1. GMATGMAT
VIVEK PONKSHEVIVEK PONKSHE
BASED ON NOTES PREPAREDBASED ON NOTES PREPARED
BY DR VIVEK KULKARNIBY DR VIVEK KULKARNI

2. DANCING DIGITS ANDDANCING DIGITS AND
ALPHABETSALPHABETS
 Count the number of placesCount the number of places
 Divide into parts and mark by pencilDivide into parts and mark by pencil
initially. Partial repetition at the end makesinitially. Partial repetition at the end makes
the problem difficult.the problem difficult.
 Match the corresponding places.Match the corresponding places.
 Look for repetition, rotation, systematicLook for repetition, rotation, systematic
change.change.
 Take help from the answers.Take help from the answers.

3. PROBLEMS DANCING DIGITSPROBLEMS DANCING DIGITS
 01-01-11010110-0-10101-01-11010110-0-101
 1-1011-0-1101-1-1-1011-0-1101-1-
 12-45-2-41-3-2112-45-2-41-3-21
 1-0110-1-0011-1-0110-1-0011-
 11-01-110-111-11-01-110-111-
 11-0-111-0011-11-0-111-0011-

4. PROBLEMS DANCINGPROBLEMS DANCING
ALPHABETSALPHABETS
 ab-dea-cdea-cdeab-deab-dea-cdea-cdeab-de
 ab-dab-da-cd-bab-dab-da-cd-b
 ab-aab-a-bbaa-baab-aab-a-bbaa-ba
 a-cdb-dc-da-cdb-dc-d
 ab-cdd-fgg-ijkab-cdd-fgg-ijk
 a-cab-cb-c-aa-cab-cb-c-a

5. NUMBER SERIESNUMBER SERIES
 Try to find logic of developing the series.Try to find logic of developing the series.
 Difference method is generally followed.Difference method is generally followed.
 The series may be based on quadratic/cubic equation,The series may be based on quadratic/cubic equation,
multiplications or consecutive number relationships.multiplications or consecutive number relationships.
 For large number of terms, look for alternate series.For large number of terms, look for alternate series.
 Try to judge the speed of rise.Try to judge the speed of rise.
 In consecutive relationships a term is generated byIn consecutive relationships a term is generated by
mathematically processing previous term.mathematically processing previous term.
 The equations could be based on natural, odd, even,The equations could be based on natural, odd, even,
prime numbers as the base series.prime numbers as the base series.
 Difference method will not work if the base series is ofDifference method will not work if the base series is of
prime numbers.prime numbers.

6. PROBLEMS NUMBER SERIESPROBLEMS NUMBER SERIES
 05 08 11 14 17 ?05 08 11 14 17 ?
 05 10 17 26 37 ?05 10 17 26 37 ?
 03 20 55 114 203 ?03 20 55 114 203 ?
 04 12 36 108 324 ?04 12 36 108 324 ?
 03 04 07 08 12 16 18 ?03 04 07 08 12 16 18 ?
 05 11 17 23 31 ?05 11 17 23 31 ?
 06 12 30 56 132 ?06 12 30 56 132 ?

7. ODD TERM OUTODD TERM OUT
 Try to find common rule or process amongTry to find common rule or process among
all but one of the given terms.all but one of the given terms.
 Don’t try trivial or very complicated logic.Don’t try trivial or very complicated logic.
 Commonly followed rules are equationsCommonly followed rules are equations
( square, cube), rules of divisibility,( square, cube), rules of divisibility,
individual digits of the numbers processed.individual digits of the numbers processed.
 Do not look for difference method.Do not look for difference method.

8. PROBLEMS ODD MAN OUTPROBLEMS ODD MAN OUT
 3 21 13 30 57 733 21 13 30 57 73
 4 9 25 49 121 1444 9 25 49 121 144
 4 36 76 135 144 36 76 135 14
 33 121 132 154 5633 121 132 154 56
 533 460 361 262 190 82533 460 361 262 190 82

9. RATIO AND PROPORTIONRATIO AND PROPORTION
 a : b :: c : d implies ad = bc. Try this first.a : b :: c : d implies ad = bc. Try this first.
 But the question normally involves findingBut the question normally involves finding
a relation between a and b ( rarelya relation between a and b ( rarely
between a and c ) and apply the same forbetween a and c ) and apply the same for
c and d.c and d.
 Very rarely a series type pattern is askedVery rarely a series type pattern is asked
under this structure.under this structure.

