numerical aptitude
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8/10/2019 Numerical Aptitude
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NUMERICAL
APTITUDE
GAURA
V
KUMAR
CHIR
AGJAIN
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General Pattern
TCS: 30 Questions in 80
Minutes
Negative MarkingFactor- 1/3
Star Questions-
Have iger!eigtage an" asHiger NegativeMarking
L&T InfoTech :
#0 Questions in #0 Minutes 30 Questions eac in
Quantitative $%titu"e
&ogical ' $nal(tical )easoning
*er+al $%titu"e
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General Pattern
Infosys: 10 Questions in
Quantitative
$%titu"e,3 Min. 1 Questions in
&ogical ' $nal(tical)easoning, Min.
0 Questions in*er+al $%titu"e,3Min.
Cognizn!:
1 Questions in Quantitative$%titu"e,1 Min.
1 Questions in &ogical ' $nal(tical)easoning,1 Min.
Questions in *er+al $%titu"e,30Min.
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2o%ics
Pro+les on Po4ers 5locks 5alen"ars
Pro+les on 2rains Pro+a+ilit( &ogarits
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Pro+les on Po4ers6
Questions to 7n" nit9s an" 2en9s igit M;2H +( =? te )eain"er is 0- )aise te @ase to %o4er o? 1- )aise te @ase to %o4er o? 1 - )aise te @ase to %o4er o? 3- )aise te @ase to %o4er o? 3
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;>a%les
Fin" te nit9s igit o? ,3A #A BB1.
Po4ers/ )eain"er
iC / 1iiC #/ 3
iiiC B1/ 3
31D3E 3D1E B3D33
nit9s igit in te %ro"uct Dnit9s igit o? ,3AA3.D
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2rick( Question
Fin" te last t4o "igits in ,1#1.383 ,1#1.181 ,25S 013.
Sortcut to 7n" last t4o "igits ?or nu+er en"ing4it 1:
Multi%l( tens "igit 4it te unit "igit in te %o4erC2akete unit "igit in te resultant %ro"uct ?ollo4e" +( 1C Here 4e ave ,1#1.383CHence A3 D 1CHence
&ast t4o "igitsD1 For ,1#1.181A1D0CHence last t4o "igits D 1
So last t4o "igits in te entire euation D 11 D8
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No" so#$e yo%se#f '
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Pro+les
Fin" te unit9s "igit in ,B#I 38.
iC B
iiC 0iiiC
ivC
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Pro+les
Fin" te unit9s "igit in ,B#I 38.
iC B
iiC 0iiiC
ivC
$ns4er D
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Solution
Fin" te unit9s "igit in ,B#I 38.
J nit9s "igit in B# D 3
nit9s "igit in 38 D #
Since B# K 38
nit9s igit D 13 -# D
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Pro+les
Fin" tereain"er 4en31is "ivi"e" +(
CiC 1
iiC
iiiC 3ivC
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Pro+les
Fin" te reain"er 4en 31is "ivi"e"+( C
nit9s igit o? 31 D 8
So )eain"er D 3
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Pro+les
!at are te last t4o "igits o? B008L
=C 1
==C 1
===C 01
=*C 1
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Pro+les
!at are te last t4o "igits o? B008L 008 is "ivisi+le +( CC+ut "oesn9t ave
re%eate" last "igits ?or ulti%les o? C
BD # E BD 01 5eck ?or ulti%les o? :
,B. D B801
=n te sae 4a( ,B.34ill also ave last "igit 01
+ecause 01A01 D01C so result o? ,B.k4ill ave last "igit 01 ?or an(
ve integer k +ecause 01A01A01A66 k ties D01C
Since 008 is ulti%le o? so ans4er is 01C
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5lock Pro+les
S%ee" o? te our an" D 0C "egrees%er inute ,"%.
S%ee" o? te inute an" D "%
$t n9 o9 clock te angle o? te ouran" ?ro te vertical is 30nC
@et4een ever( t4o ours te( are
%er%en"icular to eac oter t4o tiese>ce%t +et4een to an" 8 to 10 C
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5lock Pro+les
=n 0 inutes te inute an" gains inutes on te our an"C
!en te t4o an"s are at rigt angles
te( are 1 inute s%aces a%artC!en te an"s are in o%%osite"irections te( are 30 inute s%aces
a%artC
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5lock Pro+les
F
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;>a%les
$t 4at tie +et4een # an" 10 oclock 4ill te an"s o? aclock +e in te sae straigt line +ut not togeter L
$t # oclock our an" 1 in s%ace a%art ?ro inute an"C
$lso inute an" as gain o? ,30-1.D 1 in s%aces a%artover our an"For +ot an" to +e straigt +ut not togeter te( 4ill +e 30in s%ace a%artC
in s%ace gaine" +( in an" in 0 inC
So 1 in s%ace 4ill +e gaine" in D D ,. inC
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;>a%les
$ clock is set rigt at aCC 2e clock loses 1inutes in oursC !at 4ill +e te true tie4en te clock in"icates 10 %CC on t "a(L
2ie ?ro aCC on a "a( to 10 %CC on t "a( D8# ours
3 rs inC o? tis clock D ours o? correctclock
rs o? tis clock D ours o? correct clock 8# rs o? tis clock D , > > 8#. rs o? correctclock
D #0 rs o? correct clock So te correct tie is 11 %C
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No" so#$e yo%se#f '
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Pro+les
Ho4 an( ties a "a( te an"s o? a clockare straigtL
a.
