GRE Math Question (Set 1 of 1 Explained)

Page 1

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

# HTCEVKQP YKVJ C PGICVKXG UKIP KP GKVJGT VJG PWOGTCVQT QT KP VJG FGPQOKPCVQT ECP DG YTKVVGP YKVJ VJG PGICVKXG UKIP KP HTQPV QH VJG HTCEVKQP (QT GZCORNG


9JKEJ QH VJG HQNNQYKPI KU C (#.5' UVCVGOGPV!

# 6JG RTQFWEV QH VYQ RQUKVKXG KPVGIGTU KU C RQUKVKXG KPVGIGT $ 6JG RTQFWEV QH VYQ PGICVKXG KPVGIGTU KU C RQUKVKXG KPVGIGT % 6JG RTQFWEV QH C RQUKVKXG KPVGIGT CPF C PGICVKXG KPVGIGT KU C PGICVKXG KPVGIGT & 9JGP KPVGIGTU CTG OWNVKRNKGF GCEJ QH VJG OWNVKRNKGF KPVGIGTU KU ECNNGF C HCEVQT QT FKXKUQT QH VJG TGUWNVKPI RTQFWEV ' KU C OWNVKRNG QH QPN[ KPVGIGTU

%QTTGEV #PUYGT '

'ZRNCPCVKQP

' KU C OWNVKRNG QH QPN[ PQV KPVGIGTU CPF VJGKT PGICVKXG EQWPVGTRCTVU CPF $ (QT GZCORNG % (QT GZCORNG & (QT GZCORNG ' (QT GZCORNG UQ CPF CTG HCEVQTU QH 6JG KPVGIGTU CPF CTG CNUQ HCEVQTU QH UKPEG CPF 6JG RQUKVKXG HCEVQTU QH CTG CPF 6JG PGICVKXG HCEVQTU QH CTG VJG KPVGIGTU CPF CTG CNUQ HCEVQTU QH UKPEG 6JGTG CTG PQ QVJGT HCEVQTU QH 9G UC[ VJCV KU C OWNVKRNG QH GCEJ QH KVU HCEVQTU CPF VJCV KU FKXKUKDNG D[ GCEJ QH KVU FKXKUQTU


&GHKPKVKQP 6JG KPVGIGTU CTG VJG YJQNG PWODGTU CPF UQ QP VQIGVJGT YKVJ VJGKT PGICVKXGU CPF +PVGIGTU CTG CNYC[U YJQNG PWODGTU

&GHKPKVKQP 6JG RQUKVKXG KPVGIGTU CTG YJQNG PWODGTU ITGCVGT VJCP &GHKPKVKQP 6JG PGICVKXG KPVGIGTU CTG YJQNG PWODGTU NGUU VJCP

&GHKPKVKQP KU CP KPVGIGT VJCV KU PGKVJGT RQUKVKXG PQT PGICVKXG

#RRNKGF &GHKPKVKQP 9JGP QPG KPVGIGT CPF CPQVJGT KPVGIGT CTG LQKPGF VQIGVJGT KP CFFKVKQP KP UWDVTCEVGF CPF KP OWNVKRNKECVKQP VJG TGUWNV KU CNYC[U CP KPVGIGT

#RRNKGF &GHKPKVKQP $WV YJGP QPG KPVGIGT CPF CPQVJGT KPVGIGT CTG LQKPGF VQIGVJGT KP FKXKUKQP VJG TGUWNV YKNN DG GKVJGT CP KPVGIGT QT C PQP KPVGIGT 'XGT[ TGUWNV QH FKXKUKQP VJCV KU C PQP KPVGIGT KU NCDGNGF WUKPI QPG QH VJTGG U[PQP[OU HTCEVKQP FGEKOCN SWQVKGPV YKVJ TGOCKPFGT

&GHKPKVKQP (CEVQTU KFGPVKECNN[ MPQYP CU &KXKUQTU CTG C UGV QH KPVGIGTU LQKPGF VQIGVJGT D[ OWNVKRNKECVKQP VQ RTQFWEG C UKPING TGUWNV ECNNGF VJG OWNVKRNG QH VJG HCEVQTU (CEVQTU KFGPVKECNN[ MPQYP CU &KXKUQTU OWUV DG KPVGIGTU CPF YKNN DG DQVJ PGICVKXG CPF RQUKVKXG

