Transcript GMAT - erc

GMAT
VIVEK PONKSHE
BASED ON NOTES PREPARED BY
DR VIVEK KULKARNI
DANCING DIGITS AND ALPHABETS
Count the number of places
 Divide into parts and mark by pencil
initially. Partial repetition at the end makes
the problem difficult.
 Match the corresponding places.
 Look for repetition, rotation, systematic
change.
 Take help from the answers.

PROBLEMS DANCING DIGITS
01-01-11010110-0-101
 1-1011-0-1101-1 12-45-2-41-3-21
 1-0110-1-0011 11-01-110-111 11-0-111-0011
PROBLEMS DANCING ALPHABETS
ab-dea-cdea-cdeab-de
 ab-dab-da-cd-b
 ab-aab-a-bbaa-ba
 a-cdb-dc-d
 ab-cdd-fgg-ijk
 a-cab-cb-c-a

NUMBER SERIES
Try to find logic of developing the series.
Difference method is generally followed.
 The series may be based on quadratic/cubic equation,
multiplications or consecutive number relationships.
 For large number of terms, look for alternate series.
 Try to judge the speed of rise.
 In consecutive relationships a term is generated by
mathematically processing previous term.
 The equations could be based on natural, odd, even,
prime numbers as the base series.
 Difference method will not work if the base series is of
prime numbers.


PROBLEMS NUMBER SERIES
05
 05
 03
 04
 03
 05
 06

08
10
20
12
04
11
12
11
17
55
36
07
17
30
14 17 ?
26 37 ?
114 203 ?
108 324 ?
08 12 16 18 ?
23 31 ?
56 132 ?
ODD TERM OUT
Try to find common rule or process among
all but one of the given terms.
 Don’t try trivial or very complicated logic.
 Commonly followed rules are equations
( square, cube), rules of divisibility,
individual digits of the numbers processed.
 Do not look for difference method.

PROBLEMS ODD MAN OUT
3 21 13 30 57 73
 4 9 25 49 121 144
 4 36 76 135 14
 33 121 132 154 56
 533 460 361 262 190 82

RATIO AND PROPORTION
a : b :: c : d implies ad = bc. Try this first.
 But the question normally involves finding
a relation between a and b ( rarely
between a and c ) and apply the same for
c and d.
 Very rarely a series type pattern is asked
under this structure.

PROBLEMS RATIO PROPORTION
50 : 82 : : 122 : ?
 8 : 27 : : 9 : ?
 2 : ? : : 10 : 30
 ? : 29 : : 4 : 23
 43 : 7 : : 59 : ?

ARRANGEMENT OF NUMBERS
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These questions can range from very simple to
very difficult with lot of scope in variety of
structures.
No particular logic or method to decipher the
rule.
Needs divergent thinking with quick trials and
errors.
Generally mathematical operations involved are
not more than three.
Oral accurate calculations and tables saves time.
8
9
7
120
216
?
6
5
8
6
3
256
5
16
49
6
64
16
9
148
4
4
27
81
10
32
?
8
16
216
?
36
3 BY 3 MATRIX
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Common structure with lot of internal variety.
Try for a series by arranging the given eight
terms in ascending order.
If not then try row wise or column wise
relationship among three terms.
Sometimes the central term relates the
remaining eight terms into four pairs.
Very rarely there are three triplets forming nine
terms.
PROBLEMS 3 BY 3 MATRIX
?
243
9
?
13
14
3
2187
81
11
7
9
27
6561
729
28
15
21
11
8
3
4
8
4
2
?
10
7
?
9
9
4
9
3
8
5
PROBLEMS NUMBERS RELATIONS

06
08
12
11 ( 25 )
06 ( 16 )
05 ( ? )

