gmat flashcards v7.2

8/17/2019 GMAT Flashcards v7.2

http://slidepdf.com/reader/full/gmat-flashcards-v72 1/119

!"#$ %&'( )&#*+%#

!"#$ %&'( )&#*+%#

! #$%& '()* – contributing to each other’s learning

!"#$ &'() "*+,-./'*0-

!"#$ &'"( )#$ *&'+, -,+)& .,++ /,*$01&( ),+ )2)"3)43+

.*, $*5#3*)$ .,*6 &'+ 789: ;304 8),<+&/3)1+=

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$+)3( &* ()2+ &'+ 6*(& 6*#+> *# 4**<(? &+(&(?1*0,(+(? "@'*#+ 9//(? )#$ )$6"(("*#( 1*#(03&"#-=

'&&/ABB-6)&1304=1*6B6),<+&/3)1+

GMAT Club 2011 2

http://gmatclub.com/marketplace



GMAT MATH

!"#$"%&

+,-. /0 .,1 213415. 6738)(-9

:7; 8)4, /0 <= 213415. 76 >?9

()*+, )-.*+(/*.0

1


!"#$"%& 2 )%34"#3

@13415. A738)(-B

@-3. C @13415. D +,7(1

A73 1D-82(1E <=F 76 >? /0B15

100∗ 2 0 =

300

100= 3

()*+, )-.*+(/*.0

5


!"#$"%& 5

+,-. /0 .,1 6738)(- 673 213415. 4,-5G19

H6 I-4J G7. - 3-/01 6378 K<= 213 ,7)3 .7 K<L

213 ,7)3E ;,-. ;-0 .,1 213415. /5431-019

()*+, )-.*+(/*.0

6


!"#$"%& 5 2 )%34"#3

!"#$"%& 078%9" :;#<=>8,

× 100%

Jack’s Raise: 18 − 15

15 × 100% =

3

15× 100% =

100

5= 20%

? $-J1 0)31 M7) )01 .,1 73/G/5-( -87)5. N<=OE 57.

.,1 51; 751 N<LO

()*+, )-.*+(/*.0

@

GMAT Club 2011 4

!"#$"%& 6

H6 .,1 237P)4./75 76 ,M*3/P 4-30 .3/2(1P (-0. M1-3E *M

,7; 8-5M 213415. P/P /. /5431-019 <??F

>??F

>=?F

Q??F

QQQF

()*+, )-.*+(/*.0

A


!"#$"%& 6 2 )%34"#3

*7" $;##"$& 8%34"# B3 C – B%$#"83"D EF 5GGH

A73 1D-82(1E /6 237P)4./75 ;-0 <? 4-30E -5P /.

.3/2(1P .7 Q? 4-30E .,1 /5431-01 ;-0 >? 4-30E ;,/4,/0 >??F 76 <?

()*+, )-.*+(/*.0

I


!"#$"%& @

=?F 76 >= /0 >=F 76 ;,/4, 5)8*139

()*+, )-.*+(/*.0

J


!"#$"%& @ 2 )%34"#3

&,131 -31 > 07()./750 .7 .,/0 237*(18B

R75G 751B

=?F 76 >= /0 <>S= <>S= T<?? C D T >=

D C =?

U,73. 751 *). - ,-3P13 .7 4781 )2 ;/.,B

=?F T >= C D T >=F

=? C D

()*+, )-.*+(/*.0

K

GMAT Club 2011 5

LDDM/N"% -=>"3

07"$O F;=# O%;4>"D9" ;P LDDM/N"% #=>"3

VPP W VPP C 9 VPP – XY15 C 9

XY15 W VPP C 9

VPP D VPP C 9

VPP ÷ XY15 C 9

VPP D XY15 C 9

+B%&, .3M 2/4J/5G 5)8*130

()*+, )-.*+(/*.0

Q


LDDM/N"% -=>"3 2 )%34"#3

VPP W VPP C <W < C > NXY15O

VPP – XY15 C Q – > C < NVPPO

XY15 W VPP C > W < C Q NVPPO VPP D VPP C Q D Q C Z NVPPO

VPP ÷ XY15 C Q ÷ > C <S= N[7. -5 /5.1G13\O

VPP D XY15 C Q D > C ] NXY15O

()*+, )-.*+(/*.0

1G


LDDM/N"% -=>"3 5

H0 ? 7PP 73 1Y159

()*+, )-.*+(/*.0

11


LDDM/N"% -=>"3 5 2 )%34"#3

? N^137O /0 XY15

H. /0 -(07 57. 270/./Y1 73 51G-./Y1

– /. /0 51).3-(

()*+, )-.*+(/*.0

15

GMAT Club 2011 6

! #$%& '()* –

contributing to each other’s learning

LDDM/N"% -=>"3 6

H6 ! /0 -5 7PP 5)8*13E ;,/4, 76 .,1 67((7;/5G

8)0. *1 1Y159!" 2 − 3

#";

$"

− 1

&" + 2

'" 2 + 2

()*+, )-.*+(/*.0

16


LDDM/N"% -=>"3 6 2 )%34"#3

Use the “plug numbers” method to check each

answer choice. Let’s take 1:

%S

>T< – Q C _< NVPPO#"

;

C ? NXY15O – however, just in case, let’s try 3.

;

= 1 NVPPOS H. )0)-((M /0 - G77P /P1- .7 3)5

.,37)G, > P/661315. 5)8*130 /6 M7) G1. ^137 73 0/8/(-3

$"

− 1 = −

N57. -5 /5.15G13O

`S < W > C Q NVPPO

XS > W > C a NXY15O

()*+, )-.*+(/*.0

1@

! #$%& '()* –

contributing to each other’s learning

LDDM/N"% -=>"3 @ RS>&#8 +8#DT

H0 %WbW' 1Y15 73 7PP9

% – ' – b /0 1Y15

;

/0 7PP

()*+, )-.*+(/*.0

1A


LDDM/N"% -=>"3 @ 2 )%34"#3

U.-.1815.0 N<O -5P N>O 478*/51P -31 /50)66/4/15.S

'750/P13 %C]E bCaE -5P 'C> N.,1 -50;13 /0 cM10cO

-5P %C?S=E bC?SQE -5P 'C?S> N.,1 -50;13 /0 c57cOS

U; %;& 833=<" &78& &7" %=<E"#3 8#" B%&"9"#3 BP

&7" V="3&B;% D;"3 %;& <"%&B;% B&W

*7" $;##"$& 8%34"# B3 /W

()*+, )-.*+(/*.0

1I

GMAT Club 2011 7

UBNB3BEB>B&F -=>"3

H0 =adL? P/Y/0/*(1 *M >9

H0 <]d< P/Y/0/*(1 *M Q9 H0 =]Q> P/Y/0/*(1 *M a9

H0 QLQ? P/Y/0/*(1 *M =9

H0 >]=L P/Y/0/*(1 *M ]9

H0 QZ] P/Y/0/*(1 *M Z9

()*+, )-.*+(/*.0

1J


UBNB3BEB>B&F -=>"3 2 )%34"#3

e10S `/Y/0/*/(/.M *M > – (-0. P/G/. 76 - 5)8*13 /0 1Y15

e10S `/Y/0/*/(/.M *M Q – 0)8 76 -(( P/G/.0 /0 - 8)(./2(1

76 Q e10S `/Y/0/*/(/.M *M a – (-0. > P/G/.0 /0 - 8)(./2(1 76 a

e10S `/Y/0/*/(/.M *M = – .,1 (-0. P/G/. /0 1/.,13 ? 73 =

e10S `/Y/0/*/(/.M *M ] – .,1 0)8 76 P/G/.0 /0 - 8)(./2(1

76 Q -5P .,1 (-0. P/G/. /0 1Y15

e10S `/Y/0/*/(/.M *M Z – .,1 0)8 76 P/G/.0 /0 - 8)(./2(1

76 Z

()*+, )-.*+(/*.0

1K


UBNB3BEB>B&F 5 R+8#DT

H0 /5.1G13 P/Y/0/*(1 *M Z9

# /0 -5 /5.1G13 P/Y/0/*(1 *M Q #$ /0 -5 /5.1G13 P/Y/0/*(1 *M Z

()*+, )-.*+(/*.0

1Q


UBNB3BEB>B&F 5 2 )%34"#3

&,1 *10. ;-M .7 -2237-4, .,/0 f)10./75 /0 .7 2()G

/5 01Y13-( 01.0 76 5)8*130

$-5M -31 .182.1P .7 2()G Q 673 D -5P .,15 673 U>E.,1 75(M Y-()1 M 4-5 ,-Y1 /0 Qg /5 .,-. 4-01E .,1

-50;13 /0 e10S

b). /6 ;1 .3M DCL< -5P MC

E .,15 D /0 -5 /5.1G13

P/Y/0/*(1 *M QE DM /0 -5 /5.1G13 P/Y/0/*(1 *M ZE *).