&GHKPKVKQP &KXKUQTU CNUQ MPQYP CU (CEVQTU CTG C UGV QH KPVGIGTU LQKPGF VQIGVJGT D[ OWNVKRNKECVKQP VQ RTQFWEG C UKPING TGUWNV ECNNGF VJG OWNVKRNG QH VJG HCEVQTU &KXKUQTU CNUQ MPQYP CU (CEVQTU OWUV DG KPVGIGTU CPF YKNN DG DQVJ PGICVKXG CPF RQUKVKXG


6JG RQUKVKXG HCEVQTU QH

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT $

'ZRNCPCVKQP

6JG RQUKVKXG HCEVQTU QH CTG CPF 6JCVÊU RQUKVKXG HCEVQTU 6JKU SWGUVKQP KU UKORNG UWRGTHKEKCNN[ 2TGEKUKQP YTKVKPI KU QPG QH VJG EWTTGPV OCTMGV OQFGNU OQUV KORQTVCPV UMKNNU QH FGNGICVKPI YKVJ VCNGPV HKFGNKV[ &GUKIP [QWT UETCVEJ RCRGT YKVJ JQTK\QPVCN UGPVGPEGU CPF PGCVN[ EQPUVTWEVGF NGVVGTU 9TKVKPI NKUVU KU KORQTVCPV


#NN QH VJG KPVGIGTU VJCV KU C OWNVKRNG QH

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

KU PQV C OWNVKRNG QH CP[ KPVGIGT GZEGRV CPF #NUQ KU C HCEVQT QH GXGT[ KPVGIGT

6JGTCRGWVKECNN[ RNGCUG MPQY VJG FGEKUKQP VQ RJTCUG VJG SWGUVKQP DNWTTKPIN[ KU KPVGPVKQPCN 6JG ECFGPEG CPF YQTF UGPUG QH VJG TGCN VGUV KU DCHHNKPI HQT WPRTGRCTGF VGUV VCMGTU #V HKTUV DNWUJ VJG UGPVGPEG KU FKUQTKGPVKPI VTCPUNCVG YKVJ CNGTVPGUU YJKNG [QW RTCEVKEG CPF [QW YKNN DGEQOG VGUV FC[ NKVGTCVG


#NN QH VJG KPVGIGTU VJCV KU C HCEVQT QH

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

KU C HCEVQT QH GXGT[ KPVGIGT KU PQV C OWNVKRNG QH CP[ KPVGIGT GZEGRV CPF 6JG RJTCUKPI KP VJG SWGUVKQP KU KPVGPVKQPCN


#NN QH VJG KPVGIGTU VJCV KU C HCEVQT QH

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

KU C OWNVKRNG QH GXGT[ KPVGIGT KU PQV C HCEVQT QH CP[ KPVGIGT GZEGRV


#NN QH VJG KPVGIGTU VJCV KU C OWNVKRNG QH

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

KU C OWNVKRNG QH GXGT[ KPVGIGT KU PQV C HCEVQT QH CP[ KPVGIGT GZEGRV


6JG NGCUV EQOOQP OWNVKRNG QH CPF

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

6JG NGCUV EQOOQP OWNVKRNG QH CPF KU 6JKU KU DGECWUG VJG RQUKVKXG OWNVKRNGU QH CTG GVE CPF VJG RQUKVKXG OWNVKRNGU QH CTG GVE 6JWU VJG EQOOQP RQUKVKXG OWNVKRNGU QH CPF CTG GVE CPF VJG NGCUV QH VJGUG KU


&GHKPKVKQP 6JG NGCUV EQOOQP OWNVKRNG QH VYQ KPVGIGTU UC[ KPVGIGT C CPF KPVGIGT D KU C VJKTF KPVGIGT UC[ E YJKEJ KU VJG NGCUV XCNWG ÌUOCNNGUVÍ OWNVKRNG UJCTGF D[ DQVJ C CPF D +PVGIGTU C CPF D UJCTG OCP[ OWNVKRNGU UC[ E F G H E KU VJG NGCUV QT NGCUV XCNWG QT ÌUOCNNGUVÍ EQOOQP OWNVKRNG

