directions to solve

8/15/2019 Directions to Solve

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Directions to Solve

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, 1, (1/2), (1/4), ... What number should come next?

A. (1/3) B. (1/)

C. (2/) D. (1/1!)

Answer & Explanation

Answer: "#tion B

Explanation:

$his is a sim#le di%ision series& each number is one'hal o the #re%ious number.

n other terms to sa*, the number is di%ided b* 2 successi%el* to +et the next result.

4/2 = 2 2/2 = 1 1/2 = 1/2 (1/2)/2 = 1/4 (1/4)/2 = 1/8 and so on.

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2.

Look at this series: , 1-, , 11, , 12, ... What number should come next?

A. B. 1-

C. 12 D. 13


Answer: "#tion B

Explanation:

$his is a sim#le alternatin+ addition and subtraction series. n the irst #attern, 3 is

added& in the second, 2 is subtracted.


3.

Look at this series: 3!, 34, 3-, 2, 24, ... What number should come next?

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A. 2- B. 22

C. 23 D. 2!


Answer: "#tion B

Explanation:

$his is an alternatin+ number subtraction series. irst, 2 is subtracted, then 4, then 2,

and so on.


4.

Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next?

A. 22 B. 24

C. 20 D. 2!


Answer: "#tion C

Explanation:

n this sim#le alternatin+ subtraction and addition series& 1 is subtracted, then 2 isadded, and so on.


0.

Look at this series: 03, 03, 4-, 4-, 2, 2, ... What number should come next?

A. 12 B. 14

C. 2 D. 03


Answer: "#tion B

Explanation:



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A. B. 1-

C. 14 D. 10


Answer: "#tion D

Explanation:

$his alternatin+ addition series be+ins ith 3& then 1 is added to +i%e 4& then 3 is added

to +i%e & then 1 is added, and so on.


.

Look at this series: , 22, , 2, , ... What number should come next?

A. B. 2

C. 32 D. 34


Answer: "#tion D

Explanation:

$his is a sim#le addition series ith a random number, , inter#olated as e%er* other

number. n the series, ! is added to each number exce#t , to arri%e at the next number.


1-.

Look at this series: 31, 2, 24, 22, 1, ... What number should come next?

A. 10 B. 14

C. 13 D. 12


Answer: "#tion A

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Explanation:

$his is a sim#le alternatin+ subtraction series, hich subtracts 2, then 0.

Directions to Solve



11.

Look at this series: 1.0, 2.3, 3.1, 3., ... What number should come next?

A. 4.2 B. 4.4

C. 4. D. 0.1


Answer: "#tion C

Explanation:

n this sim#le addition series, each number increases b* -..


12.

Look at this series: 14, 2, 2-, 4-, 32, !4, ... What number should come next?

A. 02 B. 0!

C. ! D. 12


Answer: "#tion B

Explanation:

$his is an alternatin+ multi#lication and subtractin+ series: irst, multi#l* b* 2 and then

subtract .




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7/32

Explanation:

$his is a sim#le subtraction series. ach number is 30 less than the #re%ious number.

Directions to Solve



1!.

Look at this series: -, 1-, -, 10, !-, ... What number should come next?

A. 2- B. 20

C. 3- D. 0-


Answer: "#tion A

Explanation:

$his is an alternatin+ addition and subtraction series. n the irst #attern, 1- is

subtracted rom each number to arri%e at the next. n the second, 0 is added to each

number to arri%e at the next.


1.

Look at this series: 2, !, 1, 04, ... What number should come next?

A. 1- B. 14

C. 1!2 D. 21!


Answer: "#tion C

Explanation:

$his is a sim#le multi#lication series. ach number is 3 times more than the #re%ious

number.




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1.

Look at this series: 0.2, 4., 4.4, 4, ... What number should come next?

A. 3 B. 3.3

C. 3.0 D. 3.!


Answer: "#tion D

Explanation:

n this sim#le subtraction series, each number decreases b* -.4.


1.

Look at this series: , !, , 23, , ... What number should come next?

A. 12 B. 22!

C. 324 D. 42


Answer: "#tion D

Explanation:

x 1 ' 2 !

