GMATGMAT

VIVEK PONKSHEVIVEK PONKSHE

BASED ON NOTES PREPARED BASED ON NOTES PREPARED BY DR VIVEK KULKARNIBY DR VIVEK KULKARNI

DANCING DIGITS AND DANCING DIGITS AND ALPHABETSALPHABETS

Count the number of placesCount the number of places Divide into parts and mark by pencil Divide into parts and mark by pencil

initially. Partial repetition at the end initially. Partial repetition at the end makes the problem difficult.makes the problem difficult.

Match the corresponding places.Match the corresponding places. Look for repetition, rotation, Look for repetition, rotation,

systematic change.systematic change. Take help from the answers.Take help from the answers.

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-

PROBLEMS DANCING PROBLEMS 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

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 The series may be based on quadratic/cubic

equation, multiplications or consecutive number equation, multiplications or consecutive number relationships.relationships.

For large number of terms, look for alternate For large number of terms, look for alternate series.series.

Try to judge the speed of rise.Try to judge the speed of rise. In consecutive relationships a term is generated In consecutive relationships a term is generated

by mathematically processing previous term.by mathematically processing previous term. The equations could be based on natural, odd, The equations could be based on natural, odd,

even, prime numbers as the base series.even, prime numbers as the base series. Difference method will not work if the base series Difference method will not work if the base series

is of prime numbers.is of prime numbers.

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 ?

ODD TERM OUTODD TERM OUT

Try to find common rule or process Try to find common rule or process among all but one of the given terms.among all but one of the given terms.

Don’t try trivial or very complicated Don’t try trivial or very complicated logic.logic.

Commonly followed rules are equations Commonly followed rules are equations ( square, cube), rules of divisibility, ( square, cube), rules of divisibility, individual digits of the numbers individual digits of the numbers processed.processed.

Do not look for difference method.Do not look for difference method.

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

RATIO AND PROPORTIONRATIO AND PROPORTION

a : b :: c : d implies ad = bc. Try this a : b :: c : d implies ad = bc. Try this first.first.

But the question normally involves But the question normally involves finding a relation between a and b finding a relation between a and b ( rarely between a and c ) and apply ( rarely between a and c ) and apply the same for c and d.the same for c and d.

Very rarely a series type pattern is Very rarely a series type pattern is asked under this structure.asked under this structure.

PROBLEMS RATIO PROPORTIONPROBLEMS RATIO PROPORTION

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 : ?

ARRANGEMENT OF ARRANGEMENT OF NUMBERSNUMBERS

These questions can range from very These questions can range from very simple to very difficult with lot of scope in simple to very difficult with lot of scope in variety of structures.variety of structures.

No particular logic or method to decipher No particular logic or method to decipher the rule.the rule.

Needs divergent thinking with quick trials Needs divergent thinking with quick trials and errors.and errors.

Generally mathematical operations Generally mathematical operations involved are not more than three.involved are not more than three.

Oral accurate calculations and tables Oral accurate calculations and tables saves time.saves time.

120 216 ?

8

6 5

9

8 6

7

10 4

3

27

9

81

4

6416

256

6

216

36

?

148 325

?

8 161649

3 BY 3 MATRIX3 BY 3 MATRIX

Common structure with lot of internal Common structure with lot of internal variety.variety.

Try for a series by arranging the given eight Try for a series by arranging the given eight terms in ascending order.terms in ascending order.

If not then try row wise or column wise If not then try row wise or column wise relationship among three terms.relationship among three terms.

Sometimes the central term relates the Sometimes the central term relates the remaining eight terms into four pairs.remaining eight terms into four pairs.

Very rarely there are three triplets forming Very rarely there are three triplets forming nine terms. nine terms.

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

PROBLEMS NUMBERS PROBLEMS 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

PROBLEMS NUMBER PROBLEMS NUMBER RELATIONSRELATIONS

CIRCULAR ARRANGEMENTCIRCULAR ARRANGEMENT

13 19 ?8

12

9

7

15

18 6

8

13

9

6

14

40 ?72812

15

4

6

320 9

15

30

108

ARRANGEMENT OF NUMBERS ARRANGEMENT OF NUMBERS PYRAMIDPYRAMID

11 2 29 28 2 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 : ?