= 1 -5P /0 57. P/Y/0/*(1 *M ZS

*7" 8%34"# B3 /

()*+, )-.*+(/*.0

5G

GMAT Club 2011 8

X=<E"# !#;Y"#&B"3

+,/4, 76 .,1 67((7;/5G /5.1G130 31231015.0 - 0)8

76 Q 475014)./Y1 1Y15 /5.1G1309 >??

Q?Q

a??

==a

=d?

()*+, )-.*+(/*.0

51


X=<E"# !#;Y"#&B"3 2 )%34"#3

&7 -50;13 .,1 f)10./75E 4,14J ;,/4, /5.1G13 /0

*7., P/Y/0/*(1 *M Q N0/541 .,131 -31 Q /5.1G130O -5P

/0 1Y15S &,1 75(M 5)8*13 .,-. 6-((0 /5.7 *7., 76

.,701 > 4-.1G73/10 /0 =d?S

0;##"$& 8%34"# B3 /

()*+, )-.*+(/*.0

55


X=<E"# !#;Y"#&B"3 5 R+8#DT

H6 = + 5, = − 2, =

2, + + 7? # h ?

$ C a

()*+, )-.*+(/*.0

56


X=<E"# !#;Y"#&B"3 5 2 )%34"#3

U)*0./.).1 DE ME -5P ^ /5 .,1 73/G/5-( 1f)-./75 .7 G1. .,167((7;/5GB − 2 − 3 = 0g &,1 07()./750 .7 .,/01f)-./75 -31 DC_< -5P DCQS

U.-.1815. < /0 0)66/4/15.S H6 Dh?E .,15 .,1 75(M 07()./75/0 DCQS &,1 310)(. /0 >dW<]W] CaZE ;,/4, /0 P/Y/0/*(1 *Md

U.-.1815. > /0 0)66/4/15.S H6 MCaE 2()GG/5G /5 .,/0 Y-()1/5.7 = + 5E G/Y10 )0 .,-. DCQ 73 DC_QS :7;1Y13E*-01P 75 .,1 -*7Y1E DCQ 73 DC_<S &,1316731 DCQSU)66/4/15.S

*7" $;##"$& 8%34"# B3 UW

()*+, )-.*+(/*.0

5@

GMAT Club 2011 9

X=<E"# !#;Y"#&B"3 6

:7; 8-5M P/0./54. /5.1G130 -31

.,131 *1.;115 < -5P >< /54()0/Y19

()*+, )-.*+(/*.0

5A


X=<E"# !#;Y"#&B"3 6 2 )%34"#3

Most often GMAT questions wil l say “inclusive” butsometimes they don’t – 511P .7 31818*13 .74,14J

&,1 6738)(- 673 4-(4)(-./5G .,1 5)8*13 76 /5.1G130*1.;115 .;7 5)8*130 /0B [_$W<

&,1316731E .,1 -50;13 /0B >< – < W < C ><

e7) 4-5 -(07 ;3/.1 7). -(( 76 .,1 5)8*130 .,7)G, /./0 57. -(;-M0 2700/*(1 *). i)0. /5 4-01B

<E >E QE aE =E ]E dE LE ZE <?E <<E <>E <QE <aE <=E <]E <dE<LE <ZE >?E ><

()*+, )-.*+(/*.0

5I


(=>&BY>"3

+,-. /0 - 8)(./2(19

H0 = - 8)(./2(1 76 == 73 /0 == -

8)(./2(1 76 =9

()*+, )-.*+(/*.0

5J


(=>&BY>"3 2 )%34"#3

*7" <=>&BY>" 76 - 5)8*13 /0 .,1

237P)4. 76 .,1 5)8*13 -5P -5M

7.,13 ;,7(1 5)8*13S %&'( )#*+,-).

/.0.1.2 *() +3-45,-)6 '7 /8

&,1316731 == /0 - 8)(./2(1 76 =

A73 1D-82(1E ] ,-0 6-4.730 <E >E QE ]g

and multiples that are 6, 12, 24, 36…

()*+, )-.*+(/*.0

5K

GMAT Club 2011 10

(=>&BY>"3 5

H0 ? N^137O - 8)(./2(1 76 <??9

()*+, )-.*+(/*.0

5Q


(=>&BY>"3 5 2 )%34"#3

e10E ? N^137O /0 - 8)(./2(1 76

1Y13M.,/5G

9':);)(. 54 56 3<-5=)-$ 4>*4 ?@AB

:5-- 4)64 4>56 ,(',)(4$ !34 54 >)-,6 4'

()+)+!)(

()*+, )-.*+(/*.0

6G


(=>&BY>"3 6

:7; .7 6/5P - R1-0. '78875

$)(./2(1 NR'$O9

()*+, )-.*+(/*.0

61


(=>&BY>"3 6 2 )%34"#3

LY&B;% 1,

U.12 B $)(./2(M .,1 )5/f)1 6-4.730 N1D4()P1P)2(/4-.10O

LY&B;% 5,

U.12 B A/5P -5M 6-4.730 .,1 .;7 5)8*130 0,-31

U.12 QB `/Y/P1 .,1 237P)4. /5 U.12 < *M .,1 6-4.730

.,-. .,1 .;7 5)8*130 ,-Y1 /5 478875

()*+, )-.*+(/*.0

65

GMAT Club 2011 11

(=>&BY>"3 @

+,-. /0 .,1 R1-0. '78875

$)(./2(1 76 <L -5P >a9

()*+, )-.*+(/*.0

66


(=>&BY>"3 5 )%34"#3

LY&B;% 1

A/5P .,1 6-4.730 76 <L -5P >aB

<L C Q D Q D >

>a C Q D > D > D >

$)(./2(M .,1 )5/f)1 6-4.730B Q D Q D > D > D > C d>

LY&B;% 5

$)(./2(M .,1 > 5)8*130B <L D >a C aQ>

U,-31P 6-4.730B > -5P Q

`/Y/P1 aQ> *M > -5P Q C d>

()*+, )-.*+(/*.0

6@


*#8%3>8&"

&,1 237P)4. 76 .,311 -5P 67)3 /0 31P)41P *M6/Y1 -5P .,15 /5431-01P *M .,1 P/66131541

*1.;115 .,1 73/G/5-( 237P)4. -5P 1/G,. C 9

()*+, )-.*+(/*.0

6A


*#8%3>8&" )%34"#3

Q D a C <>

<> – = C d <> – L C a

d W a C <<

)%34"#, 11

()*+, )-.*+(/*.0

6I

GMAT Club 2011 12

)#B&7<"&B$ &; ("<;#BZ"

=

=

=

=

C

=

()*+, )-.*+(/*.0

6J


)#B&7<"&B$ &; ("<;#BZ" 2 )%34"#3

= 50%

= >=F

= 40%

= 5%

C <>S=F

= 16.67%

()*+, )-.*+(/*.0

6K


)#B&7<"&B$ &; ("<;#BZ" 5

=

=

=

d=F C

>?F C

16

% =

83

% =

()*+, )-.*+(/*.0

6Q


)#B&7<"&B$ &; ("<;#BZ" 5 2 )%34"#3

= LSQQF

= 87.5%

= 75%

d=F C j

>?F C

16

% =

83

% =

()*+, )-.*+(/*.0

@G

GMAT Club 2011 13

)#B&7<"&B$ &; ("<;#BZ" 6

2 C

2 = 2 =

2 =

2 =

2 =

()*+, )-.*+(/*.0

@1


)#B&7<"&B$ &; ("<;#BZ" 6 2 )%34"#3

2 C a

2 = 8

2 = <] 2 = Q>

2 = 64

2 = <>L

()*+, )-.*+(/*.0

@5


)#B&7<"&B$ &; ("<;#BZ" @

3 C

3 = 3 =

3 =

4 =

4 =

4 =

()*+, )-.*+(/*.0

@6


)#B&7<"&B$ &; ("<;#BZ" @ 2 )%34"#3

3 C Z

3 = >d

3 = L< 3 = >aQ

4 = <]

4 = ]a

4 = >=]

()*+, )-.*+(/*.0

@@

GMAT Club 2011 14

)#B&7<"&B$ &; ("<;#BZ" A

5 C

5

C 11 C

12 C

13 C

14 C

15 C

16 C

()*+, )-.*+(/*.0

@A


)#B&7<"&B$ &; ("<;#BZ" A 2 )%34"#3

5 C >=

5 C <>=

11

C <>< 12 C <aa

13 C <]Z

14 C <Z]

15 C >>=

16 C >=]

()*+, )-.*+(/*.0

@I


)#B&7<"&B$ &; ("<;#BZ" I

0;<Y>"&" &7" P;>>;4B%9,LE <]E >aE Q>E a?E …… <]?