! x 2 ' 3

x 3 ' 4 23

23 x 4 ' 0

x 0 ' ! 42 ...

Directions to Solve

ook carefully for the pattern, and then choose which pair of numbers comes ne!t.

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1.

2 20 0 21 1 0 14

A. 11 0 B. 1-

C. 11 D. 0 1-

E. 1- 0


Answer: "#tion A

Explanation:

$his is an alternatin+ subtraction series ith the inter#olation o a random number, 0,

as e%er* third number. n the subtraction series, 3 is subtracted, then 4, then 3, and so

on.


2.

11 21 10 1 21 22

A. 20 1 B. 20 21

C. 20 2 D. 24 21

E. 22 2!


Answer: "#tion B

Explanation:

$his is an alternatin+ addition series, ith a random number, 21, inter#olated as e%er*

third number. $he addition series alternates beteen addin+ 3 and addin+ 4. $he

number 21 a##ears ater each number arri%ed at b* addin+ 3.


3.

1! 23 3- 3 44 01

A. 0 !! B. 0! !2



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C. 0 !! D. 0 !0

E. 04 !1


Answer: "#tion D

Explanation:

ere is a sim#le addition series, hich be+ins ith and adds .


4.

2 14 2- 2! 32 3

A. 2 4! B. 44 0-

C. 42 4 D. 4- 42

E. 32 2!


Answer: "#tion B

Explanation:

$his is a sim#le addition series, hich be+ins ith 2 and adds !.


0.

11 33 13 10 33 1

A. 1 33 B. 33 30

C. 33 1 D. 10 33

E. 1 21


Answer: "#tion A



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Explanation:

n this alternatin+ re#etition series, a random number, 33, is inter#olated e%er* third

number into a sim#le addition series, in hich each number increases b* 2.

Directions to Solve


!.

2 3 4 0 ! 4

A. 1- B. 4

C. 1- 4 D. 4

E.


Answer: "#tion D

Explanation:

$his is an alternatin+ addition series ith a random number, 4, inter#olated as e%er*

third number. n the main series, 1 is added, then 2 is added, then 1, then 2, and so on.


.

1 1 34 2- 2- 31 23

A. 2! 23 B. 34 2-

C. 23 33 D. 2 2

E. 23 2


Answer: "#tion E

Explanation:

$his is an alternatin+ subtraction series ith re#etition. $here are to dierent #atterns

here. n the irst, a number re#eats itsel& then 3 is added to that number to arri%e at



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the next number, hich also re#eats. $his +i%es the series 1, 1, 2-, 2-, 23, and so on.

%er* third number ollos a second #attern, in hich 3 is subtracted rom each number

to arri%e at the next: 34, 31, 2.


.

! 2- 14 1- 12

A. 14 1- B. 2 1

C. 4 12 D. 2 14

E. 14 14


Answer: "#tion D

Explanation:

$his is an alternatin+ addition and subtraction series. n the irst #attern, 2 is added to

each number to arri%e at the next& in the alternate #attern, ! is subtracted rom each

number to arri%e at the next.


.

21 20 1 2 33 1

A. 43 1 B. 41 44

C. 3 1 D. 3 41

E. 3 41


Answer: "#tion D

Explanation:

$his is a sim#le addition series ith a random number, 1, inter#olated as e%er* third

number. n the series, 4 is added to each number exce#t 1, to arri%e at the next

number.


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1-.

0 !0 0 00 40 0 30

A. 20 10 B. 20 0

C. 30 20 D. 0 30

E. 20 0


Answer: "#tion B

Explanation:

$his is a sim#le subtraction series in hich a random number, 0, is inter#olated ase%er* third number. n the subtraction series, 1- is subtracted rom each number to

arri%e at the next.

Directions to Solve


11.

11 1! 21 2! 31 3! 41

A. 4 02 B. 4! 02

C. 40 4 D. 4! 01


Answer: "#tion D

Explanation:

n this sim#le addition series, each number is 0 more than the #re%ious number.


12.

3 13 1 23 2 33

A. 3 44 B. 3 44



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Explanation:

$his is a sim#le subtraction ith re#etition series. t be+ins ith 2-, hich is re#eated,

then 3 is subtracted, resultin+ in 1, hich is re#eated, and so on.