#RRNKGF &GHKPKVKQP 6JG NGCUV EQOOQP OWNVKRNG QH VYQ KPVGIGTU UC[ KPVGIGT CPF KPVGIGT KU C VJKTF KPVGIGT YJKEJ KU VJG NGCUV XCNWG ÌUOCNNGUVÍ OWNVKRNG UJCTGF D[ DQVJ CPF +PVGIGTU CPF UJCTG OCP[ OWNVKRNGU UC[ KU VJG NGCUV QT NGCUV XCNWG QT ÌUOCNNGUVÍ EQOOQP OWNVKRNG

#RRNKGF &GHKPKVKQP 6JG NGCUV EQOOQP OWNVKRNG QH VYQ KPVGIGTU UC[ KPVGIGT CPF KPVGIGT KU C VJKTF KPVGIGT YJKEJ KU VJG NGCUV XCNWG ÌUOCNNGUVÍ OWNVKRNG UJCTGF D[ DQVJ CPF +PVGIGTU CPF UJCTG OCP[ OWNVKRNGU UC[ KU VJG NGCUV QT NGCUV XCNWG QT ÌUOCNNGUVÍ EQOOQP OWNVKRNG

#RRNKGF &GHKPKVKQP 6JG NGCUV EQOOQP OWNVKRNG QH VYQ KPVGIGTU UC[ KPVGIGT CPF KPVGIGT KU C VJKTF KPVGIGT YJKEJ KU VJG NGCUV XCNWG ÌUOCNNGUVÍ OWNVKRNG UJCTGF D[ DQVJ CPF +PVGIGTU CPF UJCTG OCP[ OWNVKRNGU UC[ KU VJG NGCUV QT NGCUV XCNWG QT ÌUOCNNGUVÍ EQOOQP OWNVKRNG


6JG ITGCVGUV EQOOQP FKXKUQT QH CPF

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

6JG ITGCVGUV EQOOQP FKXKUQT QH CPF KU 6JKU KU DGECWUG VJG RQUKVKXG FKXKUQTU QH CTG CPF CPF VJG RQUKVKXG FKXKUQTU QH CTG CPF 6JWU VJG EQOOQP RQUKVKXG FKXKUQTU QH CPF CTG CPF CPF VJG ITGCVGUV QH VJGUG KU


&GHKPKVKQP 6JG ITGCVGUV EQOOQP FKXKUQT QT ITGCVGUV EQOOQP HCEVQT QH VYQ KPVGIGTU UC[ KPVGIGT I CPF KPVGIGT H KU C VJKTF KPVGIGT UC[ G YJKEJ KU VJG ITGCVGUV XCNWG ÌNCTIGUVÍ FKXKUQT HCEVQT UJCTGF D[ DQVJ I CPF H +PVGIGTU I CPF H OC[ UJCTG OCP[ FKXKUQTU HCEVQTU UC[ G F E D C G KU VJG ITGCVGUV QT ITGCVGUV XCNWG QT ÌNCTIGUVÍ EQOOQP FKXKUQT HCEVQT

#RRNKGF &GHKPKVKQP 6JG ITGCVGUV EQOOQP FKXKUQT QT ITGCVGUV EQOOQP HCEVQT QH VYQ KPVGIGTU UC[ KPVGIGT CPF KPVGIGT KU C VJKTF KPVGIGT YJKEJ KU VJG ITGCVGUV XCNWG ÌNCTIGUVÍ FKXKUQT HCEVQT UJCTGF D[ DQVJ CPF +PVGIGTU CPF UJCTG OCP[ FKXKUQTU HCEVQTU KU VJG ITGCVGUV QT ITGCVGUV XCNWG QT ÌNCTIGUVÍ EQOOQP FKXKUQT HCEVQT