10. PROBLEMS RATIOPROBLEMS RATIO
PROPORTIONPROPORTION
 50 : 82 : : 122 : ?50 : 82 : : 122 : ?
 8 : 27 : : 9 : ?8 : 27 : : 9 : ?
 2 : ? : : 10 : 302 : ? : : 10 : 30
 ? : 29 : : 4 : 23? : 29 : : 4 : 23
 43 : 7 : : 59 : ?43 : 7 : : 59 : ?

11. ARRANGEMENT OFARRANGEMENT OF
NUMBERSNUMBERS
 These questions can range from very simple toThese questions can range from very simple to
very difficult with lot of scope in variety ofvery difficult with lot of scope in variety of
structures.structures.
 No particular logic or method to decipher theNo particular logic or method to decipher the
rule.rule.
 Needs divergent thinking with quick trials andNeeds divergent thinking with quick trials and
errors.errors.
 Generally mathematical operations involved areGenerally mathematical operations involved are
not more than three.not more than three.
 Oral accurate calculations and tables savesOral accurate calculations and tables saves
time.time.

12. 120 216 ?
8
6 5
9
8 6
7
10 4
3
27
9
81
4
64
16
256
6
216
36
?
148 32
5
?
8 1616
49

13. 3 BY 3 MATRIX3 BY 3 MATRIX
 Common structure with lot of internal variety.Common structure with lot of internal variety.
 Try for a series by arranging the given eightTry for a series by arranging the given eight
terms in ascending order.terms in ascending order.
 If not then try row wise or column wiseIf not then try row wise or column wise
relationship among three terms.relationship among three terms.
 Sometimes the central term relates theSometimes the central term relates the
remaining eight terms into four pairs.remaining eight terms into four pairs.
 Very rarely there are three triplets forming nineVery rarely there are three triplets forming nine
terms.terms.

14. PROBLEMS 3 BY 3 MATRIXPROBLEMS 3 BY 3 MATRIX
?? 243243 99
33 21872187 8181
2727 65616561 729729
?? 1313 1414
1111 77 99
2828 1515 2121
1111 88 33
22 ?? 1010
99 44 99
44 88 44
77 ?? 99
33 88 55

15. PROBLEMS NUMBERSPROBLEMS NUMBERS
RELATIONSRELATIONS
 06 11 ( 25 )06 11 ( 25 )
08 06 ( 16 )08 06 ( 16 )
12 05 ( ? )12 05 ( ? )
 51 ( 11 ) 6151 ( 11 ) 61
64 ( 30 ) 3264 ( 30 ) 32
35 ( ? ) 4235 ( ? ) 42
 03 ( 19 ) 0503 ( 19 ) 05
05 ( 39 ) 0705 ( 39 ) 07
09 ( ? ) 0509 ( ? ) 05

16. PROBLEMS NUMBERPROBLEMS NUMBER
RELATIONSRELATIONS
 CIRCULAR ARRANGEMENTCIRCULAR ARRANGEMENT
13 19 ?8
12
9
7
15
18 6
8
13
9
6
14
40 ?72
8
12
15
4
6
320 9
15
30
10
8

17. ARRANGEMENT OF NUMBERSARRANGEMENT OF NUMBERS
PYRAMIDPYRAMID
11
2 29 282 29 28
3 30 49 48 273 30 49 48 27
4 31 50 61 60 47 264 31 50 61 60 47 26
5 32 51 62 63 64 59 46 255 32 51 62 63 64 59 46 25
6 33 52 53 54 55 56 57 58 45 246 33 52 53 54 55 56 57 58 45 24
7 34 35 36 37 38 39 40 41 42 43 44 237 34 35 36 37 38 39 40 41 42 43 44 23
8 9 10 11 12 13 14 15 16 17 18 19 20 21 228 9 10 11 12 13 14 15 16 17 18 19 20 21 22
 6 7 8 : 6 35 12 : : 24 23 22 : ?6 7 8 : 6 35 12 : : 24 23 22 : ?
 5 32 4 : 3 30 2 : : 25 46 26 : ?5 32 4 : 3 30 2 : : 25 46 26 : ?
 8 6 4 : 9 33 31 : : ? : 21 45 478 6 4 : 9 33 31 : : ? : 21 45 47
 2 50 54 : 3 51 37 : : 28 60 56 : ?2 50 54 : 3 51 37 : : 28 60 56 : ?