51 ( 11 ) 61
64 ( 30 ) 32
35 ( ? ) 42

03 ( 19 ) 05
05 ( 39 ) 07
09 ( ? ) 05
PROBLEMS NUMBER RELATIONS

CIRCULAR ARRANGEMENT
8
9
15
12
9
13
18
6
19
13
?
8
7
6
14
6
4
8
12
40
15
20
9
72
15
30
8
?
10 3
ARRANGEMENT OF NUMBERS
PYRAMID
1
2 29 28
3 30 49 48 27
4 31 50 61 60 47 26
5 32 51 62 63 64 59 46 25
6 33 52 53 54 55 56 57 58 45 24
7 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 22
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6
5
8
2
7 8 :
32 4 :
6 4 :
50 54
6
3
9
:
35 12 : : 24 23 22 : ?
30 2 : : 25 46 26 : ?
33 31 : : ? : 21 45 47
3 51 37 : : 28 60 56 : ?
ALPHABET PYRAMID
a
b c d
e f g h i
j k 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 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 l
1
2
3
4
5
xzbd : kmoq : : ljhf : ?
jramz : ksbna : : pxiuj : ?
bflt : tsrq : : ? : vwxy
jeba : qzkx : : pida : ?
xkzmb : ylanc : : lwjuh : ?
ALPHABET SERIES
There can be a single alphabet or a group
of alphabets called term or string.
 Remembering 1 to 26 numbers of
corresponding alphabets and calculating
the difference between alphabets is
general method.
 The difference is generally found in first,
second, etc letters of consecutive terms in
series.

ODD TERM OUT
1 2
3
4
5 6 7
a b
c
d
e f
z y
x
w v
u
8 9 10 11 12 13
g
h I
j
k
l m
t
s
q
p
o n
r
26 25 24 23 22 21 20 19 18 17 16 15 14
PROBLEMS ALPHABET SERIES

WORD
XQUH YSXL ZUAP
?

WORD
XPSE
ZRUG CUXJ
?

WORD
VPPF
UQNH TRLJ
?

A
B
F
O
?
PROBLEMS ODD TERM OUT

dvug
zzyc
jpol

egjns
acfjo
cehmr gilpu iknrw

dogod local xyzyx dalad stats

anz
dqw

aehj
cgjl
gtt
eiln
lnmo
hrs
boy
gkno hloq
ALPHABET SERIES MATCH THE
PAIRS

(a) ABX CDV EFT GHR
(b) AZBC CXDE EVFG GTHI
(c) ACY BDX CEW DFV
(d) BCZ CDY DEX EFW
(e) AYBC BXCD CWDE
1 MNNO 2 KLQ 3 MMNO 4 MNL 5 MOM 6 XYA

(a)
(b)
(c)
(d)
(e)
TPRG WMOD VNPE SQSH PRTI
EMOV GOQT CKMX KSUP IQSR
CNLX BMKY ALJZ XIGC ZKIA
MODW GIXC LNCX NPEV FHWD
NVXM QSUJ OUWL MWYN PRTI
1 YJHB 2 EGVE 3 UOQF 4 AIKZ
RATIO PROPORTION
Question may develop a relationship by
rearranging the order of the same
alphabets in the string
 Or by changing the alphabets based on
difference or partener map
 Sometimes the relation is to be
established in reverse order
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PROBLEMS RATIO PROPORTION
WORD : XQQB : : MIND : ?
 If the word MIND is coded as MNDI how
will you code the word WORD ?
 RUSSIA : BJTRTQ : : COLOUR : ?
 DEER : WVVI : : BELT : ?
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CODE LANGUAGE

Coding information is given in two
columns or tabular or cross word form.

Coding could be done using alphabets,
digits, or symbols .
PROBLEMS CODE LANGUAGE
PAVE
JOLT
 MIXTURE
 GOVERN
 WHIP
 COPE
 BALE
 FIND
 KING
 HAZE
 SAFE
 QUOTE
 YARD
 ULTIMACY
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bckt
lxyz
bejlmpw
bhprtx
fkmo
bknx
abcz
ghms
hmqr
bcdf
bcgu
blxvw
cips
ceilmnwz
PROBLEMS CODE LANGUAGE
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(a)

(a)

(a)

(a)

(a)
CLUB
awxz (b) anwz (c) bnvw (d) amws (e) bwxy
HALT
cgmz (b) flmv (c) cflz (d) fmut (e) cmnz
DOVE
csty (b) bcst (c) bsty (d) bstx (e) btxy
WORK
mopq (b) opqx (c) oprx (d) opqy (e) mpqx
HUSK
fquw (b) frvw (c) gquv (d)fruw (e) fgrv
PROBLEMS CODE LANGUAGE
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(a)

(a)

(a)

(a)

(a)
RAZE
bcdp (b) cdpr (c) bcop (d) depr (e) cder
PEACE
ccdkn (b) bcckm (c) bbckn (d) bbcjn (e) cddjm
GUARD
cprsv (b) cpsvw (c) bcprs (d) cprsw (e) dersw
SYSTEM
beimvv (b) bbeimv (c) beiluu (d) bejmuu (e) eijmvv
SOCIAL
cdmuyz (b) dmnvyz (c) cnuvyz (d) dmpuvw (e) cmnuxz
PROBLEMS CODE LANGUAGE

If Tea is sweet is written as sue cho
rye, Sita is a sweet girl is written as
rye kim sue bis and Tea is hot is
written as rye kora cho Then which
word means girl ?