10.

!1 0 0- !1 43 3! !1

A. 2 !1 B. 2 2-

C. 31 !1 D. 22 10

E. 2 22


Answer: "#tion E

Explanation:

$his is an alternatin+ re#etition series, in hich a random number, !1, is inter#olated as

e%er* third number into an otherise sim#le subtraction series. 5tartin+ ith the second

number, 0, each number (exce#t !1) is less than the #re%ious number.

Directions to Solve


1!.

12 11 14 13 1! 10

A. 14 13 B. 1 21

C. 14 1 D. 12 13

E. 1 1


Answer: "#tion E

Explanation:



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$his is a sim#le alternatin+ addition and subtraction series. irst, 3 is added, then 1 is

subtracted, then 3 is added, 1 subtracted, and so on.


1.

4 22 12 1! 22 2- 24

A. 2 32 B. 2 22

C. 22 2 D. 32 3!

E. 22 2!


Answer: "#tion C

Explanation:

$his is an alternatin+ re#etition series, ith a random number, 22, inter#olated as e%er*

third number into an otherise sim#le addition series. n the addition series, 4 is added

to each number to arri%e at the next number.


1.

4- 4- 31 31 22 22 13

A. 13 4 B. 13 0

C. 4 13 D. 4

E. 4 4


Answer: "#tion A

Explanation:

$his is a subtraction series ith re#etition. ach number re#eats itsel and then

decreases b* .




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1.

1 1- 2- 13 3- 1

A. 2! 4- B. 2 3!

C. 4- 20 D. 20 31

E. 4- 0-


Answer: "#tion C

Explanation:

ere, e%er* other number ollos a dierent #attern. n the irst series, ! is added to

each number to arri%e at the next. n the second series, 1- is added to each number to

arri%e at the next.


2-.

1- 2- 20 30 4- 0- 00

A. - !0 B. !- -

C. !- 0 D. !- !0

E. !0 -


Answer: "#tion E

Explanation:

$his is an alternatin+ addition series, in hich 1- is added, then 0, then 1-, and so on.

Directions to Solve




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1.

42 4- 3 30 33 31 2

A. 20 22 B. 2! 23

C. 2! 24 D. 20 23

E. 2! 22


Answer: "#tion C

Explanation:

$his is an alternatin+ subtraction series in hich 2 is subtracted tice, then 3 is

subtracted once, then 2 is subtracted tice, and so on.


2.

! 1- 14 1 22 2! 3-

A. 3! 4- B. 33 3

C. 3 42 D. 34 3!

E. 34 3


Answer: "#tion E

Explanation:

$his sim#le addition series adds 4 to each number to arri%e at the next.


3. 12 13 1- 14 11

A. 14 11 B. 10 12

C. 10 D. 10 1



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E. 0


Answer: "#tion B

Explanation:

$his is an alternatin+ addition and subtraction series, in hich the addition o 4 is

alternated ith the subtraction o 3.


4.

3! 31 2 24 22 1 10

A. 13 11 B. 1- 0

C. 13 D. 12

E. 1-


Answer: "#tion E

Explanation:

$his is an alternatin+ subtraction series, hich subtracts 0, then 2, then 0, and so on.


0.

3 0 30 1- 12 30 1

A. 22 30 B. 30 1

C. 1 30 D. 1 24

E. 22 24


Answer: "#tion C

Explanation:



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$his is an alternatin+ addition series, ith a random number, 30, inter#olated as e%er*

third number. $he #attern o addition is to add 2, add 0, add 2, and so on. $he number

30 comes ater each 6add 26 ste#/

Directions to Solve


!.

13 2 10 2! 1 23 1

A. 21 23 B. 2- 21

C. 2- 1 D. 20 2

E. 22 2-


Answer: "#tion B

Explanation:

ere, there are to alternatin+ #atterns, ith e%er* other number olloin+ a dierent

#attern. $he irst #attern be+ins ith 13 and adds 2 to each number to arri%e at the

next& the alternatin+ #attern be+ins ith 2 and subtracts 3 each time.