18. ALPHABET PYRAMIDALPHABET PYRAMID
aa
b c db c d
e f g h ie f g h i
j k l m n o pj k l m n o p
q r s t u v w x yq r s t u v w x y
z a b c d e f g h i jz a b c d e f g h i j
k l m n o p q r s t u v wk l m n o p q r s t u v w
x y z a b c d e f g h i j k lx y z a b c d e f g h i j k l
1 xzbd : kmoq : : ljhf : ?
2 jramz : ksbna : : pxiuj : ?
3 bflt : tsrq : : ? : vwxy
4 jeba : qzkx : : pida : ?
5 xkzmb : ylanc : : lwjuh : ?

19. ALPHABET SERIESALPHABET SERIES
 There can be a single alphabet or a groupThere can be a single alphabet or a group
of alphabets called term or string.of alphabets called term or string.
 Remembering 1 to 26 numbers ofRemembering 1 to 26 numbers of
corresponding alphabets and calculatingcorresponding alphabets and calculating
the difference between alphabets isthe difference between alphabets is
general method.general method.
 The difference is generally found in first,The difference is generally found in first,
second, etc letters of consecutive terms insecond, etc letters of consecutive terms in
series.series.

20. ODD TERM OUTODD TERM OUT
1 2 3 4 5 6 7 8 9 10 11 12 131 2 3 4 5 6 7 8 9 10 11 12 13
a b c d e f g h I j k l ma b c d e f g h I j k l m
z y x w v u t s r q p o nz y x w v u t s r q p o n
26 25 24 23 22 21 20 19 18 17 16 15 1426 25 24 23 22 21 20 19 18 17 16 15 14

21. PROBLEMS ALPHABETPROBLEMS ALPHABET
SERIESSERIES
 WORD XQUH YSXL ZUAP ?WORD XQUH YSXL ZUAP ?
 WORD XPSE ZRUG CUXJ ?WORD XPSE ZRUG CUXJ ?
 WORD VPPF UQNH TRLJ ?WORD VPPF UQNH TRLJ ?
 A B F O ?A B F O ?

22. PROBLEMS ODD TERM OUTPROBLEMS ODD TERM OUT
 dvug zzyc jpol lnmodvug zzyc jpol lnmo
 egjns acfjo cehmr gilpu iknrwegjns acfjo cehmr gilpu iknrw
 dogod local xyzyx dalad statsdogod local xyzyx dalad stats
 anz dqw gtt hrs boyanz dqw gtt hrs boy
 aehj cgjl eiln gkno hloqaehj cgjl eiln gkno hloq

23. ALPHABET SERIES MATCH THEALPHABET SERIES MATCH THE
PAIRSPAIRS
 (a) ABX CDV EFT GHR(a) ABX CDV EFT GHR
(b) AZBC CXDE EVFG GTHI(b) AZBC CXDE EVFG GTHI
(c) ACY BDX CEW DFV(c) ACY BDX CEW DFV
(d) BCZ CDY DEX EFW(d) BCZ CDY DEX EFW
(e) AYBC BXCD CWDE(e) AYBC BXCD CWDE
1 MNNO 2 KLQ 3 MMNO 4 MNL 5 MOM 6 XYA1 MNNO 2 KLQ 3 MMNO 4 MNL 5 MOM 6 XYA
 (a) TPRG WMOD VNPE SQSH PRTI(a) TPRG WMOD VNPE SQSH PRTI
(b) EMOV GOQT CKMX KSUP IQSR(b) EMOV GOQT CKMX KSUP IQSR
(c) CNLX BMKY ALJZ XIGC ZKIA(c) CNLX BMKY ALJZ XIGC ZKIA
(d) MODW GIXC LNCX NPEV FHWD(d) MODW GIXC LNCX NPEV FHWD
(e) NVXM QSUJ OUWL MWYN PRTI(e) NVXM QSUJ OUWL MWYN PRTI
1 YJHB 2 EGVE 3 UOQF 4 AIKZ1 YJHB 2 EGVE 3 UOQF 4 AIKZ