#RRNKGF &GHKPKVKQP 6JG ITGCVGUV EQOOQP FKXKUQT QT ITGCVGUV EQOOQP HCEVQT QH VYQ KPVGIGTU UC[ KPVGIGT CPF KPVGIGT KU C VJKTF KPVGIGT YJKEJ KU VJG ITGCVGUV XCNWG ÌNCTIGUVÍ FKXKUQT HCEVQT UJCTGF D[ DQVJ CPF +PVGIGTU CPF UJCTG C UKPING FKXKUQT HCEVQT 6JWU KU VJG ITGCVGUV QT ITGCVGUV XCNWG QT ÌNCTIGUVÍ EQOOQP FKXKUQT HCEVQT

#RRNKGF &GHKPKVKQP 6JG ITGCVGUV EQOOQP FKXKUQT QT ITGCVGUV EQOOQP HCEVQT QH VYQ KPVGIGTU UC[ KPVGIGT CPF KPVGIGT KU C VJKTF KPVGIGT YJKEJ KU VJG ITGCVGUV XCNWG ÌNCTIGUVÍ FKXKUQT HCEVQT UJCTGF D[ DQVJ CPF +PVGIGTU CPF UJCTG HQWT FKXKUQTU HCEVQTU CPF KU VJG ITGCVGUV QT ITGCVGUV XCNWG QT ÌNCTIGUVÍ EQOOQP FKXKUQT HCEVQT


6JG TGUWNV YJGP KU FKXKFGF D[

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

YJGP KU FKXKFGF D[ QPG QH KVU FKXKUQTU VJG TGUWNV KU YJKEJ KU CPQVJGT FKXKUQT QH

9JGP CP KPVGIGT C KU FKXKFGF D[ CP KPVGIGT D YJGTG D KU C FKXKUQT QH C VJG TGUWNV KU CNYC[U C FKXKUQT QH C


9JKEJ QH VJG HQNNQYKPI KU C 647' UVCVGOGPV!

# 9JGP CP KPVGIGT C KU FKXKFGF D[ CP KPVGIGT D KH D KU PQV C FKXKUQT QH C VJGP VJG TGUWNV ECP DG XKGYGF KP VJTGG FKHHGTGPV YC[U C HTCEVKQP C FGEKOCN SWQVKGPV YKVJ C TGOCKPFGT $ 9JGP CP KPVGIGT C KU FKXKFGF D[ CP KPVGIGT D KH D KU PQV C FKXKUQT QH C VJGP VJG TGUWNV ECP DG XKGYGF KP VYQ FKHHGTGPV YC[U C HTCEVKQP CPF C FGEKOCN & 9JGP CP KPVGIGT C KU FKXKFGF D[ CP KPVGIGT D KH D KU PQV C FKXKUQT QH C VJGP VJG TGUWNV ECP DG XKGYGF KP QPN[ YC[ C SWQVKGPV YKVJ C TGOCKPFGT & 9JGP C FKXKUKQP TGUWNVU KP C SWQVKGPV YKVJ C TGOCKPFGT QPN[ VJG SWQVKGPV QT VJG TGOCKPFGT ECP DG CP KPVGIGT

%QTTGEV #PUYGT #

'ZRNCPCVKQP

9JGP CP KPVGIGT C KU FKXKFGF D[ CP KPVGIGT D YJGTG D KU C FKXKUQT QH C VJG TGUWNV KU CNYC[U C FKXKUQT QH C (QT GZCORNG YJGP KU FKXKFGF D[ QPG QH KVU FKXKUQTU VJG TGUWNV KU YJKEJ KU CPQVJGT FKXKUQT QH +H D KU PQV C FKXKUQT QH C VJGP VJG TGUWNV ECP DG XKGYGF KP VJTGG FKHHGTGPV YC[U 6JG TGUWNV ECP DG XKGYGF CU C HTCEVKQP QT CU C FGEKOCN QT VJG TGUWNV ECP DG XKGYGF CU C SWQVKGPV YKVJ C TGOCKPFGT & $QVJ VJG SWQVKGPV CPF VJG TGOCKPFGT CTG KPVGIGTU