+. 3c.
".
e. ?. 8
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Pro+les
Ho4 an( ties a "a( te an"s o? a clockare straigtL
a.
+. 3c.
".
e. ?. 8
$ns :
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Pro+les
$t 4at angle te an"s o? a clock areincline" at 1 inutes %ast L
a. 3C+. 3BC
c. 38C
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Pro+les
$t 4at angle te an"s o? a clock areincline" at 1 inutes %ast L
a. 3C+. 3BC
c. 38C
$ns : 3BC
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5alen"ar
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5alen"ar
5ounting o?
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5alen"ar
No9 of:--Dys
3 6 8 2 ;
< =
a( SunMon
2ue !e" 2u Fri Sat
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;>a%les
!at 4as te "a( o? te 4eek on 1t$ugust1#BL 5ounting o?
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;>a%les
2o"a( is 1Bt Nove+er 01C 2e "a( o? te4eek is !e"nes"a(C !at 4ill +e te "a( o? te4eek on tis "a( a?ter 3 (earsL
2e ne>t 3 (ears 4ill ave or"inar( (ears an"1 &ea% (earC ;ac or"inar( (ear 4ill give 1 o"" "a( an" lea%
(ear 4ill give o"" "a(s 2otal o"" "a(s a?ter 3 (ears D So te "a( o? te 4eek 4ill +e o"" "a(s
+e(on" !e"nes"a( iCeC it 4ill +e Sun"a(C
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No" so#$e yo%se#f '
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Pro+les
2e First )e%u+lic a( o? =n"ia 4as cele+rate"on tanuar( 1#0C =t 4as :
iC 2ues"a(
iiC !e"nes"a(iiiC 2urs"a(
ivC Fri"a(
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Pro+les
2e First )e%u+lic a( o? =n"ia 4as cele+rate"on tanuar( 1#0C =t 4as :
iC 2ues"a(
iiC !e"nes"a(iiiC 2urs"a(
ivC Fri"a(
$ns : 2urs"a(
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Pro+les
2e last "a( o? a centur( cannot +e :
iC Mon"a(
iiC !e"nes"a(
iiiC Fri"a(
ivC 2ues"a(
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Pro+les
2e last "a( o? a centur( cannot +e :
iC Mon"a(
iiC !e"nes"a(
iiiC Fri"a(
ivC 2ues"a(
$ns : 2ues"a(
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Pro+les on 2rains
a k/rC D ,aA /18. /sec a /sec D ,aA 18/. k/rC
24o trains oving in o%%osite "irection 4its%ee" u /sec an" v /sec ten
relative s%ee" D , u v . /sec24o trains oving in sae "irection 4it
s%ee" u /sec an" v /sec ten i? u K v
relative s%ee" D , u - v . /sec
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;>a%les
$ train running at k/r takes 0 sec to %ass a %lat?orCNe>t it takes 1 sec to %ass a an 4alking at k/r in
te sae "irection in 4ic te train is goingC Fin" telengt o? te train an" te %lat?or L
&et > D lengt o? te train ( D lengt o? te %lat?or
S%ee" o? te train relative to an D , I . k/r
D 8 k/r
D 0/3 /sec
&engt o? train D ,)elative s%ee" A 2ie.
D ,,0/3.A1. D 10
S%ee" o? train D , A /18. /sec
D 1 /sec
No4 ,> (./1 D 0 DK > ( D 300
( D 300 I 10 D 10
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No" so#$e yo%se#f '
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Pro+les
$ Togger running at # k/r alongsi"e arail4a( track is 0 aea" o? teengine o? a 10 long train running at
k/r in te sae "irectionC =n o4uc tie 4ill te train %ass te Togger L
iC 3C sec
iiC 18 sec
iiiC 3 sec
ivC B sec
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Pro+les
$ Togger running at # k/r alongsi"e arail4a( track is 0 aea" o? te engineo? a 10 long train running at k/r
in te sae "irectionC =n o4 uc tie4ill te train %ass te Togger L
iC 3C sec
iiC 18 sec
iiiC 3 sec
ivC B sec
$ns4er : 3 sec
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Solution
$ Togger running at # k/r alongsi"e a rail4a(track is 0 aea" o? te engine o? a 10 long train running at k/r in te sae"irectionC =n o4 uc tie 4ill te train %ass te
Togger LS%ee" o? train relative to Togger D , I #. k/r
D 3 k/r
D 10 /secistance to +e covere" D ,0 10.