ALPHABET PYRAMIDALPHABET PYRAMID

aab c db c d

e f g h ie f g h ij 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 yz 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 wx 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 : : ? : vwxy4 jeba : qzkx : : pida : ?5 xkzmb : ylanc : : lwjuh : ?

ALPHABET SERIESALPHABET SERIES

There can be a single alphabet or a There can be a single alphabet or a group of alphabets called term or group of alphabets called term or string.string.

Remembering 1 to 26 numbers of Remembering 1 to 26 numbers of corresponding alphabets and corresponding alphabets and calculating the difference between calculating the difference between alphabets is general method.alphabets is general method.

The difference is generally found in The difference is generally found in first, second, etc letters of first, second, etc letters of consecutive terms in series.consecutive terms in series.

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 26 25 24 23 22 21 20 19 18 17 16 15 14 14

PROBLEMS ALPHABET PROBLEMS 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 ?

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 hloq aehj cgjl eiln gkno hloq

ALPHABET SERIES MATCH THE ALPHABET 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

RATIO PROPORTIONRATIO PROPORTION

Question may develop a relationship Question may develop a relationship by rearranging the order of the same by rearranging the order of the same alphabets in the stringalphabets in the string

Or by changing the alphabets based Or by changing the alphabets based on difference or partener mapon difference or partener map

Sometimes the relation is to be Sometimes the relation is to be established in reverse orderestablished in reverse order

PROBLEMS RATIO PROPORTIONPROBLEMS RATIO PROPORTION

WORD : XQQB : : MIND : ?WORD : XQQB : : MIND : ? If the word MIND is coded as MNDI If the word MIND is coded as MNDI

how will you code the word WORD ?how will you code the word WORD ? RUSSIA : BJTRTQ : : COLOUR : ?RUSSIA : BJTRTQ : : COLOUR : ? DEER : WVVI : : BELT : ?DEER : WVVI : : BELT : ?

CODE LANGUAGECODE LANGUAGE

Coding information is given in two Coding information is given in two columns or tabular or cross word columns or tabular or cross word form.form.

Coding could be done using Coding could be done using alphabets, digits, or symbols .alphabets, digits, or symbols .

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

PROBLEMS CODE PROBLEMS CODE LANGUAGELANGUAGE

CLUBCLUB(a) awxz (b) anwz (c) bnvw (d) amws (e) (a) awxz (b) anwz (c) bnvw (d) amws (e)

bwxybwxy 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

PROBLEMS CODE PROBLEMS 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) (a) beimvv (b) bbeimv (c) beiluu (d) bejmuu (e)

eijmvveijmvv SOCIALSOCIAL(a) cdmuyz (b) dmnvyz (c) cnuvyz (d) dmpuvw (e) (a) cdmuyz (b) dmnvyz (c) cnuvyz (d) dmpuvw (e)

cmnuxzcmnuxz

PROBLEMS CODE PROBLEMS CODE LANGUAGELANGUAGE

If If Tea is sweetTea is sweet is written as is written as sue sue cho ryecho rye, , Sita is a sweet girlSita is a sweet girl is is written as written as rye kim sue bisrye kim sue bis and and Tea Tea is hotis hot is written as is written as rye kora chorye kora cho Then which word means girl ?Then which word means girl ?

How many statements in the above How many statements in the above question are not required to answer question are not required to answer it ?it ?

ALPHABET NUMBER ALPHABET NUMBER RELATIONSHIPRELATIONSHIP

Alphabet position number is operated Alphabet position number is operated mathematically to generate mathematically to generate relationshiprelationship

DOG = 420, BOAT = 600 then FOG = DOG = 420, BOAT = 600 then FOG = ??

UG100 : SI7 : : RC256 : ?UG100 : SI7 : : RC256 : ?