'CEJ XKGY KU WUGHWN FGRGPFKPI QP VJG EQPVGZV (TCEVKQPU CPF FGEKOCNU CTG WUGHWN YJGP VJG TGUWNV OWUV DG XKGYGF CU C UKPING PWODGT YJKNG SWQVKGPVU YKVJ TGOCKPFGTU CTG WUGHWN HQT FGUETKDKPI VJG TGUWNV KP VGTOU QH KPVGIGTU QPN[


KU FKXKFGF D[

6JG UWO QH VJG SWQVKGPV CPF VJG TGOCKPFGT

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

9JGP KU FKXKFGF D[ VJG TGUWNV KU ITGCVGT VJCP UKPEG DWV NGUU VJCP UKPEG $GECWUG KU OQTG VJCP YG UC[ VJCV VJG TGUWNV QH FKXKFGF D[ KU VJG SWQVKGPV YKVJ TGOCKPFGT QT UKORN[ Ì TGOCKPFGT Í

4GICTFKPI SWQVKGPVU YKVJ TGOCKPFGTU EQPUKFGT VYQ RQUKVKXG KPVGIGTU C CPF D HQT YJKEJ D KU PQV C FKXKUQT QH C

+P IGPGTCN YJGP C RQUKVKXG KPVGIGT C KU FKXKFGF D[ C RQUKVKXG KPVGIGT D [QW HKTUV HKPF VJG ITGCVGUV OWNVKRNG QH D VJCV KU NGUU VJCP QT GSWCN VQ C 6JCV OWNVKRNG QH D ECP DG GZRTGUUGF CU VJG RTQFWEV SD YJGTG S KU VJG SWQVKGPV 6JGP VJG TGOCKPFGT KU GSWCN VQ C OKPWU VJCV OWNVKRNG QH D QT T C SD YJGTG T KU VJG TGOCKPFGT 6JG TGOCKPFGT KU CNYC[U ITGCVGT VJCP QT GSWCN VQ CPF NGUU VJCP D


+P IGPGTCN YJGP C RQUKVKXG KPVGIGT KU FKXKFGF D[ C RQUKVKXG KPVGIGT [QW HKTUV HKPF VJG ITGCVGUV OWNVKRNG QH VJCV KU NGUU VJCP QT GSWCN VQ 6JCV OWNVKRNG QH ECP DG GZRTGUUGF CU VJG RTQFWEV YJGTG KU VJG SWQVKGPV 6JGP VJG TGOCKPFGT KU GSWCN VQ OKPWU VJCV OWNVKRNG QH QT YJGTG KU VJG TGOCKPFGT 6JG TGOCKPFGT KU CNYC[U ITGCVGT VJCP QT GSWCN VQ CPF NGUU VJCP


FKXKFGF D[

6JG UWO QH VJG SWQVKGPV CPF VJG TGOCKPFGT

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

FKXKFGF D[ KU TGOCKPFGT UKPEG VJG ITGCVGUV OWNVKRNG QH VJCVÊU NGUU VJCP QT GSWCN VQ KU QT YJKEJ KU NGUU VJCP 6JG UWO QH VJG SWQVKGPV CPF VJG TGOCKPFGT KU


FKXKFGF D[ S KU TGOCKPFGT

6JG ITGCVGUV OWNVKRNG QH S VJCVÊU NGUU VJCP QT GSWCN VQ

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

FKXKFGF D[ KU TGOCKPFGT UKPEG VJG ITGCVGUV OWNVKRNG QH VJCVÊU NGUU VJCP QT GSWCN VQ KU KVUGNH YJKEJ KU NGUU VJCP

+P IGPGTCN VJG TGOCKPFGT KU KH CPF QPN[ KH C KU GZCEVN[ FKXKUKDNG D[ D


KU FKXKFGF D[

6JG SWQVKGPV OKPWU VJG TGOCKPFGT

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT #

'ZRNCPCVKQP

6JG SWQVKGPV KU VJG TGOCKPFGT KU FKXKFGF D[ KU TGOCKPFGT UKPEG VJG ITGCVGUV OWNVKRNG QH VJCVÊU NGUU VJCP QT GSWCN VQ KU QT YJKEJ KU NGUU VJCP


