GRE CHALLENGING PROBLEMS...

Questions

1

_ Set 1

Start off with these simple series of numbers. Number

series questions measure your ability to reason without

words. To answer these questions, you must determine

the pattern of the numbers in each series before you will

be able to choose which number comes next. These

questions involve only simple arithmetic. Although

most number series items progress by adding or subtracting,

some questions involve simple multiplication

or division. In each series, look for the degree and

direction of change between the numbers. In other

words, do the numbers increase or decrease, and by

how much?

1. Look at this series: 2, 4, 6, 8, 10, . . . What number

should come next?

a. 11

b. 12

c. 13

d. 14

2. Look at this series: 58, 52, 46, 40, 34, . . . What

number should come next?

a. 26

b. 28

c. 30

d. 32

3. Look at this series: 40, 40, 47, 47, 54, . . . What

number should come next?

a. 40

b. 44

c. 54

d. 61

4. Look at this series: 544, 509, 474, 439, . . . What

number should come next?

a. 404

b. 414

c. 420

d. 445

5. Look at this series: 201, 202, 204, 207, . . . What

number should come next?

a. 205

b. 208

c. 210

d. 211

6. Look at this series: 8, 22, 8, 28, 8, . . . What

number should come next?

a. 9

b. 29

c. 32

d. 34

7. Look at this series: 80, 10, 70, 15, 60, . . . What

number should come next?

a. 20

b. 25

c. 30

d. 50

8. Look at this series: 36, 34, 30, 28, 24, . . . What

number should come next?

a. 20

b. 22

c. 23

d. 26

9. Look at this series: 22, 21, 23, 22, 24, 23, . . .

What number should come next?

a. 22

b. 24

c. 25

d. 26

–QUESTIONS–

2

10. Look at this series: 3, 4, 7, 8, 11, 12, . . . What

number should come next?

a. 7

b. 10

c. 14

d. 15

11. Look at this series: 31, 29, 24, 22, 17, . . . What

number should come next?

a. 15

b. 14

c. 13

d. 12

12. Look at this series: 21, 9, 21, 11, 21, 13, . . .

What number should come next?

a. 14

b. 15

c. 21

d. 23

13. Look at this series: 53, 53, 40, 40, 27, 27, . . .

What number should come next?

a. 12

b. 14

c. 27

d. 53

14. Look at this series: 2, 6, 18, 54, . . . What number

should come next?

a. 108

b. 148

c. 162

d. 216

15. Look at this series: 1,000, 200, 40, . . . What

number should come next?

a. 8

b. 10

c. 15

d. 20

16. Look at this series: 7, 10, 8, 11, 9, 12, . . . What

number should come next?

a. 7

b. 10

c. 12

d. 13

17. Look at this series: 14, 28, 20, 40, 32, 64, . . .

What number should come next?

a. 52

b. 56

c. 96

d. 128

18. Look at this series: 1.5, 2.3, 3.1, 3.9, . . . What

number should come next?

a. 4.2

b. 4.4

c. 4.7

d. 5.1

19. Look at this series: 5.2, 4.8, 4.4, 4, . . . What

number should come next?

a. 3

b. 3.3

c. 3.5

d. 3.6

20. Look at this series: 2, 1, _

1

2_, _

1

4_, . . . What number

should come next?

a. _

13

_

b. _

18

_

c. _

28

_

d. _1

1

6 _

–QUESTIONS–

3

_ Set 2 (Answers begin on page 101.)

This set contains additional, and sometimes more

difficult, number series questions. Again, each question

has a definite pattern. Some of the number series

may be interrupted by a particular number that

appears periodically in the pattern. For example, in

the series 14, 16, 32, 18, 20, 32, 22, 24, 32, the number

32 appears as every third number. Sometimes, the

pattern contains two alternating series. For example,

in the series 1, 5, 3, 7, 5, 9, 7, the pattern is add 4, subtract

2, add 4, subtract 2, and so on. Look carefully for

the pattern, and then choose which pair of numbers

comes next. Note also that you will be choosing from

five options instead of four.