<>, 24, 36…. <>?

<=, 30… <=?

()*+, )-.*+(/*.0

@J


)#B&7<"&B$ &; ("<;#BZ" I 2 )%34"#3

0;<Y>"&" &7" P;>>;4B%9 R)%34"#3T,

LE <]E >aE Q>E a?E aLE =]E ]aE d>E L?E LLE Z]E <?aE<<>E <>?

<>E >aE Q]E aLE ]?E d>E LaE Z]E <?LE <>?

<=E Q?E a=E ]?E d=E Z?E <?=E <>?

()*+, )-.*+(/*.0

@K

GMAT Club 2011 15

)#B&7<"&B$ &; ("<;#BZ" J

2 =

3 C 625 =

169 =

()*+ ,-- ./)01* 21+3114 5 ,46 78

/[&#8 +8#D \ /[&#8 0#"DB&

2 =

125

=

243

=

()*+, )-.*+(/*.0

@Q


)#B&7<"&B$ &; ("<;#BZ" J 2 )%34"#3

2 = 1.4

3 C <Sd

625 = 25

169 = 13

./)01*9 :; <; 7; =; 55; 5<; 5=; 5>; :<; :>; <5; <=; ?5; ?<;

?=

2 = 64

125

= 5

243

= 3

()*+, )-.*+(/*.0

AG


-"$BY#;$8>

+,-. /0 - 314/2374-(9

()*+, )-.*+(/*.0

A1


-"$BY#;$8> )%34"#3

k14/2374-( 673 - 5)8*13 E P157.1P *M

73

;E /0 - 5)8*13 ;,/4, ;,15 8)(./2(/1P *M

M/1(P0 <S &,1 314/2374-( 76 - 63-4./75

/0

S

A73 1D-82(1 314/2374-( 76 Q /0

k14/2374-( 76

/0

S

()*+, )-.*+(/*.0

A5

GMAT Club 2011 16

)E3;>=&" ]8>="

+,-. /0 .,1 Q_ 0.12 -2237-4, .7 07(Y/5G

1f)-./750 -5P /51f)-(/./10 ;/., -*07().1

Y-()19

()*+, )-.*+(/*.0

A6


)E3;>=&" ]8>=" 2 )%34"#3

^&"Y1, V215 87P)()0 -5P 01. 475P/./750S&7 07(Y1l7215 - 87P)()0E M7) 511P .7

4750/P13 > 0/.)-./750 .7 6/5P -(( 377.0B@70/./Y1 N73 3-.,13 575_51G-./Y1O

[1G-./Y1

^&"Y 5, U7(Y1 51; 1f)-./750 6378 U.12 <

^&"Y 6, ',14J 475P/./750 673 1-4,07()./75 6378 U.12 >

()*+, )-.*+(/*.0

A@


)E3;>=&" ]8>=" 5

H6 C#DEC F 0E ;,-. /0 .,1 Y-()1 76

# 9

()*+, )-.*+(/*.0

AA


)E3;>=&" ]8>=" 5 2 )%34"#3

U.12 B U7(Y1 .,1 1f)-./750

# F G

# F DH

U.12 QB ',14J 475P/./750 N − 1 ≥ 0 m − 1 < 0O

5 − 1 = 4 ≥ 0

_Q – < C _a n ?

()*+, )-.*+(/*.0

AI

GMAT Club 2011 17

)E3;>=&" ]8>=" 6

+,-. /0 .,1 Y-()1 76 D H6 oD – =o C <?9

()*+, )-.*+(/*.0

AJ


)E3;>=&" ]8>=" 6 2 )%34"#3

oD – =o C <?

+1 8)0. 1Y-()-.1 *7., .,1 270/./Y1 -5P 51G-./Y1outcome since the absolute value “removes” the

51G-./Y1 0/G5

&,)0E ;1 ,-Y1 > 1f)-./750B p – = C <?

p – = C _ <? N/5 4-01 /. ;-0 - 51G-./Y1 1D23100/75O

&,)0 D C <= -5P _=S N@()G /5 *7., .7 4,14JO

%*07().1 Y-()1 /51f)-(/./10 -5P 1f)-./750 ;/(( -(870.-(;-M0 ,-Y1 > -50;130l07()./750\

()*+, )-.*+(/*.0

AK


)E3;>=&" ]8>=" @

H0 @IJ9

− = ||

= 9

()*+, )-.*+(/*.0

AQ


)E3;>=&" ]8>=" @ 2 )%34"#3

U.-.1815. N<O *M /.01(6 /0 57. 0)66/4/15.S A3780.-.1815. N<OE @ /0 1/.,13 - 51G-./Y1 5)8*13 73^137S H6 @FDHE .,15 –N_QOCo_Qo 73 QCQE ;,/4, /0 57.

0)66/4/15.S U.-.1815. N>O *M /.01(6 /0 57. 0)66/4/15.S A378

0.-.1815. N>OE @ 4-5 *1 1/.,13 Q 73 _QE ;,/4, /0 57.0)66/4/15.S

U.-.1815.0 N<O -5P N>O 478*/51P -31 0)66/4/15.S H6;1 478*/51 *7., 0.-.1815.0E .,15 $C_QS

*7" $;##"$& 8%34"# B3 0W

()*+, )-.*+(/*.0

IG

GMAT Club 2011 18

:8$&;#3

:7; 8-5M .7.-( 6-4.730 P710 a]>

,-Y19

()*+, )-.*+(/*.0

I1


:8$&;#3 2 )%34"#3

%PY-541P 81.,7P 673 6/5P/5G .,1 5)8*13 76 -(( 2700/*(16-4.730B

+3/.1 7). 1-4, 23/81 6-4.73 -5P .,1/3 27;13E 673

1D-82(1E <> 4-5 *1 ;3/..15 -0 67((7;0B 2

3

5 1.4 N-(( 7.,13 23/810 ;/(( ,-Y1 - ^137 27;13O

%PP < .7 -(( 27;130 -5P 8)(./2(M .,18B N/5 .,/0 4-01 ]Oand that’s the number of factors (1, 2, 3, 4, 6, 12)

@3/81 A-4.730 76 a]> C 2, 3, 7, 11

&7.-( 5)8*13 76 6-4.730B >D>D>D> C 2C <]

()*+, )-.*+(/*.0

I5


:8$&;#3 5

`7 /5.1G130 )0)-((M ,-Y1 -5 7PP 73

1Y15 5)8*13 76 6-4.7309

()*+, )-.*+(/*.0

I6


:8$&;#3 5 2 )%34"#3

q-0. 8-i73/.M 76 /5.1G130 ,-Y1 -5 1Y15 5)8*13 76

6-4.730 0)4, -0 <> 673 1D-82(1B <E >E QE aE ]E <>S

&,)0 ;,15 6/5P/5G .,1 .7.-( 5)8*13 76 6-4.730E

8-J1 0)31 /. /0 -5 1Y15 5)8*13

&,1 75(M /5.1G130 .,-. ,-Y1 -5 7PP 5)8*13 76

factors are perfect squares (that’s numbers such as

aE ZE <]E >=E Q]E 1.4OS &3M >= 673 1D-82(1E /. ,-0

6-4.730 76 <E =E -5P >=S A-4.730 76 Q] -31 <E >E QE aE

]E ZE <>E <LE Q]S

()*+, )-.*+(/*.0

I@

GMAT Club 2011 19

-8&B;3

+,-. /0 .,1 3-./7 76 - .7 P /6

>-CQ*E

C>4E -5P Q4CP9

%O bO>B< 'O>BQ `OaBQ XO<B=

()*+, )-.*+(/*.0

IA


-8&B;3

+/., f)10./750 (/J1 .,101E )5(100 M7) 4-5 027. -

0,73.4). 3/G,. -;-ME .,1 1-0/10. ;-M .7 07(Y1 /0 .7

plug numbers: let’s pick a=6, since there is a 2 and

Q /5Y7(Y1P

>T] C Q*g * C a

?S=Ta C >4g 4 C <

QT< C Pg P C Q

&,1316731E .,1 3-./75 76 - .7 P /0 >B<

*7" $;##"$& 8%34"# B3 CW

()*+, )-.*+(/*.0

II


!;4"#3

2 + 2 + 2 + 2 = ? %O 2 + 2

bO 2

'O 2 + 2

`O 2

XO Q?