CHANGE OF CONVENTIONCHANGE OF CONVENTION

Conventional meanings of Conventional meanings of mathematical signs have been mathematical signs have been changedchanged

Rules in mathematics are applicable Rules in mathematics are applicable only after changing the signsonly after changing the signs

PROBLEMS CHANGE IN PROBLEMS CHANGE IN CONVENTIONCONVENTION

+ means division+ means division _ means addition_ means addition * means subtraction* means subtraction / means multiplication/ means multiplication1.1. (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 = ?

ASSIGNING ARTIFICIAL VALUES TO ASSIGNING ARTIFICIAL VALUES TO ARITHMATICAL DIGITS AND SIGNSARITHMATICAL DIGITS AND SIGNS

1.1. 12*21=23 10*9=19 16*9=175 12*21=23 10*9=19 16*9=175 23*14=?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=?

VENN DIAGRAMSVENN DIAGRAMS

Venn diagrams represent relationship Venn diagrams represent relationship between two or more sets.between 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 In type A discriptions of sets are to be

matched with proper venn diagrams.matched with proper venn diagrams. In type B a venn diagramatic relation is given In 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 and Following words are to be carefully noted and

understood – AND / OR , ATLEAST / ONLYunderstood – AND / OR , ATLEAST / ONLY

PROBLEMS VENN DIAGRAMSPROBLEMS VENN DIAGRAMS

Birds , Parrots , BatsBirds , Parrots , Bats

a b c d

PROBLEMS VENN DIAGRAMSPROBLEMS VENN DIAGRAMS

Diagram shows Diagram shows distribution of 140 distribution of 140 people on newspaper people 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

105

Times

Hindu

COUNTING FIGERSCOUNTING FIGERS

Generally number of squares, Generally number of squares, rectangles, triangles are to be rectangles, triangles are to be counted.counted.

Symmetry of figure could be utilized.Symmetry of figure could be utilized. Common mistakes are missing a count Common mistakes are missing a count

or repeating a count.or repeating a count. Count systematically from a smaller Count systematically from a smaller

size to a larger size by methodically size to a larger size by methodically combining smaller figures into larger.combining smaller figures into larger.

PROBLEMS COUNTING PROBLEMS COUNTING FIGURESFIGURES

DICEDICE

A surface has got 1 opposite and 4 adjacent A surface has got 1 opposite and 4 adjacent surfaces.surfaces.

If two figures have two numbers common, then If 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 two When 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 3 There is a particular relationship between 3 visible surfaces which never changes by visible surfaces which never changes by rotating the dice.rotating the dice.

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

653

Number opposite to 3 is -------

1

25 5

16 4

5

6 3

21

Number opposite to 2 is Sign opposite to

DIRECTION SENSEDIRECTION SENSE

To find final position in relation to initial To find final position in relation to initial position in magnitude and direction.position in magnitude and direction.

In another type on a particular shape In another type on a particular shape ( square, rectangle, circle ) clockwise ( square, rectangle, circle ) clockwise and anticlockwise movements are and anticlockwise movements are described and then positions after described and then positions after movements are to be compared in movements are to be compared in direction and magnitude.direction and magnitude.

PROBLEMS DIRECTION PROBLEMS DIRECTION SENSESENSE

1.1. A goes in the direction of rising sun for 3 A goes in the direction of rising sun for 3 kms , turns left and walks 3 kms , turns kms , turns left and walks 3 kms , turns right and walks 1 km.At what distance right and walks 1 km.At what distance and in which direction is A from the and in which direction is A from the start?start?

2.2. A , B , C ,D are standing on a circular A , B , C ,D are standing on a circular track. A moves 90 degrees clockwise and track. A moves 90 degrees clockwise and B goes to opposite position. In what B goes to opposite position. In what direction B is A ?direction B is A ?

B D

C

A

CUBE CUTTINGCUBE CUTTING

CUBE PAINTED ALL SIDES WITH CUBE PAINTED ALL SIDES WITH DIFFERENT COLOURSDIFFERENT COLOURS

CUBE PAINTED OPPOSITE CUBE PAINTED OPPOSITE SIDES WITH SAME COLOURSSIDES WITH SAME COLOURS

CUBE PAINTED ADJESANT CUBE PAINTED ADJESANT SIDES WITH SAME COLOURSIDES WITH SAME COLOUR