GRE CHALLENGING PROBLEMS....

_ Set 3

This set will give you additional practice dealing with

number series questions.

41. 44 41 38 35 32 29 26

a. 24 21

b. 22 19

c. 23 19

d. 29 32

e. 23 20

42. 6 10 14 18 22 26 30

a. 36 40

b. 33 37

c. 38 42

d. 34 36

e. 34 38

43. 34 30 26 22 18 14 10

a. 8 6

b. 6 4

c. 14 18

d. 6 2

e. 4 0

44. 2 44 4 41 6 38 8

a. 10 12

b. 35 32

c. 34 9

d. 35 10

e. 10 52

45. 32 29 26 23 20 17 14

a. 11 8

b. 12 8

c. 11 7

d. 32 29

e. 10 9

46. 14 14 26 26 38 38 50

a. 60 72

b. 50 62

c. 50 72

d. 62 62

e. 62 80

47. 8 12 9 13 10 14 11

a. 14 11

b. 15 12

c. 8 15

d. 15 19

e. 8 5

48. 4 7 26 10 13 20 16

a. 14 4

b. 14 17

c. 18 14

d. 19 13

e. 19 14

49. 3 8 10 15 17 22 24

a. 26 28

b. 29 34

c. 29 31

d. 26 31

e. 26 32

50. 17 14 14 11 11 8 8

a. 8 5

b. 5 2

c. 8 2

d. 5 5

e. 5 8

51. 13 29 15 26 17 23 19

a. 21 23

b. 20 21

c. 20 17

d. 25 27

e. 22 20

–QUESTIONS–

6

52. 16 26 56 36 46 68 56

a. 80 66

b. 64 82

c. 66 80

d. 78 68

e. 66 82

53. 7 9 66 12 14 66 17

a. 19 66

b. 66 19

c. 19 22

d. 20 66

e. 66 20

54. 3 5 35 10 12 35 17

a. 22 35

b. 35 19

c. 19 35

d. 19 24

e. 22 24

55. 36 31 29 24 22 17 15

a. 13 11

b. 10 5

c. 13 8

d. 12 7

e. 10 8

56. 42 40 38 35 33 31 28

a. 25 22

b. 26 23

c. 26 24

d. 25 23

e. 26 22

57. 11 14 14 17 17 20 20

a. 23 23

b. 23 26

c. 21 24

d. 24 24

e. 24 27

58. 17 32 19 29 21 26 23

a. 25 25

b. 20 22

c. 23 25

d. 25 22

e. 27 32

59. 10 34 12 31 14 28 16

a. 25 18

b. 30 13

c. 19 26

d. 18 20

e. 25 22

60. 32 31 32 29 32 27 32

a. 25 32

b. 31 32

c. 29 32

d. 25 30

e. 29 30

–QUESTIONS–

7

_ Set 4

This set contains additional number series questions,

some of which are in Roman numerals. These items differ

from Sets 1, 2, and 3 because they ask you to find the

number that fits somewhere into the middle of the

series. Some of the items involve both numbers and letters;

for these questions, look for a number series and

a letter series. (For additional practice in working letter

series questions, see Set 5.)

61. Look at this series: 8, 43, 11, 41, __, 39, 17, . . .

What number should fill in the blank?

a. 8

b. 14

c. 43

d. 44

62. Look at this series: 15, __, 27, 27, 39, 39, . . .

What number should fill the blank?

a. 51

b. 39

c. 23

d. 15

63. Look at this series: 83, 73, 93, 63, __, 93, 43, . . .

What number should fill the blank?

a. 33

b. 53

c. 73

d. 93

64. Look at this series: 4, 7, 25, 10, __, 20, 16, 19, . . .

What number should fill the blank?

a. 13

b. 15

c. 20

d. 28

65. Look at this series: 72, 76, 73, 77, 74, __, 75, . . .

What number should fill the blank?

a. 70

b. 71

c. 75

d. 78

66. Look at this series: 70, 71, 76, __, 81, 86, 70, 91, . . .

What number should fill the blank?

a. 70

b. 71

c. 80

d. 96

67. Look at this series: 664, 332, 340, 170, __, 89, . . .

What number should fill the blank?

a. 85

b. 97

c. 109

d. 178

68. Look at this series: 0.15, 0.3, __, 1.2, 2.4, . . .

What number should fill the blank?

a. 4.8

b. 0.006

c. 0.6

d. 0.9

69. Look at this series: _

1

9_, _

1

3_, 1, __, 9, . . . What number

should fill the blank?

a. _

23

_

b. 3

c. 6

d. 27

70. Look at this series: U32, V29, __, X23, Y20, . . .

What number should fill the blank?

a. W26

b. W17

c. Z17

d. Z26

–QUESTIONS–

8

71. Look at this series: J14, L16, __, P20, R22, . . .

What number should fill the blank?

a. S24

b. N18

c. M18

d. T24

72. Look at this series: F2, __, D8, C16, B32, . . .

What number should fill the blank?

a. A16

b. G4

c. E4

d. E3

73. Look at this series: V, VIII, XI, XIV, __, XX, . . .

What number should fill the blank?

a. IX

b. XXIII

c. XV

d. XVII

74. Look at this series: XXIV, XX, __, XII, VIII, . . .

What number should fill the blank?

a. XXII

b. XIII

c. XVI

d. IV

75. Look at this series: VI, 10, V, 11, __, 12, III, . . .

What number should fill the blank?

a. II

b. IV

c. IX

d. 14

ANSWERS:

41. e. This is a simple subtraction series, in which

3 is subtracted from each number to arrive

at the next.