()*+, )-.*+(/*.0

IJ


!;4"#3 2 )%34"#3

2 + 2 + 2 + 2 = ? &,131 -31 57 3)(10 673 -PP/5G 73

0)*.3-4./5G 27;130S &,/0 f)10./75 /0

07(Y1P *M *3).1 67341B

a W L W <] W > C Q?

&,1 473314. -50;13 /0 NXO

()*+, )-.*+(/*.0

IK

GMAT Club 2011 20

!;4"#3 5

2 × 2 × 2 × 2 × 2 = ?

%O 2

bO 32

'O 2

`O 2

XO ]>

()*+, )-.*+(/*.0

IQ


!;4"#3 5 2 )%34"#3

2 × 2 × 2 × 2 × 2 = 2

+,15 27;130 ;/., .,1 0-81 *-01 N>

/5 .,/0 4-01O -31 8)(./2(/1PE .,1 27;130

-31 0)881P -5P .,1 *-01 /0 ,1(P

4750.-5.S &,)0E /. /0 > .7 .,1 27;13 76

>WQWaW=W<C<=S

&,1 473314. -50;13 /0 N'O 2

()*+, )-.*+(/*.0

JG


!;4"#3 6

×

× =?

()*+, )-.*+(/*.0

J1


!;4"#3 6 2 )%34"#3

×

× =

= 2 `/Y/0/75 76 27;130 ;/., .,1 0-81 *-01

N>O /0 ,-5P(1P 0/8/(-3(M .7 8)(./2(/4-./75

1D412. .,1 27;13 Y-()10 -31 P1P)4.1PS

&,1 *-01 0.-M0 )54,-5G1P

()*+, )-.*+(/*.0

J5

GMAT Club 2011 21




!;4"#3 @

(3) = ?

()*+, )-.*+(/*.0

J6


!;4"#3 @ 2 )%34"#3

(3) = 3

+,15 - 5)8*13 .-J15 .7 - 27;13 /0

.-J15 .7 -57.,13 27;13E M7) 511P .7

8)(./2(M .,1 1D27515.0 N> T QO

()*+, )-.*+(/*.0

J@


!;4"#3 A

3 C 9

()*+, )-.*+(/*.0

JA


!;4"#3 A 2 )%34"#3

3 = 3 U.-3. 7213-./750 6378 7).0/P1 -5P ;73J M7)3 ;-M

/5B Q .-J15 .7 .,1 27;13 76 Q /0 >dS &,)0 .,1 *-01 76

Q /0 .-J15 .7 .,1 27;13 76 >dS

()*+, )-.*+(/*.0

JI

GMAT Club 2011 22

!;4"#3 I

2; × 2; × 2 × 2; =?

()*+, )-.*+(/*.0

JJ


!;4"#3 I 2 )%34"#3

2; × 2; × 2 × 2; = 2; =

=

[1G-./Y1 27;130 .)35 - 5)8*13 .7 -

314/2374-( 5)8*13 .-J15 .7 .,-. 27;13S

A73 1D-82(1 2; C

C

()*+, )-.*+(/*.0

JK


!;4"#3 J

5 = ?

()*+, )-.*+(/*.0

JQ


!;4"#3 J 2 )%34"#3

5 = 1

%5M 5)8*13 N270/./Y1 7351G-./Y1O .-J15 .7 .,1 27;13 76 ?N^137O 1f)-( .7 <S

[7. .10.1P 75 .,1 #$%&E ^137 .7.,1 27;13 76 ^137 /0 -(07 <S

()*+, )-.*+(/*.0

KG

GMAT Club 2011 23

!;4"#3 K

4

= ?

()*+, )-.*+(/*.0

K1


!;4"#3 K 2 )%34"#3

4

= 4 = 2

A3-4./75 27;130 -31 /5.13231.1P -0

67((7;0B .,1 P1578/5-.73 /0 .,1 377. -5P

5)813-.73 /0 .,1 27;13S A73 1D-82(1

3

= 3

73 2

= 2

()*+, )-.*+(/*.0

K5


!;4"#3 Q RS>&#8 +8#DT

H6 + -5P < -31 270/./Y1 /5.1G130E /0 .,1 318-/5P13 76:

(-3G13 .,-5 .,1 318-/5P13 76

:

9 + K <

&,1 318-/5P13 76

/0 >

()*+, )-.*+(/*.0

K6


!;4"#3 Q 2 )%34"#3

U.-.1815. N<O *M /.01(6 /0 /50)66/4/15.S H5 1D23100/7510 + E .,1 0)8 76 P/G/.0 76 10 /0 -(;-M0 < -5P /. /0

.,1 Y-()1 76 < .,-. P1.138/510 .,1 318-/5P13 76:

S H6 M7) 2()G /5 +F/E <FE N.,1 -50;13 /0 cM10cO -5P +FHE<F/ N.,1 -50;13 /0 c57cOS

U.-.1815. N>O *M /.01(6 /0 0)66/4/15.S H6 .,1 318-/5P13 76

/0 >E -0 U> 0.-.10E .,15 /0 >E =E 73 L -5P .,1 0)8 76 .,1

P/G/.0 76:

/0 P/Y/0/*(1 *M QS &,1316731E .,1

318-/5P13 76:

/0 ?E ;,/4, 4-557. *1 (-3G13 .,-.

.,1 318-/5P13 76:

57 8-..13 ;,-. + /0S

*7" $;##"$& 8%34"# B3 CW

()*+, )-.*+(/*.0

K@

GMAT Club 2011 24

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

!"#$"%&'(")

72-356 80/6. .26. 6+,/2 936 3. .42 :;.4 <2/+2-.0'2 0-

3 +'366 ,8 =>; 6.(?2-.6@ A- 3-,.42/ .26.B >C ,(. ,8

>;; 6.(?2-.6 6+,/2? )2..2/ .43- 72-3@ D8 -,),?E

43? 72-356 6+,/2B 943. 06 72-356 <2/+2-.0'2 38.2/

.42 .9, .26.6F

*+,-. +/0,-*1,02

34

!"#$"%&'(") 5 +%)6"#)

%3G2 23+4 .26. /26('. 62<3/3.2'EH

%26. =H =>; I :;.4 J KL M642 6+,/2? )2..2/ .43- KL

6.(?2-.6N

%26. >H O42 6+,/2? )2..2/ .43- =PL 6.(?2-.6 M>;; * >CN

O(Q (< .42 /26('.6H

KL R =PL J >P>

37

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

28%)"$9&':" ;9<="#)

T43. 06 .42 6(Q ,8 +,-62+(

‐KB‐:B‐PB‐LB‐VB‐CB‐SB‐>B‐=B;B=B

3>

28%)"$9&':" ;9<="#) 5

O(Q ,8 +,-62+(.0U2 0-.212/6 2W(3

Q('.0<'02? )E .42 -(Q)2/ ,8 .2/Q6

+,-62+(.0U2 0-.212/6 ‐KB‐:B‐PB‐LB‐VB

3.5MQ23- 2W(

3U2/312 ,8 .42 80/6. 3-? '36. .2/Q6N

2W(3'6 ., 3.5 12 42 @

33

/N"%>F ̂ Y8$"D ̂ "&

+,-. /0 .,1 0)8 76 -(( 818*130 76

.,1 01. ZE<>E<=E<LE><E>a 9

()*+, )-.*+(/*.0

KQ


/N"%>F ^Y8$"D ^"& 2 )%34"#3

&,1 0)8 76 1(1815.0 76 1Y15(M 02-41P 01. /0 G/Y15

*M .,1 6738)(-

Sum =

:

× &,1316731E

:

× 6 = 99

()*+, )-.*+(/*.0

QG


-"$=##B%9 U"$B<8>

Express 0.393939… in a fraction format

()*+, )-.*+(/*.0

Q1


-"$=##B%9 U"$B<8> 2 )%34"#3

*; $;%N"#& 8 #"$=##B%9 D"$B<8> &; P#8$&B;%, <S U12-3-.1 .,1 314)33/5G 5)8*13 6378 .,1 P14/8-(63-4./75

>S %551D P1578/5-.73 ;/., cZc -0 8-5M ./810 -0 .,1(15G., 76 .,1 314)33/5G 5)8*13QS k1P)41 .,1 63-4./75 .7 /.0 (7;10. .1380

/[8<Y>" _1, '75Y13. 0.3939… to - 63-4./75B

_ .,1 5)8*13 /0 > P/G/.0 07 .;7 5/510 -31 -PP1P

QB k1P)4/5G /. .7 (7;10. .1380B

()*+, )-.*+(/*.0

Q5

GMAT Club 2011 26




:#8$&B;%3 R/[&#8 +8#DT

H6 -E *E -5P 4 -31 270/./Y1 P/0./54.

/5.1G130E /0 (

) -5 /5.1G139

L F /

* F ! M L

()*+, )-.*+(/*.0

Q6


:#8$&B;%3 2 )%34"#3

U.-.1815. H /0 /50)66/4/15. 0/541 /. P710 57. 237Y/P1

157)G, /56738-./75 -*7). * 73 4

U.-.1815. HHB +1 4-5 31;3/.1(

)

-0

[7; 2()G /5 .,1 Y-()1 673 - 6378 U>B:

=

+

0/541 * -5P 4 -31 P/0./45. 270/./Y1 /5.1G130 -5P * /0

57. 1f)-( .7 4E .,1 1D23100/75 4-557. *1 -5 /5.1G13

*7" $;##"$& 8%34"# B3 C

()*+, )-.*+(/*.0

Q@

GMAT Club 2011 27

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

!"#$%&' ()'&*+

78 23+4 29:/2660,- (-;2/ .42 6<(3/2 /,,. 06 1/23.2/

.43- ,/ 2<(3' ., => ?43. 06

2 3@

2

2 2

2 3

2 2

2

,!-). !/0123!

4

!"#$%&' 5 !678$&7

A362; ,- .42 62.(: B3-; #3.4 :/0-+0:'26 .26.2; ,-

.42 "#$%C> 2 436 ., )2 D %42/28,/2

2.

3 3

A2+3(62 2> 3

>

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

!"#$%&#

78 .42 392/312 ,8 : +,-62+(.092 0-.212/6 06

;<= >43. 06 .42 392/312 ,8 .42 292- ,-'?

0-.212/6@

;A

;<

;BC:

;D

BE

'!()*

+(!(,+(,-+

.

!"#$%&#

/

!012#$1

F0/6.= 80-G .42 +,-62+(.092 0-.212/6C H0-+2

.42/2 3/2 := .42/2 I3? )2 20.42/ < ,/ B 292-

0-.212/6C %4262 0-.212/6 3/2 ;A= ;;= .3= ;B= ;JC

%42

392/312

,8

.42

292-

0-.212/6

06

;<

36

>2''

K;AL;<L;J M BEC N090G2 BE )? B 3-G ?,( >0''

12. ;<O

3

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

!"#$%&#

3

F,/ .42 P36. Q G3?6= .42 392/31

I23-O -(I)2/ ,8 +(P+3R26 )3R

:: P2/ G3?C %,G3? T,4- 42'P2G

.42? )3R2G ;AA +(P+3R26= >40+

392/312 ., EA +(P+3R26 P2/ G3?

93'(2 ,8 Q@

$OD VOW &O;A

;

!"#$%&#

3

/

!012#$1

%42 .,.3' -(I)2/ ,8 +(P+3R26 )3R

::Q= >40+4 I23-6 .43. .42 .,.3' -

+(P+3R26

)3R2G

0-

QL;

G3?6

>36

:

< = >: !012#$ 81 !

$-,.42/ 23602/ ,P.0,- 06 ., )3+R6,

?

601

10055

K

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!"#$

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,

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$/0.4<2.0+

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=

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=

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3DD23/2: .80+2 @- .42 3//3C G B H H I I

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>>

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+), -. /01(23 -. %45 678/01(2 29)/(3 : ;</6 =/0 >2 3/? /*-)6 38@23 -. / 678/01(2:

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-6<27 6>- /0@ 83 /(>/?3 172/627 6</0 6<2 @8..2720=2

-. 6<2 -6<27 6>-

% 781<6 678/01(2 83 6<2 -02 6</6 </3 / EC @21722

/01(2 F86 </3 6<2 781<6 /01(2GH % 678/01(2 =/0 -0(?

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7


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AH %72/ L

× ℎℎ

2. Hero’s formula: ( − )( − )( − ) ><272 /M*M= /72 38@23 -. / 678/01(2 /0@ ) 83 32,8N

O278,2627 = ::

JH P. ?-) Q0-> R 38@23 -. / 678/01(2 *)6 0-6 863 <281<6M

?-) =/0 /@@ /0 29)/((? 38S2@ 678/01(2 6- =72/62 /

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9

GMAT Club 2011 41

!"#$%&'() 8

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38@2V

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-0 6<2 #2-,267? 32=68-0

JM WM Z

YM BM AC

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ARM AYM RC

[M RWM RZ

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/01(23:

+,!-. /01+0!23

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ECM WZM WZ @217223

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GMAT Club 2011 42

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

!"#$%&'() *

7382 36 83-9 :/,:2/.026;

/2'3.0,-640:6; 3-< =,/8('36 9,(

>-,? 3),(. 3-< 2@(0'3.2/3' ./03-1'2

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4

!"#$%&'() * 5 ,%)6(")

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$ 42014. 06 A

78

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

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H# 06 .42 +2-.2/ ,= 3 +0/+'2I

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/0@ 6<2 <?O-620)32 83 RX F@-)*(2 6<2

38S2 -. 6<2 3,/((236 38@2G

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49


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P3 6<2 /72/ -. 6<2 678/01(2 %\' (233 6</0 A:

%\' ] EC @217223

^278,2627 -. 678/01(2 %\' 83 172/627 6</0

+,!-. /01+0!23

4:


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&<2 /72/ -. 6<2 678/01(2 %\' 83

+

=

+6/62,206 FAG *? 8632(. 83 3)..8=8206H P0 6<2 2X672,2 =/32><20 %01(2 %\' 83 781<6M 6<2 678/01(2 \D' 83 83-3=2(23

/0@ 6<)3 =

/0@ 6<2 /72/ -. 6<2 678/01(2 %\' 83 / L

AH P. /01(2 %\' 83 3,/((27 6</0 EC @217223M 6<20 6<2/72/ 2X=22@3 A @)2 6- 6<2 80=72/32 -. 6<2 <281<6 H

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6</0

&<2 =-772=6 /03>27 83 %H

+,!-. /01+0!23

4;

GMAT Club 2011 44

C#"D'()

E'($)( A(F#%( @G( FH''H6#%&.

'20627 N :

U/@8)3 N :

`8/,2627 N :

'87=),.2720=2 N :

%72/ N :

'<-7@ N :

&/01206 N :

+2=/06 N :

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'20627 – % O-806 8038@2 6<2 =87=(2H %(( O-8063 -0 6<2=87=(2 /72 29)8@836/06 .7-, 6<2 =20627

U/@8)3 – @836/0=2 *26>220 6<2 =20627 /0@ /0? O-806 -06<2 =87=(2H P6 83 </(. 6<2 @8/,2627

`8/,2627 – / =<-7@ O/33801 6<7-)1< 6<2 =20627

'87=),.2720=2 – @836/0=2 /7-)0@ 6<2 =87=(2

%72/ – / 7218-0 20=(-32@ *? 6<2 =87=(2

'<-7@ – / (802 321,206 (80Q801 /0? 6>- O-8063 -0 /=87=(2

&/01206 – (802 6-)=<801 6<2 =87=(2 /6 -02 O-806 -0(?a6/01206 (8023 /72 /(>/?3 /6 EC @217223 6- 6<2 7/@8)3

+2=/06 – / (802 6</6 8062732=63 / =87=(2 80 R O-8063

+,!-. /01+0!23

4=


C#"D'() 7

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= ?