24. RATIO PROPORTIONRATIO PROPORTION
 Question may develop a relationship byQuestion may develop a relationship by
rearranging the order of the samerearranging the order of the same
alphabets in the stringalphabets in the string
 Or by changing the alphabets based onOr by changing the alphabets based on
difference or partener mapdifference or partener map
 Sometimes the relation is to beSometimes the relation is to be
established in reverse orderestablished in reverse order

25. PROBLEMS RATIOPROBLEMS RATIO
PROPORTIONPROPORTION
 WORD : XQQB : : MIND : ?WORD : XQQB : : MIND : ?
 If the word MIND is coded as MNDI howIf the word MIND is coded as MNDI how
will you code the word WORD ?will you code the word WORD ?
 RUSSIA : BJTRTQ : : COLOUR : ?RUSSIA : BJTRTQ : : COLOUR : ?
 DEER : WVVI : : BELT : ?DEER : WVVI : : BELT : ?

26. CODE LANGUAGECODE LANGUAGE
 Coding information is given in twoCoding information is given in two
columns or tabular or cross word form.columns or tabular or cross word form.
 Coding could be done using alphabets,Coding could be done using alphabets,
digits, or symbols .digits, or symbols .

27. PROBLEMS CODE LANGUAGEPROBLEMS CODE LANGUAGE
 PAVE bcktPAVE bckt
 JOLT lxyzJOLT lxyz
 MIXTURE bejlmpwMIXTURE bejlmpw
 GOVERN bhprtxGOVERN bhprtx
 WHIP fkmoWHIP fkmo
 COPE bknxCOPE bknx
 BALE abczBALE abcz
 FIND ghmsFIND ghms
 KING hmqrKING hmqr
 HAZE bcdfHAZE bcdf
 SAFE bcguSAFE bcgu
 QUOTE blxvwQUOTE blxvw
 YARD cipsYARD cips
 ULTIMACY ceilmnwzULTIMACY ceilmnwz

28. PROBLEMS CODEPROBLEMS CODE
LANGUAGELANGUAGE
 CLUBCLUB
(a) awxz (b) anwz (c) bnvw (d) amws (e) bwxy(a) awxz (b) anwz (c) bnvw (d) amws (e) bwxy
 HALTHALT
(a) cgmz (b) flmv (c) cflz (d) fmut (e) cmnz(a) cgmz (b) flmv (c) cflz (d) fmut (e) cmnz
 DOVEDOVE
(a) csty (b) bcst (c) bsty (d) bstx (e) btxy(a) csty (b) bcst (c) bsty (d) bstx (e) btxy
 WORKWORK
(a) mopq (b) opqx (c) oprx (d) opqy (e) mpqx(a) mopq (b) opqx (c) oprx (d) opqy (e) mpqx
 HUSKHUSK
(a) fquw (b) frvw (c) gquv (d)fruw (e) fgrv(a) fquw (b) frvw (c) gquv (d)fruw (e) fgrv

29. PROBLEMS CODEPROBLEMS CODE
LANGUAGELANGUAGE
 RAZERAZE
(a)(a) bcdp (b) cdpr (c) bcop (d) depr (e) cderbcdp (b) cdpr (c) bcop (d) depr (e) cder
 PEACEPEACE
(a) ccdkn (b) bcckm (c) bbckn (d) bbcjn (e) cddjm(a) ccdkn (b) bcckm (c) bbckn (d) bbcjn (e) cddjm
 GUARDGUARD
(a) cprsv (b) cpsvw (c) bcprs (d) cprsw (e) dersw(a) cprsv (b) cpsvw (c) bcprs (d) cprsw (e) dersw
 SYSTEMSYSTEM
(a) beimvv (b) bbeimv (c) beiluu (d) bejmuu (e) eijmvv(a) beimvv (b) bbeimv (c) beiluu (d) bejmuu (e) eijmvv
 SOCIALSOCIAL
(a) cdmuyz (b) dmnvyz (c) cnuvyz (d) dmpuvw (e) cmnuxz(a) cdmuyz (b) dmnvyz (c) cnuvyz (d) dmpuvw (e) cmnuxz