.

14 14 2! 2! 3 3 0-

A. !- 2 B. 0- !2

C. 0- 2 D. !2 !2

E.!2 -


Answer: "#tion B

Explanation:

n this sim#le addition ith re#etition series, each number in the series re#eats itsel,



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and then increases b* 12 to arri%e at the next number.


.

44 41 3 30 32 2 2!

A. 24 21 B. 22 1

C. 23 1 D. 2 32

E. 23 2-


Answer: "#tion E

Explanation:

$his is a sim#le subtraction series, in hich 3 is subtracted rom each number to arri%e

at the next.


.

34 3- 2! 22 1 14 1-

A. ! B. ! 4

C. 14 1 D. ! 2

E. 4 -


Answer: "#tion D

Explanation:

$his is a sim#le subtraction series, in hich 4 is subtracted rom each number to arri%e

at the next.


1-.

32 31 32 2 32 2 32



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A. 20 32 B. 31 32

C. 2 32 D. 20 3-

E. 2 3-


Answer: "#tion A

Explanation:

$his is an alternatin+ re#etition series. $he number 32 alternates ith a series in hich

each number decreases b* 2.

Directions to Solve


11.

!! 12 14 !! 1

A. 1 !! B. !! 1

C. 1 22 D. 2- !!

E. !! 2-


Answer: "#tion A

Explanation:

$his is an alternatin+ addition series ith re#etition, in hich a random number, !!, is

inter#olated as e%er* third number. $he re+ular series adds 2, then 3, then 2, and so on,

ith !! re#eated ater each 6add 26 ste#.


12.

3 1- 10 1 22 24



23/32

A. 2! 2 B. 2 34

C. 2 31 D. 2! 31

E. 2! 32


Answer: "#tion C

Explanation:

$his is an alternatin+ addition series that adds 0, then 2, then 0, and so on.


13.

4 2! 1- 13 2- 1!

A. 14 4 B. 14 1

C. 1 14 D. 1 13

E. 1 14


Answer: "#tion E

Explanation:

$o #atterns alternate here, ith e%er* third number olloin+ the alternate #attern. n

the main series, be+innin+ ith 4, 3 is added to each number to arri%e at the next. n

the alternatin+ series, be+innin+ ith 2!, ! is subtracted rom each number to arri%e at

the next.


14.

32 2 2! 23 2- 1 14

A. 11 B. 12

C. 11 D. 32 2

E. 1-



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Answer: "#tion A

Explanation:

n this sim#le subtraction series, the numbers decrease b* 3.


10.

1! 2! 0! 3! 4! ! 0!

A. - !! B. !4 2

C. !! - D. !

E. !! 2


Answer: "#tion C

Explanation:

ere, e%er* third number ollos a dierent #attern rom the main series. n the main

series, be+innin+ ith 1!, 1- is added to each number to arri%e at the next. n the

alternatin+ series, be+innin+ ith 0!, 12 is added to each number to arri%e at the next.

Directions to Solve


1!.

2 44 4 41 ! 3

A. 1- 12 B. 30 32

C. 34 D. 30 1-

E. 1- 02


Answer: "#tion D



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Explanation:

ere, there are to alternatin+ #atterns, one addition and one subtraction. $he irst

starts ith 2 and increases b* 2& the second starts ith 44 and decreases b* 3.


1.

1 32 1 2 21 2! 23

A. 20 20 B. 2- 22

C. 23 20 D. 20 22

E. 2 32


Answer: "#tion C

Explanation:

ere, there are to alternatin+ #atterns. $he irst be+ins ith 1 and adds 2& the

second be+ins ith 32 and subtracts 3.


1.1 14 14 11 11

A. 0 B. 0 2

C. 2 D. 0 0

E. 0


Answer: "#tion D

Explanation:

n this sim#le subtraction ith re#etition series, each number is re#eated, then 3 is

subtracted to +i%e the next number, hich is then re#eated, and so on.




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27/32

1.

Look at this series: 2, 77, 8, 91!, 32, ... What number should ill the blank?