+,!-. /01+0!23

4I


C#"D'() 7 5 ,%)6(")

%72/ -. / =87=(2 L

K2016< -. / =87=(2 L 2

= 3.14 ≈ 3 ≈

7

+,!-. /01+0!23

7J

GMAT Club 2011 45

CHH"A#%$@( /(HK(@"L

;</6 83 6<2 29)/68-0 -. 6<23(-O2 -. / (802:

+,!-. /01+0!23

74


CHH"A#%$@( /(HK(@"L 5 ,%)6(")

+(-O2 -. / (802 29)/68-0V

=

−

−

;<272 X /0@ ? /72 =--7@80/623 -.O-806 A/0@ O-806 R -0 6</6 (802H

+,!-. /01+0!23

77


CHH"A#%$@( /(HK(@"L 7

P. / (802 </3 / 021/68I2 3(-O2 (233

6</0 A – ></6 @-23 86 3/? /*-)6 6<2

(802:

+,!-. /01+0!23

78


CHH"A#%$@( /(HK(@"L 7 5 ,%)6(")

421/68I2 3(-O2 – ,2/03 (802 ,-I23 .7-, 6<2 )OO27

(2.6 </0@ 9)/7/06 FbRG 6- 6<2 *-66-, 781<6 </0@

9)/@7/06 FbWG -7 80 38,O(2 627,3M 86 83 / @2=72/3801

(802H ^-3868I2 3(-O2 ,2/03 6<2 -OO-3862 F@)<G +80=2 6<2 3(-O2 83 (233 6</0 AM 86 83 / .(/6 (802 F/3

-OO-32@ 6- 3622OGH +80=2 3(-O2 83 7832 -I27 7)0M 80

6<83 =/32M 6<272 83 (233 7832 6</0 7)0

+,!-. /01+0!23

79

GMAT Club 2011 46

CHH"A#%$@( /(HK(@"L 8

;</6 3(-O23 @- K8023 %M \M /0@ ' </I2:

^-3868I2T421/68I2:

K233T#72/627 6</0 A: %

\

'

+,!-. /01+0!23

7:


CHH"A#%$@( /(HK(@"L 8 5 ,%)6(")

M#%( ,

^-3868I2 +(-O2

+(-O2 172/627 6</0 A

M#%( N

+(-O2 83 0286<27

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+(-O2 83 )[email protected]@

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7;


CHH"A#%$@( /(HK(@"L 9

d-> 6- .80@ 6<2 e /0@ 5 80627=2O63

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+,!-. /01+0!23

7<


CHH"A#%$@( /(HK(@"L 9 5 ,%)6(")

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29)/68-0 -. 6<2 (802

f-7 2X/,O(2M / (802 83 ! # $% & '

&- .80@ 6<2 5 80627=2O6 F6<83 83 ><20 6<2 (802 =7-3323

6<2 5 /X83 /0@ 6<)3 e 83 S27-G 3-(I2V ? L *

&- .80@ e 80627=2O6 F6<83 83 ><20 6<2 (802 =7-3323 6<2

e /X83 /0@ 5 83 S27-G 3-(I2V ( # $% & '

&<2 678=Q 83 6- )32 5 L C ><20 (--Q801 .-7 e

80627=2O6 /0@ e L C ><20 (--Q801 .-7 5 80627=2O6

+,!-. /01+0!23

7=

GMAT Club 2011 47

CHH"A#%$@( /(HK(@"L :

P. (802 ) >86< / 3(-O2 -.

1-23 6<7-)1< O-8063 %FNZM

NRG /0@ \FWM JGM ></6 83 6<2 (2016< -. 6<2 321,206

%\:

+,!-. /01+0!23

7I


CHH"A#%$@( /(HK(@"L : 5 ,%)6(")

&<2 3(-O2 80.-7,/68-0 80 6<838772(2I/06

&- .80@ @836/0=2 *26>220 %

/0@ \ 83 =/(=)(/62@ )3801 6<2^?6</1-72/0 &<2-72, *?@7/>801 / 678/01(2

9 + 5 =

81+ 25 =

= 106

+,!-. /01+0!23

8J


CHH"A#%$@( /(HK(@"L ;

f80@ 6<2 29)/68-0 -. / (802 O/33801

6<7-)1< 6<2 O-8063 , >:O9B /0@ N >7O8B

+,!-. /01+0!23

84


CHH"A#%$@( /(HK(@"L ; 5 ,%)6(")

, >:O9B /0@ N >;O8B

&- .80@ /0 29)/68-0 -. / (802 */32@ -0 6>-

O-8063M )32 6<83 .-7,)(/V

=

=

;

=

! + 4 = − 5

= − + 9

+,!-. /01+0!23

87

GMAT Club 2011 48

CHH"A#%$@( /(HK(@"L <

P. (8023 % /0@ \ /72 O27O20@8=)(/7 6- 2/=<

-6<27M ></6 83 6<2 72(/68-03<8O *26>220 6<287

3(-O23:

%H P0I2732

\H DOO-3862

'H ^-3868I2

`H U2=8O7-=/(

gH U2=8O7-=/( /0@ 421/68I2

+,!-. /01+0!23

88


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&<2 72(/68-03<8O *26>220

3(-O23 -. R O27O20@8=)(/7

(8023 83 021/68I2 72=8O7-=/(

−

H P0 -6<27 >-7@3M 6<2

6>- (8023 /72 O27O20@8=)(/7

8. /0@ -0(? 8. 6<2 O7-@)=6 -.

6<287 3(-O23 83 NAH

gH1H 3 × −

LNA

+,!-. /01+0!23

89


CHH"A#%$@( /(HK(@"L =

%72 6<2 6>- (8023 *2(-> O27O20@8=)(/7:

+,!-. /01+0!23

8:


CHH"A#%$@( /(HK(@"L = 5 ,%)6(")

&- /03>27M .80@ 6<2 3(-O2 -. 2/=< (802 /0@ 6<20

=<2=Q 6- 322 8. -02 3(-O2 83 6<2 021/68I2 72=8O7-=/(

-. 6<2 -6<27 -7 8. 6<287 O7-@)=6 29)/(3 6- NAH

+(-O2 %\ L

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=

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=

= −

$)(68O(? 6<2 3(-O23V

×

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PH@ E("Q(%A#DR'$"

+,!-. /01+0!23

8;

GMAT Club 2011 49

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1 1

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+2-.2/ ,= .42 +0/+'2 06 =(/.42/ .43- @ (-0.6 3?3G =/,C

.42

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$= $ /23;0-1 3),:2 RP 82/+2-. #,<#%&$)* .42

<3-(93+.(/0-1 2+,-,<7 $+ @) 12-2/3''7

2Q83-;0-1=

U= $ /23;0-1 3),:2 RP 82/+2-. #,<#%&$)* $7&$ .42

<3-(93+.(/0-1 2+,-,<7 #* 12-2/3''7 2Q83-;0-1=

&= $ /23;0-1 3),:2 RP 82/+2-. #,<#%&$)* .42

<3-(93+.(/0-1 2+,-,<7

#* 12-2/3''7

2Q83-;0-1=

FOW

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= $ /23;0-1 3),:2 RP 82/+2-. #,<#%&$)* .42

<3-(93+.(/0-1 2+,-,<7 $+ @) 12-2/3''7

2Q83-;0-1=

U= $ /23;0-1 3),:2 RP 82/+2-. #,<#%&$)* $7&$ .42

FSZ

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,

8J T, %+,$"&*$ $+ .42 90/6. .?, ,8.

;2+060,- <3G0-1M 3 &38 3-; %/3

2J 8* %+,$"&*$)< N#$7 .42 90/6. .?

3-; %/3;2 676.2< N#'' <)%),$"&

<3G0-1=

!J T, %+,$"&*$ $+ .42 90/6. .?, ,8.

%/3;2 676.2<

N#''

<)%),$"&'#I)

FSF

T<#+9*

&,//2+. 3-6?2/B

8J T, %+,$"&*$ $+ .42 90/6. .?, ,8.