21. 84 78 72 66 60 54 48

a. 44 34

b. 42 36

c. 42 32

d. 40 34

e. 38 32

22. 3 8 13 18 23 28 33

a. 39 44

b. 38 44

c. 38 43

d. 37 42

e. 33 38

23. 20 20 17 17 14 14 11

a. 8 8

b. 11 11

c. 11 14

d. 8 9

e. 11 8

24. 18 21 25 18 29 33 18

a. 43 18

b. 41 44

c. 37 18

d. 37 41

e. 38 41

25. 9 11 33 13 15 33 17

a. 19 33

b. 33 35

c. 33 19

d. 15 33

e. 19 21

26. 2 8 14 20 26 32 38

a. 2 46

b. 44 50

c. 42 48

d. 40 42

e. 32 26

27. 28 25 5 21 18 5 14

a. 11 5

b. 10 7

c. 11 8

d. 5 10

e. 10 5

28. 9 12 11 14 13 16 15

a. 14 13

b. 18 21

c. 14 17

d. 12 13

e. 18 17

29. 75 65 85 55 45 85 35

a. 25 15

b. 25 85

c. 35 25

d. 85 35

e. 25 75

–QUESTIONS–

4

30. 1 10 7 20 13 30 19

a. 26 40

b. 29 36

c. 40 25

d. 25 31

e. 40 50

31. 10 20 25 35 40 50 55

a. 70 65

b. 60 70

c. 60 75

d. 60 65

e. 65 70

32. 40 40 31 31 22 22 13

a. 13 4

b. 13 5

c. 4 13

d. 9 4

e. 4 4

33. 17 17 34 20 20 31 23

a. 26 23

b. 34 20

c. 23 33

d. 27 28

e. 23 28

34. 2 3 4 5 6 4 8

a. 9 10

b. 4 8

c. 10 4

d. 9 4

e. 8 9

35. 61 57 50 61 43 36 61

a. 29 61

b. 27 20

c. 31 61

d. 22 15

e. 29 22

36. 9 16 23 30 37 44 51

a. 59 66

b. 56 62

c. 58 66

d. 58 65

e. 54 61

37. 8 22 12 16 22 20 24

a. 28 32

b. 28 22

c. 22 28

d. 32 36

e. 22 26

38. 6 20 8 14 10 8 12

a. 14 10

b. 2 18

c. 4 12

d. 2 14

e. 14 14

39. 11 16 21 26 31 36 41

a. 47 52

b. 46 52

c. 45 49

d. 46 51

e. 46 52

40. 8 11 21 15 18 21 22

a. 25 18

b. 25 21

c. 25 29

d. 24 21

e. 22 26

ANSWERS:

1. b. This is a simple addition series. Each number

increases by 2.

2. b. This is a simple subtraction series. Each

number is 6 less than the previous number.

3. c. This is an alternation with repetition series

in which each number repeats itself and

then increases by 7.

4. a. This is a simple subtraction series. Each

number is 35 less than the previous number.

5. d. In this addition series, 1 is added to the first

number; 2 is added to the second number; 3

is added to the third number; and so forth.

6. d. This is a simple addition series with a random

number, 8, interpolated as every other

number. In the series, 6 is added to each

number except 8, to arrive at the next

number.

7. a. This is an alternating addition and subtraction

series. In the first pattern, 10 is subtracted

from each number to arrive at the

next. In the second, 5 is added to each number

to arrive at the next.

8. b. This is an alternating number subtraction

series. First, 2 is subtracted, then 4, then 2,

and so on.

9. c. In this simple alternating subtraction and

addition series; 1 is subtracted, then 2 is

added, and so on.

10. d. This alternating addition series begins with

3; then 1 is added to give 4; then 3 is added

to give 7; then 1 is added, and so on.

11. a. This is a simple alternating subtraction

series, which subtracts 2, then 5.

12. c. In this alternating repetition series, the random

number 21 is interpolated every other

number into an otherwise simple addition

series that increases by 2, beginning with

the number 9.

13. b. In this series, each number is repeated, then

13 issubtracted to arrive at the next number.

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

number is 3 times more than the previous

number.

15. a. This is a simple division series. Each number

is divided by 5.

99

16. b. This is a simple alternating addition and

subtraction series. In the first pattern, 3 is

added; in the second, 2 is subtracted.

17. b. This is an alternating multiplication and

subtracting series: First, multiply by 2 and

then subtract 8.

18. c. In this simple addition series, each number

increases by 0.8.

19. d. In this simple subtraction series, each number

decreases by 0.4.

20. b. This is a simple division series; each number

is one-half of the previous number.

–ANSWERS–

100

_ Set 2 (Page 4)

21. b. In this simple subtraction series, each number

is 6 less than the previous number.

22. c. In this simple addition series, each number

is 5 greater than the previous number.

23. e. This is a simple subtraction with repetition

series. It begins with 20, which is repeated,

then 3 is subtracted, resulting in 17, which

is repeated, and so on.

24. d. This is a simple addition series with a random

number, 18, interpolated as every third

number. In the series, 4 is added to each

number except 18, to arrive at the next

number.

25. a. In this alternating repetition series, a random

number, 33, is interpolated every third

number into a simple addition series, in

which each number increases by 2.

26. b. This is a simple addition series, which

begins with 2 and adds 6.

27. a. This is an alternating subtraction series with

the interpolation of a random number, 5, as

every third number. In the subtraction series,

3 is subtracted, then 4, then 3, and so on.

28. e. This is a simple alternating addition and

subtraction series. First, 3 is added, then 1 is

subtracted, then 3 is added, 1 subtracted,

and so on.

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

random number, 85, is interpolated as every

third number. In the subtraction series, 10 is

subtracted from each number to arrive at the

next.

30. c. Here, every other number follows a different

pattern. In the first series, 6 is added to each

number to arrive at the next. In the second

series, 10 is added to each number to arrive at

the next.

31. e. This is an alternating addition series, in

which 10 is added, then 5, then 10, and

so on.

32. a. This is a subtraction series with repetition.

Each number repeats itself and then

decreases by 9.

33. e. This is an alternating subtraction series with

repetition. There are two different patterns

here. In the first, a number repeats itself;

then 3 is added to that number to arrive at

the next number, which also repeats. This

gives the series 17, 17, 20, 20, 23, and so on.

Every third number follows a second pattern,

in which 3 is subtracted from each

number to arrive at the next: 34, 31, 28.

34. d. This is an alternating addition series with a

random number, 4, interpolated as every

third number. In the main series, 1 is added,

then 2 is added, then 1, then 2, and so on.

35. e. This is an alternating repetition series, in

which a random number, 61, is interpolated

as every third number into an otherwise

simple subtraction series. Starting with the

second number, 57, each number (except

61) is 7 less than the previous number.

36. d. Here is a simple addition series, which

begins with 9 and adds 7.

37. c. This is an alternating repetition series, with a

random number, 22, interpolated as every

third number into an otherwise simple addition

series. In the addition series, 4 is added

to each number to arrive at the next number.

38. d. This is an alternating addition and subtraction

series. In the first pattern, 2 is added to

each number to arrive at the next; in the

alternate pattern, 6 is subtracted from each

number to arrive at the next.

39. d. In this simple addition series, each number

is 5 more than the previous number.

40. b. This is an alternating addition series, with a

random number, 21, interpolated as every

third number. The addition series alternates

between adding 3 and adding 4. The number

21 appears after each number arrived at

by adding 3.