42. e. This simple addition series adds 4 to each

number to arrive at the next.

43. d. This is a simple subtraction series, in which

4 is subtracted from each number to arrive

at the next.

44. d. Here, there are two alternating patterns, one

addition and one subtraction. The first

starts with 2 and increases by 2; the second

starts with 44 and decreases by 3.

45. a. In this simple subtraction series, the numbers

decrease by 3.

46. b. In this simple addition with repetition

series, each number in the series repeats

itself, and then increases by 12 to arrive at

the next number.

47. b. This is an alternating addition and subtraction

series, in which the addition of 4 is

alternated with the subtraction of 3.

48. e. Two patterns alternate here, with every

third number following the alternate pattern.

In the main series, beginning with 4, 3

is added to each number to arrive at the

next. In the alternating series, beginning

with 26, 6 is subtracted from each number

to arrive at the next.

49. c. This is an alternating addition series that

adds 5, then 2, then 5, and so on.

50. d. In this simple subtraction with repetition

series, each number is repeated, then 3 is

subtracted to give the next number, which is

then repeated, and so on.

51. b. Here, there are two alternating patterns,

with every other number following a different

pattern. The first pattern begins with 13

and adds 2 to each number to arrive at the

next; the alternating pattern begins with 29

and subtracts 3 each time.

52. c. Here, every third number follows a different

pattern from the main series. In the main

series, beginning with 16, 10 is added to

each number to arrive at the next. In the

alternating series, beginning with 56, 12 is

added to each number to arrive at the next.

53. a. This is an alternating addition series with

repetition, in which a random number, 66,

is interpolated as every third number. The

regular series adds 2, then 3, then 2, and so

on, with 66 repeated after each “add 2” step.

54. c. This is an alternating addition series, with a

random number, 35, interpolated as every

third number. The pattern of addition is to

add 2, add 5, add 2, and so on. The number

35 comes after each “add 2” step.

55. e. This is an alternating subtraction series,

which subtracts 5, then 2, then 5, and so on.

56. c. This is an alternating subtraction series in

which 2 is subtracted twice, then 3 is subtracted

once, then 2 is subtracted twice, and

so on.

57. a. This is a simple addition series with repetition.

It adds 3 to each number to arrive at

the next, which is repeated before 3 is added

again.

58. c. Here, there are two alternating patterns.

The first begins with 17 and adds 2; the second

begins with 32 and subtracts 3.

59. a. Two patterns alternate here. The first pattern

begins with 10 and adds 2 to each

number to arrive at the next; the alternating

pattern begins with 34 and subtracts 3 each

time.

60. a. This is an alternating repetition series. The

number 32 alternates with a series in which

each number decreases by 2.

–ANSWERS–

102

_ Set 4 (Page 8)

61. b. This is a simple alternating addition and

subtraction series. The first series begins

with 8 and adds 3; the second begins with

43 and subtracts 2.

62. d. In this simple addition with repetition

series, each number in the series repeats

itself, and then increases by 12 to arrive at

the next number.

63. b. This is a simple subtraction series in which

a random number, 93, is interpolated as

every third number. In the subtraction

series, 10 is subtracted from each number to

arrive at the next.

64. a. Two series alternate here, with every third

number following a different pattern. In the

main series, 3 is added to each number to

arrive at the next. In the alternating series, 5

is subtracted from each number to arrive at

the next.

65. d. This series alternates the addition of 4 with

the subtraction of 3.

66. a. In this series, 5 is added to the previous

number; the number 70 is inserted as every

third number.

67. d. This is an alternating division and addition

series: First, divide by 2, and then add 8.

68. c. This is a simple multiplication series. Each

number is 2 times greater than the previous

number.

69. b. This is a multiplication series; each number

is 3 times the previous number.

70. a. In this series, the letters progress by 1; the

numbers decrease by 3.

71. b. In this series, the letters progress by 2, and

the numbers increase by 2.

72. c. The letters decrease by 1; the numbers are

multiplied by 2.

73. d. This is a simple addition series; each number

is 3 more than the previous number.

74. c. This is a simple subtraction series; each

number is 4 less than the previous number.

75. b. This is an alternating addition and subtraction

series. Roman numbers alternate with

Arabic numbers. In the Roman numeral

pattern, each number decreases by 1. In the

Arabic numeral pattern, each number

increases by 1.