;2+060,- <3G0-1M 3 &38 3-; %/3

2J 8* %+,$"&*$)< N#$7 .42 90/6. .?

3-; %/3;2 676.2< N#'' <)%),$"&

FSA

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,//2+.S

$= qW )2'02:2 .43. ?23'.4 06 & 9)&,* K+" 3- 2-;M -,.

3- 2-; 0- 0.62'9q=

U= qW )2'02:2 .43. ?23'.4 06 & 9)&,* +K 3- 2-;M -,.

3- 2-; 0- 0.62'9q=

&= qW )2'02:2 .43. ?23'.4 06 & 9)&,* $+ 3- 2-;M -,.

3- 2-; 0- 0.62'9q=

FS`

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= qW )2'02:2 .43. ?23'.4 06 & 9)&,* K+" 3- 2-;M -,.

3- 2-; 0- 0.62'9q=

U= qW )2'02:2 .43. ?23'.4 06 & 9)&,* +K 3- 2-;M -,.

3- 2-; 0- 0.62'9q=

FSa

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,

$= %42 3-+02-. &40-262 %3,06.6 <#*

0-.2/+,(/62 &,< ,/136<=

U= %42 3-+02-. &40-262 %3,06.6 <#*

0-.2/+,(/62 K"+9 ,/136<=

&= %42 3-+02-. &40-262 %3,06.6 <#*

@)$N)), 0-.2/+,(/62 &,< ,/13

FSW

T<#+9*

&,//2+. 3-6?2/B

$= %42 3-+02-. &40-262 %3,06.6 <#*

0-.2/+,(/62 &,< ,/136<=

U= %42 3-+02-. &40-262 %3,06.6 <#*

0-.2/+,(/62 K"+9 ,/136<=

F_Z

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= W. ?,('; 43:2 )22- )&*L ),+1-7 K+" 42/ $+ @1L 3

/3-+4‐6.7'2 4,(62 .43. 642 +,('; 2360'7 3-; ',10+3''7

;2+,/3.2 ?0.4 D+3-;0-3:03-‐6.7'2 9(/-0.(/2=

U= W. ?,('; 43:2 )22- )&*L ),+1-7 *+ $7&$ 642 @+1-7$

3 /3-+4‐6.7'2 4,(62 .43. 642 +,('; 2360'7 3-; ',10+3''7

;2+,/3.2 ?0.4 D+3-;0-3:03-‐6.7'2 9(/-0.(/2=

&=

W.

?,(';

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)&*L

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&*

$+

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/3-+4‐

6.7'2 4,(62 .43. 642 +,('; 2360'7 3-; ',10+3''7

;2+,/3.2 ?0.4 D+3-;0-3:03-‐6.7'2 9(/-0.(/2=

F_F

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= W. ?,('; 43:2 )22- )&*L ),+1-7 K+" 42/ $+ @1L 3

/3-+4‐6.7'2 4,(62 .43. 642 +,('; 2360'7 3-; ',10+3''7

;2+,/3.2 ?0.4 D+3-;0-3:03-‐6.7'2 9(/-0.(/2=

U= W. ?,(';

43:2

)22-

)&*L

),+1-7

*+

$7&$ 642

@+1-7$

3 /3-+4 6.7'2 4,(62 .43. 642 +,('; 2360'7 3-; ',10+3''7

F_A

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,

$= 0@4,-2 (62/6 ;,?-',3; .?, .,9&,L 9+") 13<26M :0;2,M 3-;$7&, ,.42/ 6<3/.84,-2 (62/6=

U= 0@4,-2 (62/6 ;,?-',3; .?, .,9&,L 9+") 13<26M :0;2,M 3-;,.42/ 6<3/.84,-2 (62/6=

&= 0@4,-2 (62/6 ;,?-',3; .?, .,9&,L 13<26M

:0;2,M

3-;

,.42/

6<3/.84,-2 (62/6=

F_M

T<#+9*

&,//2+. 3-6?2/B

$= 0@4,-2 (62/6 ;,?-',3; .?, .,9&,L 9+") 13<26M :0;2,M 3-;$7&, ,.42/ 6<3/.84,-2 (62/6=

U= 0@4,-2 (62/6

;,?-',3;

.?,

.,

9&,L 9+") 13<26 :0;2, 3-;

F_O

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= N2 43:2 +,) %7&,%) #, & 9#''#+, +K ?0--0-1 .42

N,/'; &(8=

U= N2 43:2 +,) #, & 9#''#+, %7&,%)* $+ ?0- .42

N,/'; &(8=

&= N2 43:2 +,) %7&,%) #, & 9#''#+, K+" ?0--0-1 .42

N,/'; &(8=

F_S

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= N2 43:2 +,) %7&,%) #, & 9#''#+, +K ?0--0-1 .42

N,/'; &(8=

U= N2 43:2 +,) #, & 9#''#+, %7&,%)* $+ ?0- .42

N,/'; &(8=

F__

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,

$= X(/ 2+,-,<0+ ?2''‐)20-1 06 12K"+9 .42 3<,(-. ,9 1,,;6 3-;+,-6(<2=

U= X(/ 2+,-,<0+ ?2''‐)20-1 06 12@L .42 3<,(-. ,9 1,,;6 3-; 62+,-6(<2=

&= X(/ 2+,-,<0+ ?2''‐)20-1 06 12$7"+1-7 .42

3<,(-.

,9

1,,;6

?2 +,-6(<2=

F_`

T<#+9*

&,//2+. 3-6?2/B

$= X(/ 2+,-,<0+ ?2''‐)20-1 06 12K"+9 .42 3<,(-. ,9 1,,;6 3-;+,-6(<2=

U= X(/ 2+,-,<0+

?2''

‐)20-1

06

12

@L .42 3<,(-. ,9 1,,;6 3-; 62

F_a

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= D42 #* %")<#$)< K+" 6,':0-1 -(<2/,(6 +3626=

U= D42 #* %")<#$)< N#$7 6,':0-1 -(<2/,(6 +3626=

&= D42 #* %")<#$)< &* @)#,- 3 1/23. ;2.2+.0:2=

F_W

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= D42 #* %")<#$)< K+" 6,':0-1 -(<2/,(6 +3626=

U= D42 #* %")<#$)< N#$7 6,':0-1 -(<2/,(6 +3626=

&= D42

#*

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@)#,- 3

1/23.

;2.2+.0:2=

F`Z

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,

$= N47 436-a. &,-1/266 9&,<&$)8/2<0(< +,6. @) 64,?- 36 ?36.() )(. -,. .3Q2;S

U= N47 436-a. &,-1/266 & 9&,<&8/2<0(< +,6. $+ @) 64,?- 36 ?6.() )(. -,. .3Q2;S

&= N47 436-a. &,-1/266 9&,<&$)

8/2<0(< +,6.

&") 64,?-

36

?3

6.() )(. -,. .3Q2;S

F`F

T<#+9*

&,//2+. 3-6?2/B

$= N47 436-a. &,-1/266 9&,<&$)8/2<0(< +,6. @) 64,?- 36 ?36.() )(. -,. .3Q2;S

U= N47 436-a.

&,-1/266

& 9&,<&

8/2<0(< +,6. $+ @) 64,?- 36 ?