A. ;1! B. , >=, 77, >>, ... What number should ill the blank?

A. > B. >>

C. >= D. >=


Answer: "#tion D

Explanation:



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$his is a sim#le addition series& each number is 3 more than the #re%ious number.


4.

Look at this series: -, 1, !, 77, 1, !, -, 1, ... What number should ill the blank?

A. - B. 1

C. - D. !


Answer: "#tion A

Explanation:

n this series, 0 is added to the #re%ious number& the number - is inserted as e%er*

third number.


0.

Look at this series: , 43, 11, 41, 77, 3, 1, ... What number should ill in the blank?

A. B. 14

C. 43 D. 44


Answer: "#tion B

Explanation:

$his is a sim#le alternatin+ addition and subtraction series. $he irst series be+ins ith

and adds 3& the second be+ins ith 43 and subtracts 2.

Directions to Solve

Find the number that fits somewhere into the middle of the series. "ome of the items in#ol#e

both numbers and letters



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!.

Look at this series: =, 1-, =, 11, 77, 12, , ... What number should ill the blank?

A. B. =

C. > D. 14


Answer: "#tion B

Explanation:

$his is an alternatin+ addition and subtraction series. oman numbers alternate ith

;rabic numbers. n the oman numeral #attern, each number decreases b* 1. n the

;rabic numeral #attern, each number increases b* 1.


.

Look at this series: (1/), (1/3), 1, 7777 , , ... What number should ill the blank?

A. (2/3) B. 3

C. ! D. 2


Answer: "#tion B

Explanation:

$his is a multi#lication series& each number is 3 times the #re%ious number.


.

Look at this series: 3, 3, 3, !3, 77, 3, 43, ... What number should ill the blank?

A. 33 B. 03

C. 3 D. 3


Answer: "#tion B



30/32

Explanation:

$his is a sim#le subtraction series in hich a random number, 3, is inter#olated as

e%er* third number. n the subtraction series, 1- is subtracted rom each number to

arri%e at the next.


.

Look at this series: 10, 77, 2, 2, 3, 3, ... What number should ill the blank?

A. 01 B. 3

C. 23 D. 10


Answer: "#tion D

Explanation:

n this sim#le addition ith re#etition series, each number in the series re#eats itsel,

and then increases b* 12 to arri%e at the next number.


1-.

Look at this series: 2, !, 3, , 4, 77, 0, ... What number should ill the blank?

A. - B. 1

C. 0 D.


Answer: "#tion D

Explanation:

$his series alternates the addition o 4 ith the subtraction o 3.

Directions to Solve

Find the number that fits somewhere into the middle of the series. "ome of the items in#ol#e

both numbers and letters



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11.

Look at this series: @14, L1!, 77, A2-, 22, ... What number should ill the blank?

A. 524 B. B1

C. C1 D. $24


Answer: "#tion B

Explanation:

n this series, the letters #ro+ress b* 2, and the numbers increase b* 2.


12.

Look at this series: 4, , 20, 1-, 77, 2-, 1!, 1, ... What number should ill the blank?

A. 13 B. 10

C. 2- D. 2


Answer: "#tion A

Explanation:

$o series alternate here, ith e%er* third number olloin+ a dierent #attern. n the

main series, 3 is added to each number to arri%e at the next. n the alternatin+ series,

0 is subtracted rom each number to arri%e at the next.


13.

Look at this series: >>=, >>, 77, >, =, ... What number should ill the blank?

A. >> B. >

C. >= D. =


Answer: "#tion C



32/32

Explanation:

$his is a sim#le subtraction series& each number is 4 less than the #re%ious number.


14.

Look at this series: -.10, -.3, 7777, 1.2, 2.4, ... What number should ill the blank?

A. 4. B. -.--!

C. -.! D. -.


Answer: "#tion C

Explanation:

$his is a sim#le multi#lication series. ach number is 2 times +reater than the #re%ious

number.


10.

Look at this series: D32, =2, 77, >23, E2-, ... What number should ill the blank?

A. W2! B. W1

C. F1 D. F2!


Answer: "#tion A

Explanation:

n this series, the letters #ro+ress b* 1& the numbers decrease b* 3.

directions to solve

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