D 30
No4 2ie taken D ,30/10. sec
D 3 sec
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Pro+les
$ B0 long train running at a s%ee" o?10 k/r crosses anoter train running ino%%osite "irection at te s%ee" o? 80 k/r
in # secC !at is te lengt o? te otertrain L
iC 30 iiC 0
iiiC 30
ivC 30
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Pro+les
$ B0 long train running at a s%ee" o? 10k/r crosses anoter train running ino%%osite "irection at te s%ee" o? 80 k/r in
# secC !at is te lengt o? te oter train L
iC 30
iiC 0
iiiC 30
ivC 30
$ns4er : 30
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Solution
$ B0 long train running at a s%ee" o? 10k/r crosses anoter train running ino%%osite "irection at te s%ee" o? 80 k/r in
# secC !at is te lengt o? te oter train L)elative S%ee" D ,10 80. k/r
D 00 k/r
D ,00/#. /sec
&et > D &engt o? te oter train
No4 ,> B0./# D 00/#
DK > B0 D 00
DK > D 30
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Pro+a+ilit(
Sa%le S%ace ,S. : Set o? all %ossi+leoutcoes o? an e>%erientC
;vent ,;.: Su+set o? a Sa%le S%aceC
Pro+a+ilit( o? occurrence o? an ;vent P,;. :P,;. D n,;./n,S.
0 >P,;. > 1
For an( events $ an" @P,$ U @. D P,$. P,@. I P,$ V @. Pro+a+ilit( o? occurrence o? an event cannot
+e ore tan 1an" is eual to 1C
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Pro+a+ilit(
5oin : Has t4o %ossi+le outcoes Hea" ,H. an"2ail ,2.ice: Has %ossi+le outcoes 1 3
Pack o? 5ar"s : total car"s13 car"s o? eac Suits nael( S%a"es 5lu+s
Hearts iaon"s5ar"s o? Hearts an" iaon"s are )e" in 5olour5ar"s o? S%a"es an" 5lu+s are @lack in 5olour$ces Wings Queens acks are Face 5ar"s in
eac Suits
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;>a%les
24o car"s are "ra4n at ran"o ?ro a %ack o? car"sC !at is te %ro+a+ilit( tat eiter +ot are+lack or +ot are Queens L
!e ave n,S. D 5D D 13
$ D event o? getting +ot +lack car"s@ D event o? getting +ot Queens
$ V @ D event o? getting +ot ueens o? +lack car"s
n,$. D 5D D 3
n,@. D 5D D an" n,$ V @. D 5D 1
P,$. D D P0@4D D P,$ V @. D D
P,$ U @. D P,$. P,@. I P,$ V @. D , . D D
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No" so#$e yo%se#f '
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Pro+les
24o "ice are tro4n togeterC !at is te%ro+a+ilit( tat te su o? te nu+ers onte t4o ?ace is "ivisi+le +( or L
iC
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Pro+les
24o "ice are tro4n togeterC !at is te%ro+a+ilit( tat te su o? te nu+ers onte t4o ?ace is "ivisi+le +( or L
$ns4er :
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Solution
24o "ice are tro4n togeterC !at iste %ro+a+ilit( tat te su o? tenu+ers on te t4o ?ace is "ivisi+le +(
or LHere n,S. D A D 3
; D event tat te su o? te nu+ers
on te t4o ?ace is "ivisi+le +( or n,;. D 1
P,;. D D D
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Pro+les
Four %ersons are cose at ran"o ?ro agrou% o? 3 en 4oen an" cil"renC
2e cance tat e>actl( o? te are
cil"ren is :
iC
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Pro+les
Four %ersons are cose at ran"o ?ro agrou% o? 3 en 4oen an" cil"renC
2e cance tat e>actl( o? te are
cil"ren is :
iC
$ns4er :
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Solution
Four %ersons are cose at ran"o ?ro agrou% o? 3 en 4oen an" cil"renC
2e cance tat e>actl( o? te are
cil"ren is :S D sa%le s%ace
; D event o? coosing %ersons suc tat
o? te are cil"renn,S. D #5D D 1
n,;. D ,5A 5. D A D 0
P,;. D D D
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&ogarit
log a+ D log a log + D D log a I log + log D + log a
D 1D 0
!en +ase is not given it is assue" as 10
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;>a%les
=? C D 3 ten 7n" >C
!e kno4 +( cange o? +ase rule
D C
C D D 3
D 3
D 3 D
X D D
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No" so#$e yo%se#f '
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Pro+les
Fin" te logarit o?1B8 to te +ase o?
iC
iiC
iiiC
ivC B
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Pro+les
Fin" te logarit o?1B8 to te +ase o?
iC
iiC
iiiC
ivC B
$ns4er :
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Solution
Fin" te logarit o?1B8 to te +ase o?
&et > D
D 1B8 D
Hence > D
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Pro+les
=? log 0C31BD0C333 an" log 0C318D0C33ten 7n" log 0C31# D
iC 0C33#iiC 0C33
iiiC 0C338#
ivC 0C33##
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l i
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Solution
=? log 0C31BD0C333 an" log 0C318D0C33ten 7n" log 0C31# D
Given D 0C333 an" D 0C33
2enD , - .
D 0C33#
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=t9s
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