30. PROBLEMS CODEPROBLEMS CODE
LANGUAGELANGUAGE
 IfIf Tea is sweetTea is sweet is written asis written as sue chosue cho
ryerye,, Sita is a sweet girlSita is a sweet girl is written asis written as
rye kim sue bisrye kim sue bis andand Tea is hotTea is hot isis
written aswritten as rye kora chorye kora cho Then whichThen which
word means girl ?word means girl ?
 How many statements in the aboveHow many statements in the above
question are not required to answer it ?question are not required to answer it ?

31. ALPHABET NUMBERALPHABET NUMBER
RELATIONSHIPRELATIONSHIP
 Alphabet position number is operatedAlphabet position number is operated
mathematically to generate relationshipmathematically to generate relationship
 DOG = 420, BOAT = 600 then FOG = ?DOG = 420, BOAT = 600 then FOG = ?
 UG100 : SI7 : : RC256 : ?UG100 : SI7 : : RC256 : ?

32. CHANGE OF CONVENTIONCHANGE OF CONVENTION
 Conventional meanings of mathematicalConventional meanings of mathematical
signs have been changedsigns have been changed
 Rules in mathematics are applicable onlyRules in mathematics are applicable only
after changing the signsafter changing the signs

33. PROBLEMS CHANGE INPROBLEMS CHANGE IN
CONVENTIONCONVENTION
 + means division+ means division
 _ means addition_ means addition
 * means subtraction* means subtraction
 / means multiplication/ means multiplication
1.1. (18 * 12) / (11 – 5) + (8 / 8) = ?(18 * 12) / (11 – 5) + (8 / 8) = ?
2.2. 20 / 4 – 10 / 2 * 53 = ?20 / 4 – 10 / 2 * 53 = ?
3.3. (13 – 17) / 5 + 15 = ?(13 – 17) / 5 + 15 = ?
4.4. 10 / 3 – 5 / 5 * 11 / 5 = ?10 / 3 – 5 / 5 * 11 / 5 = ?
5.5. (5 / 9) + (28 * 13) / 5 = ?(5 / 9) + (28 * 13) / 5 = ?

34. ASSIGNING ARTIFICIAL VALUES TOASSIGNING ARTIFICIAL VALUES TO
ARITHMATICAL DIGITS AND SIGNSARITHMATICAL DIGITS AND SIGNS
1.1. 12*21=23 10*9=19 16*9=175 23*14=?12*21=23 10*9=19 16*9=175 23*14=?
2.2. ( 3 ? 4 ) ? 2 ? 7 = 7( 3 ? 4 ) ? 2 ? 7 = 7
3.3. 6 ? 3 ? 4 ? 9 = 236 ? 3 ? 4 ? 9 = 23
4.4. 0=1 2=4 3=10 4=?0=1 2=4 3=10 4=?
5.5. 7*4=22 3*2=10 4*6=20 11*4=?7*4=22 3*2=10 4*6=20 11*4=?