9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU KU (#.5'! # FKXKFGF D[ KU TGOCKPFGT % FKXKFGF D[ KU TGOCKPFGT & FKXKFGF D[ KU TGOCKPFGT ' 9JGP [QW FKXKFG D[ VJG TGOCKPFGT KU ( 9JGP [QW FKXKFG D[ VJG TGOCKPFGT KU %QTTGEV #PUYGT &

'ZRNCPCVKQP

& 9JGP [QW FKXKFG D[ VJG TGOCKPFGT KU # % & ( 7UG C ECNEWNCVQT CPF FKXKFG D[ [QW YKNN EQORWVG 1H EQWTUG KH YG OWNVKRN[ CPF YG EQORWVG 6JWU FKXKFGF D[ KU TGOCKPFGT


# RQUKVKXG QFF KPVGIGT KU FKXKFGF D[

6JG TGOCKPFGT

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

9JGP C RQUKVKXG QFF KPVGIGT KU FKXKFGF D[ VJG TGOCKPFGT KU CNYC[U 6JG UGV QH GXGP KPVGIGTU KU ] _ CPF VJG UGV QH QFF KPVGIGTU KU ] _


6JG NKUV DGNQY EQPVCKPU VJTGG 647' UVCVGOGPVU CPF VJTGG (#.5' UVCVGOGPVU

䃋6JG UWO QH VYQ GXGP KPVGIGTU KU CP GXGP KPVGIGT 䃌6JG UWO QH VYQ QFF KPVGIGTU KU CP GXGP RTKOG KPVGIGT 䃍6JG UWO QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU GKVJGT CP QFF KPVGIGT QT CP GXGP KPVGIGT 䃎6JG RTQFWEV QH VYQ GXGP KPVGIGTU KU CP GXGP KPVGIGT 䃏6JG RTQFWEV QH VYQ QFF KPVGIGTU KU KU GKVJGT CP QFF KPVGIGT QT CP GXGP KPVGIGT 䃐6JG RTQFWEV QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU CP GXGP KPVGIGT

6JG UWO QH VJG XCNWGU PGZV VQ VJG VJTGG (#.5' UVCVGOGPVU

6JG UWO QH VJG XCNWGU PGZV VQ VJG VJTGG 647' UVCVGOGPVU

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT $

'ZRNCPCVKQP

䃌 䃍 䃏 (#.5' 䃋 䃎 䃐 647' 䃋6JG UWO QH VYQ GXGP KPVGIGTU KU CP GXGP KPVGIGT 647' 䃌6JG UWO QH VYQ QFF KPVGIGTU KU CP GXGP RTKOG KPVGIGT (#.5' TGOQXG ÌRTKOGÍ


䃍6JG UWO QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU GKVJGT CP QFF KPVGIGT QT CP GXGP KPVGIGT (#.5' TGOQXG ÌQT CP GXGP KPVGIGTÍ

䃎6JG RTQFWEV QH VYQ GXGP KPVGIGTU KU CP GXGP KPVGIGT 647' 䃏6JG RTQFWEV QH VYQ QFF KPVGIGTU KU KU GKVJGT CP QFF KPVGIGT QT CP GXGP KPVGIGT (#.5' TGOQXG ÌQT CP GXGP KPVGIGTÍ

䃐6JG RTQFWEV QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU CP GXGP KPVGIGT 647'


#P '8'0 TGUWNV KU YQTVJ RQKPV CPF CP 1&& TGUWNV KU YQTVJ RQKPVU

ඎ 6JG RTQFWEV QH VYQ QFF KPVGIGTU ඏ 6JG UWO QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT ඐ 6JG UWO QH VYQ GXGP KPVGIGTU එ 6JG UWO QH VYQ QFF KPVGIGTU ඒ 6JG RTQFWEV QH VYQ GXGP KPVGIGTU ඓ 6JG RTQFWEV QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT

6JG RTQFWEV QH VJG 6JG RTQFWEV QH VJG RQKPVU HTQO ඎ ඐ CPF RQKPVU HTQO ඏ එ ඒ ඓ

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

ඎ 6JG RTQFWEV QH VYQ QFF KPVGIGTU KU QFF ඏ 6JG UWO QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU QFF ඐ 6JG UWO QH VYQ GXGP KPVGIGTU KU GXGP එ 6JG UWO QH VYQ QFF KPVGIGTU KU GXGP ඒ 6JG RTQFWEV QH VYQ GXGP KPVGIGTU KU GXGP ඓ 6JG RTQFWEV QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU GXGP

ඎ 2QKPVU 6JG RTQFWEV QH VYQ QFF KPVGIGTU KU QFF ඏ 2QKPVU 6JG UWO QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU QFF


ඐ 2QKPV 6JG UWO QH VYQ GXGP KPVGIGTU KU GXGP එ 2QKPV 6JG UWO QH VYQ QFF KPVGIGTU KU GXGP ඒ 2QKPV 6JG RTQFWEV QH VYQ GXGP KPVGIGTU KU GXGP ඓ 2QKPV 6JG RTQFWEV QH CP GXGP KPVGIGT CPF CP QFF KPVGIGT KU GXGP

6JG RTQFWEV QH VJG RQKPVU HTQO ඎ ඐ CPF ඓ 6JG RTQFWEV QH VJG RQKPVU HTQO ඏ එ ඒ


6JG UWO QH VJG HKTUV VGP RTKOG PWODGTU

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

6JG HKTUV VGP RTKOG PWODGTU CTG CPF

KU KU Ì Í KU 6Q CFF VQ VJG TGUV CFF CPF UWDVTCEV

# RTKOG PWODGT KU CP KPVGIGT ITGCVGT VJCP VJCV JCU QPN[ VYQ RQUKVKXG FKXKUQTU CPF KVUGNH 6JG KPVGIGT KU PQV C RTKOG PWODGT UKPEG KV JCU HQWT RQUKVKXG FKXKUQTU CPF 6JG KPVGIGT KU PQV C RTKOG PWODGT CPF VJG KPVGIGT KU VJG QPN[ RTKOG PWODGT VJCV KU GXGP


6JG PWODGT QH RTKOG HCEVQTU QH

6JG PWODGT QH RTKOG HCEVQTU QH

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT %

'ZRNCPCVKQP

'XGT[ KPVGIGT ITGCVGT VJCP GKVJGT KU C RTKOG PWODGT QT ECP DG WPKSWGN[ GZRTGUUGF CU C RTQFWEV QH HCEVQTU VJCV CTG RTKOG PWODGTU QT RTKOG FKXKUQTU 5WEJ CP GZRTGUUKQP KU ECNNGF C RTKOG HCEVQTK\CVKQP *GTG CTG UKZ GZCORNGU QH RTKOG HCEVQTK\CVKQPU

s à³– s à³— s


6JG /'&+#0 QH 6JG /'#0 QH VJG HKTUV VJG HKTUV VGP VGP EQORQUKVG PWODGTU EQORQUKVG PWODGTU

# 6JG SWCPVKV[ QP VJG NGHV KU ITGCVGT $ 6JG SWCPVKV[ QP VJG TKIJV KU ITGCVGT % $QVJ CTG GSWCN & 6JG TGNCVKQPUJKR ECPPQV DG FGVGTOKPGF YKVJQWV HWTVJGT KPHQTOCVKQP

%QTTGEV #PUYGT $

'ZRNCPCVKQP

/'&+#0 4CPMGF /KFFNG /'#0 #XGTCIG

#P KPVGIGT ITGCVGT VJCP VJCV KU PQV C RTKOG PWODGT KU ECNNGF C EQORQUKVG PWODGT 6JG HKTUV VGP EQORQUKVG PWODGTU CTG CPF

6JG NKUV JCU CP GXGP COQWPV QH PWODGTU VGP 6JWU VJG OGFKCP KU VJG CXGTCIG QH VJG VYQ OKFFNG PWODGTU +P VJKU ECUG VJG CXGTCIG QH CPF KU 6JG /GCP KU VJG VQVCN FKXKFGF D[ VJG PWODGT QH VGTOU YJKEJ KU


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