How many statements in the above
question are not required to answer it ?
ALPHABET NUMBER
RELATIONSHIP

Alphabet position number is operated
mathematically to generate relationship

DOG = 420, BOAT = 600 then FOG = ?
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UG100 : SI7 : : RC256 : ?
CHANGE OF CONVENTION

Conventional meanings of mathematical
signs have been changed

Rules in mathematics are applicable only
after changing the signs
PROBLEMS CHANGE IN
CONVENTION
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1.
2.
3.
4.
5.
+ means division
_ means addition
* means subtraction
/ means multiplication
(18 * 12) / (11 – 5) + (8 / 8) = ?
20 / 4 – 10 / 2 * 53 = ?
(13 – 17) / 5 + 15 = ?
10 / 3 – 5 / 5 * 11 / 5 = ?
(5 / 9) + (28 * 13) / 5 = ?
ASSIGNING ARTIFICIAL VALUES TO
ARITHMATICAL DIGITS AND SIGNS
1.
12*21=23 10*9=19 16*9=175 23*14=?
2.
(3?4)?2?7=7
3.
6 ? 3 ? 4 ? 9 = 23
4.
0=1 2=4 3=10 4=?
5.
7*4=22 3*2=10 4*6=20 11*4=?
VENN DIAGRAMS
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Venn diagrams represent relationship between
two or more sets.
The shape or size is not significant.
In type A discriptions of sets are to be matched
with proper venn diagrams.
In type B a venn diagramatic relation is given
and questions are asked on the numbers.
Following words are to be carefully noted and
understood – AND / OR , ATLEAST / ONLY
PROBLEMS VENN DIAGRAMS

Birds , Parrots , Bats
a
b
c
d
PROBLEMS VENN DIAGRAMS
Diagram shows
distribution of 140
people on newspaper
choiceHow many read
1. Only 2 newspapers
2. Atleast 2 newspapers
3. Only Times
4. Times or Express
5. Express and Hindu

Express
50
10
10
Hindu
5
15
20
30
Times
COUNTING FIGERS
Generally number of squares, rectangles,
triangles are to be counted.
 Symmetry of figure could be utilized.
 Common mistakes are missing a count or
repeating a count.
 Count systematically from a smaller size to
a larger size by methodically combining
smaller figures into larger.

PROBLEMS COUNTING FIGURES
DICE
A surface has got 1 opposite and 4 adjacent
surfaces.
 If two figures have two numbers common, then
third numbers are opposite to each other.
 When only one number is common in two
figures, then all 4 adjacent surfaces are visible.
 There is a particular relationship between 3
visible surfaces which never changes by rotating
the dice.

PROBLEMS DICE
2
3
1
1
3
4
2
1
5
1
1
1
5
5
6
5
4
4
5
2
6
2
6
3
6
1
2
Number opposite to 3 is -------
Find the opposite pairs
2
6
4
3
Number opposite to 2 is
1
Sign opposite to
5
DIRECTION SENSE
To find final position in relation to initial
position in magnitude and direction.
 In another type on a particular shape
( square, rectangle, circle ) clockwise and
anticlockwise movements are described
and then positions after movements are to
be compared in direction and magnitude.

PROBLEMS DIRECTION SENSE
1.
2.
A goes in the direction of rising sun for 3 kms ,
turns left and walks 3 kms , turns right and
walks 1 km.At what distance and in which
direction is A from the start?
A , B , C ,D are standing on a circular track. A
moves 90 degrees clockwise and B goes to
opposite position. In what direction B is A ?
A
B
D
CUBE CUTTING
CUBE PAINTED ALL SIDES WITH
DIFFERENT COLOURS
CUBE PAINTED OPPOSITE SIDES
WITH SAME COLOURS
CUBE PAINTED ADJESANT SIDES
WITH SAME COLOUR