced

25

20
(in thousands)

15

10

0
1980 1981 1982 1983 1984 1985 1986

14
No. of Honey Producing colonies

12

10
(in thousands)

0
1980 1981 1982 1983 1984 1985 1986
 150
Average price per Pound of Honey

125

100
(in cents)

75

50

25
1980 1981 1982 1983 1984 1985 1986

Question F

For what year depicted in the graphs was the percent decrease from the previous year of the number of
honey producing colonies most similar to the average percent increase of the average price of a pound
of honey for the six year period?

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 G
2002 Airplane inventory for Airlines A and B by year of purchase
(As a percentage of 2002 inventory)

Airline A Airline B
(Total 2002 inventory: 250) (Total 2002 inventory: 450)

6% 2002 4%
% %
8% 2001 6%
% %
10% 2000 4%
% %
10% 1999 6%
% %
14% 1998 8%
% %
20% 1997 12%
% %
12% 1996 10%
% %
6% 1995 16%
% %
4% 1994 14%
% %
10% 1993 20%
% %

Question G

New regulations go into effect in 2003 that require all planes in inventory to be newer than ten years
old. Each year following 2002, both airlines need to sell the planes the regulations force them to
eliminate from inventory, and then use the proceeds of those sales to increase their inventory by 10%
(rounded down because they are unable to buy fractions of planes). What is the combined number of
planes owned by the two companies following their sales and purchases in 2004?
Answers to the Drill Questions

1. 1/6 34. 5.66

2. 19 35. 64:1
3. 25 36. 3.4
4. 1 37. 40
5. 24 38. 29
6. 20 39. 8
7. 4 40. 1/3
8. 56 41. 505
9. 1625 42. 5.5
10. 10.5 43. 8
11. 7 44. 35
12. 10 45. 12
13. 7/45 46. 135
14. 90 47. √(y-1)
15. 160 48. 3
16. 49.50 49. 19
17. 3/20 50. 64
18. 15 51. 1/27
19. 120 52. 2
20. 0<x<90 53. 10/3
21. 3/10 54. 17
22. 12 55. 736
23. 41 56. 468000
24. 4,6,10,14 57. 60
25. 6 58. 504
26. 5 59. 840
27. 29456 60. 720
28. 20 61. 1320
29. 24 62. 56
30. 3 63. 2 + √2
31. 30 64. 9
32. x=1 65. 2
33. 10 66. 4

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Answers to Drill Questions based on Charts and Graphs

Sr No Question Answer

1 A1 1:1

2 A2 464

3 A3 Answer cannot be determined from the given information

4 A4 109

5 B1 3

6 B2 285

7 C1 11111

8 C2 2

9 D 8

10 E 1986

11 F 2010

12 G 626