35. VENN DIAGRAMSVENN DIAGRAMS
 Venn diagrams represent relationship betweenVenn diagrams represent relationship between
two or more sets.two or more sets.
 The shape or size is not significant.The shape or size is not significant.
 In type A discriptions of sets are to be matchedIn type A discriptions of sets are to be matched
with proper venn diagrams.with proper venn diagrams.
 In type B a venn diagramatic relation is givenIn type B a venn diagramatic relation is given
and questions are asked on the numbers.and questions are asked on the numbers.
 Following words are to be carefully noted andFollowing words are to be carefully noted and
understood – AND / OR , ATLEAST / ONLYunderstood – AND / OR , ATLEAST / ONLY

36. PROBLEMS VENN DIAGRAMSPROBLEMS VENN DIAGRAMS
 Birds , Parrots , BatsBirds , Parrots , Bats
a b c d

37. PROBLEMS VENN DIAGRAMSPROBLEMS VENN DIAGRAMS
 Diagram showsDiagram shows
distribution of 140distribution of 140
people on newspaperpeople on newspaper
choice-choice-
How many readHow many read
1.1. Only 2 newspapersOnly 2 newspapers
2.2. Atleast 2 newspapersAtleast 2 newspapers
3.3. Only TimesOnly Times
4.4. Times or ExpressTimes or Express
5.5. Express and HinduExpress and Hindu
Express
50
20
301510
10
5
Times
Hindu

38. COUNTING FIGERSCOUNTING FIGERS
 Generally number of squares, rectangles,Generally number of squares, rectangles,
triangles are to be counted.triangles are to be counted.
 Symmetry of figure could be utilized.Symmetry of figure could be utilized.
 Common mistakes are missing a count orCommon mistakes are missing a count or
repeating a count.repeating a count.
 Count systematically from a smaller sizeCount systematically from a smaller size
to a larger size by methodically combiningto a larger size by methodically combining
smaller figures into larger.smaller figures into larger.

39. PROBLEMS COUNTINGPROBLEMS COUNTING
FIGURESFIGURES

40. DICEDICE
 A surface has got 1 opposite and 4 adjacentA surface has got 1 opposite and 4 adjacent
surfaces.surfaces.
 If two figures have two numbers common, thenIf two figures have two numbers common, then
third numbers are opposite to each other.third numbers are opposite to each other.
 When only one number is common in twoWhen only one number is common in two
figures, then all 4 adjacent surfaces are visible.figures, then all 4 adjacent surfaces are visible.
 There is a particular relationship between 3There is a particular relationship between 3
visible surfaces which never changes by rotatingvisible surfaces which never changes by rotating
the dice.the dice.

41. PROBLEMS DICEPROBLEMS DICE
1
2
3 1
4
2 1
3
5
Find the opposite pairs
6 5
1
4
4
6
2
1 2
6
5
3
Number opposite to 3 is -------
1
2
5 5
1
6 4
5
6 3
2
1
Number opposite to 2 is Sign opposite to

42. DIRECTION SENSEDIRECTION SENSE
 To find final position in relation to initialTo find final position in relation to initial
position in magnitude and direction.position in magnitude and direction.
 In another type on a particular shapeIn another type on a particular shape
( square, rectangle, circle ) clockwise and( square, rectangle, circle ) clockwise and
anticlockwise movements are describedanticlockwise movements are described
and then positions after movements are toand then positions after movements are to
be compared in direction and magnitude.be compared in direction and magnitude.

43. PROBLEMS DIRECTIONPROBLEMS DIRECTION
SENSESENSE
1.1. A goes in the direction of rising sun for 3 kms ,A goes in the direction of rising sun for 3 kms ,
turns left and walks 3 kms , turns right andturns left and walks 3 kms , turns right and
walks 1 km.At what distance and in whichwalks 1 km.At what distance and in which
direction is A from the start?direction is A from the start?
2.2. A , B , C ,D are standing on a circular track. AA , B , C ,D are standing on a circular track. A
moves 90 degrees clockwise and B goes tomoves 90 degrees clockwise and B goes to
opposite position. In what direction B is A ?opposite position. In what direction B is A ?
B D
A

44. CUBE CUTTINGCUBE CUTTING

45. CUBE PAINTED ALL SIDES WITHCUBE PAINTED ALL SIDES WITH
DIFFERENT COLOURSDIFFERENT COLOURS

46. CUBE PAINTED OPPOSITECUBE PAINTED OPPOSITE
SIDES WITH SAME COLOURSSIDES WITH SAME COLOURS

47. CUBE PAINTED ADJESANTCUBE PAINTED ADJESANT
SIDES WITH SAME COLOURSIDES WITH SAME COLOUR