F`A

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= $ CZ‐723/‐,'; 10/' ?36 <06.3G2-'7 3);(+.2; 0- #3/+4

EPP[ )7 ./3990+G2/6 ?4, ?2/2 )2'02:2; ., 7&;)

9#*$&5), 42/ &* .42 -02+2 ,9 3 6(682+.2; ;/(1 ;23'2/=

U= $ CZ‐723/‐,'; 10/' ?36 <06.3G2-'7 3);(+.2; 0- #3/+4

EPP[ )7 ./3990+G2/6 ?4, ?2/2 )2'02:2; ., 7&;)

9#*$&5), 42/ K+" .42 -02+2 ,9 3 6(682+.2; ;/(1

;23'2/=

&= $

CZ‐

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,';

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<06.3G2-'7

3);(+.2;

0-

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9#*$&5), 42/ $+ .42 -02+2 ,9 3 6(682+.2; ;/(1 ;23'2/=

F`M

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= $ CZ‐723/‐,'; 10/' ?36 <06.3G2-'7 3);(+.2; 0- #3/+4

EPP[ )7 ./3990+G2/6 ?4, ?2/2 )2'02:2; ., 7&;)

9#*$&5), 42/ &* .42 -02+2 ,9 3 6(682+.2; ;/(1 ;23'2/=

U= $

CZ‐

723/‐

,';

10/'

?36

<06.3G2-'7

3);(+.2;

0-

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F`O

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

+,

$= U(. ),.4 %+,*#<)" .42 8/,)'2<0-+,-:2-02-+26 ., 923.(/2 .4208/,1/3<6=

U= U(. ),.4 %+,*#<)" .42 8/,)'2<0-+,-:2-02-+26 ., 923.(/2 .4208/,1/3<6=

&= U(. ),.4 %+,*#<)" .42 8/,)'2<

0-+,-:2-02-+26 .,

923.(/2

.420

8/,1/3<6=

F`S

T<#+9*

&,//2+. 3-6?2/B

$= U(. ),.4 %+,*#<)" .42 8/,)'2<0-+,-:2-02-+26 ., 923.(/2 .4208/,1/3<6=

U= U(. ),.4

%+,*#<)" .42

8/,)'2<

0-+,-:2-02-+26 ., 923.(/2 .420

F`_

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= %42 ;/(1 <3G2/ :"+:+*)< .42 '0.013.0,- @)+2-./3'0Y2; 0- .42 eD F06./0+. &,(/. 9,/ .42

T,/.42/- F06./0+. ,9 X40,=

U= %42 ;/(1 <3G2/ :"+:+*)< $7&$ .42 '0.013.0,- #* $+

@) +2-./3'0Y2; 0- .42 eD F06./0+. &,(/. 9,/ .42

T,/.42/- F06./0+. ,9 X40,=

&= %42 ;/(1 <3G2/ :"+:+*)< $7&$ .42 '0.013.0,- @)

+2-./3'0Y2; 0-

.42

eD

F06./0+.

&,(/.

9,/

.42

T,/.42/- F06./0+. ,9 X40,=

F``

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= %42 ;/(1 <3G2/ :"+:+*)< .42 '0.013.0,- @)+2-./3'0Y2; 0- .42 eD F06./0+. &,(/. 9,/ .42

T,/.42/- F06./0+. ,9 X40,=

U= %42 ;/(1

<3G2/

:"+:+*)<

$7&$ .42

'0.013.0,-

#*

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@) +2-./3'0Y2; 0- .42 eD F06./0+. &,(/. 9,/ .42

F`a

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= %42 36./,-3(.6 ?,('; 8/,)3)'7/2<30-0-1 .0<2 '0:0-1 3-; ?,/G#,*$)&< +K ;70-1 3. 4,<2=

U= %42 36./,-3(.6 ?,('; 8/,)3)'7/2<30-0-1 .0<2 '0:0-1 3-; ?,/G;70-1 3. 4,<2=

&= %42 36./,-3(.6 ?,('; 8/,)3)'7

/2<30-0-1 .0<2

'0:0-1

3-;

?,/G

$7&, ;70-1 3. 4,<2=

F`W

T<#+9*

&,//2+. 3-6?2/B

$= %42 36./,-3(.6 ?,('; 8/,)3)'7/2<30-0-1 .0<2 '0:0-1 3-; ?,/G#,*$)&< +K ;70-1 3. 4,<2=

U= %42 36./,-3(.6

?,(';

8/,)3)'7

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FaZ

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= %42 +,<83-7 ")H1#")* 40< 7+'< 6.,+G :3'(2; 3. fO=O <0''0,-M 9,(/ .0<26 406 3--(3' )362 63'3/7 ,9 fC=C <0''0,-=

U= %42 +,<83-7 ")H1#")* 40< $+ 7+'< 6.,+G :3'(2;

3. fO=O <0''0,-M 9,(/ .0<26 406 3--(3' )362 63'3/7

,9 fC=C <0''0,-=

&= %42 +,<83-7 ")H1#")* 40< 7+'<#,- 6.,+G :3'(2;

3. fO=O

<0''0,-M

9,(/

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406

3--(3'

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63'3/7

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FaF

BC(28D

T<#+9*

&,//2+. 3-6?2/B

$= %42 +,<83-7 ")H1#")* 40< 7+'< 6.,+G :3'(2; 3. fO=O <0''0,-M 9,(/ .0<26 406 3--(3' )362 63'3/7 ,9 fC=C <0''0,-=

U= %42 +,<83-7

")H1#")* 40<

$+

7+'< 6.,+G

:3'(2;

3. fO O <0''0,- 9,(/ .0<26 406 3--(3' )362 63'3/7

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! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= &()3- 8,:2/.7 #* & ")*1'$ +K .4

2<)3/1,=

2J 37) ")*1'$ +K .42 $<2/0+3- 2<

0<8,:2/0642;=

!J ()*1'$#,- K"+9 .42 $<2/0+3- 2

0<8,:2/0642;=

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T<#+9*

&,//2+. 3-6?2/B

$= &()3- 8,:2/.7 #* & ")*1'$ +K .4

2<)3/1,=

2J 37) ")*1'$ +K .42 $<2/0+3- 2<

0<8,:2/0642;=

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! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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8J 8 "#*#,- +K 2'2+./0+0.7 8/0+26 9(2''2; .42 C[ 82/+2-. 723/‐,-‐723/ I(<8 0- .42 +,<83-7a6 /2:2-(26 .,

Z=d )0''0,- Y',.76=

2J 8 "#*) #, 2'2+./0+0.7 8/0+26 9(2''2; .42 C[ 82/+2-. 723/‐,-‐723/ I(<8 0- .42 +,<83-7a6 /2:2-(26 .,

Z=d )0''0,- Y',.76=

!J 8 "&#*) #, 2'2+./0+0.7 8/0+26 9(2''2; .42 C[ 82/+2-.

723/‐,-

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.,

Z=d )0''0,- Y',.76=

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BC(28D

T<#+9*

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8J 8 "#*#,- +K 2'2+./0+0.7 8/0+26 9(2''2; .42 C[ 82/+2-. 723/‐,-‐723/ I(<8 0- .42 +,<83-7a6 /2:2-(26 .,

Z=d )0''0,- Y',.76=

2J 8 "#*)

#, 2'2+./0+0.7

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C[

82/+2-.

723/‐,-‐723/ I(<8 0- .42 +,<83-7a6 /2:2-(26 .,

Fa_

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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8J T$ *))9* '#5) .42 +,<83-7 #* 6'

,9 -2? 923.(/26 ., 3;;=

U= %42 +,<83-7 *))9* &* #K #$ #* 6

,9 -2? 923.(/26 ., 3;;=

!J T$ *))9* &* #K .42 +,<83-7 #* 6

,9 -2? 923.(/26 ., 3;;=

Fa`

T<#+9*

&,//2+. 3-6?2/B

8J T$ *))9* '#5) .42 +,<83-7 #* 6'

,9 -2? 923.(/26 ., 3;;=

U= %42 +,<83-7 *))9* &* #K #$ #* 6

,9 -2? 923.(/26 ., 3;;=

Faa

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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$= D?22. 8,.3.,26 3/2 ,&$#;) #, &2-./3' $<2/0+3 3-;

@2/(=

U= D?22. 8,.3.,26 3/2 ,&$#;) K"+9 &2-./3' $<2/0+3

3-; @2/(=

&= D?22. 8,.3.,26 3/2 ,&$#;) $+ &2-./3' $<2/0+3 3-;

@2/(=

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T<#+9*

&,//2+. 3-6?2/B

$= D?22. 8,.3.,26 3/2 ,&$#;) #, &2-./3' $<2/0+3 3-;

@2/(=

U= D?22. 8,.3.,26 3/2 ,&$#;) K"+9 &2-./3' $<2/0+3

3-; @2/(=

FWZ

! "#$% &'() * +,-./0)(.0-1 ., 23+4 ,.42/56 '23/-0-1

T<#+9*

N40+4 62-.2-+2

06

0;0,<3.0+3''7

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8J C;)"L :"+<1%$ (62 *#9#'&" /2+7+3/;),3/; 3-; ,.42/ <3.2/03'6'23;‐9/22 830-.6M -,- .,Q0+ 1'(2

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!J C&%7 :"+<1%$ (62 *#9#'&" /2+7+

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