Aptitude methods

7/21/2019 Aptitude methods

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QUANTITATIVE APTITUDE – NUMBERS

Some Basic Formulae:

I.Numeral : In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8,

called digits to re!resent any number"

A #rou! o$ di#its, denotin# a number is called a numeral.

%e re!resent a number, say 68745132 as s&own below :

'en

(rore

s

)108*

(rore

s)107

*

'en

+acs

)illions

* )106*

+acs)

105*

'en

'&ous

ands

)104*

'&ou

sand

s

)103*

Hund

reds

)102*

'en

s)1

01*

-ni

ts)

100

*

6 8 9 7 4 5 1 3 2

%e read it as : ./ityei#&t crores, ninetyseen lacs, $ortye t&ousand, one

&undred and t&irtytwo."

II Place Value or Local Value of a Digit in a Numeral :

In t&e aboe numeral :

lace alue o$ 2 is )2 1* 2 lace alue o$ 3 is )3 10* 30

lace alue o$ 1 is )1 100* 100 and so on"

lace alue o$ 6 is 6 10 8 600000000

III.Face Value : '&e face value o$ a di#it in a numeral is t&e alue o$ t&e di#it

itsel$ at w&ateer !lace it may be" In t&e aboe numeral, t&e $ace alue o$ 2 is 2

t&e $ace alue o$ 3 is 3 and so on"

IV.!P"# $F N%&'"(#

1.Natural Num)er* : (ountin# numbers 1, 2, 3, 4, 5," "" "" are cal led

natural

numbers.

2.+,ole Num)er* : All countin# numbers to#et&er wit& ero $orm t&e set o$

whole

numbers. '&us,

(i) 0 is t&e only w&ole number w&ic& is not a natural number"



(ii) ery natural number is a w&ole number"

3"Integer* : All natural numbers, 0 and ne#aties o$ countin# numbers i.e.,

9, 3 , 2 , 1 , 0, 1, 2, 3,""; to#et&er $orm t&e set o$ inte#ers"

(i) Po*iti-e Integer* : 91, 2, 3, 4, ""; is t&e set o$ all !ositie inte#ers"

(ii) Negati-e Integer* : {- 1, 2, 3,""; is t&e set o$ all ne#atie inte#ers"

(iii) NonPo*iti-e an/ NonNegati-e Integer* : 0 is neit&er !ositie nor

ne#atie" /o, 90, 1, 2, 3,"; re!resents t&e set o$ nonne#atie inte#ers, w&ile

90, 1 , 2 , 3 , ""; re!resents t&e set o$ non!ositie inte#ers"

4. "-en Num)er* 0 A number diisible by 2 is called an een number, e"#", 2, 4, 6,

8, 10, etc"

5. $// Num)er* 0 A number not diisible by 2 is called an odd number" e"#", 1, 3,5, 7, , 11, etc"

6. Prime Num)er* 0 A number #reater t&an 1 is called a !rime number, i$ it &as

eactly two $actors, namely 1 and t&e number itsel$"

rime numbers u!to 100 are : 2, 3, 5, 7, 11, 13, 17, 1, 23, 2, 31, 37, 41, 43,

47, 53, 5, 61, 67, 71, 73, 7, 83, 8, 7"

rime numbers <reater t&an 100 : +et! be a #ien number #reater t&an 100" 'o nd

out w&et&er it is !rime or not, we use t&e $ollowin# met&od :

=ind a w&ole number nearly #reater t&an t&e s>uare root o$ !" +et ? @ B!" 'est

w&et&er ! is diisible by any !rime number less t&an ?" I$ yes, t&en ! is not !rime"

Ct&erwise, ! is !rime"

e"#,,%e &ae to nd w&et&er 11 is a !rime number or not" Dow, 14 @ E11"

rime numbers less t&an 14 are 2, 3, 5, 7, 11, 13"

11 is not diisible by any o$ t&em" /o, 11 is a !rime number"

7.omo*ite Num)er* 0 Dumbers #reater t&an 1 w&ic& are not !rime, are ?nown

as com!osite numbers, e"#", 4, 6, 8, , 10, 12"

Note 0 )i* 1 is neit&er !rime nor com!osite"

)ii* 2 is t&e only een number w&ic& is !rime"

)iii* '&ere are 25 !rime numbers between 1 and 100"



8. orime* 0 'wo numbers a and b are said to be co!rimes, i$ t&eir H"("=" is 1"

e"#", )2, 3*, )4, 5*, )7, *, )8, 11*, etc" are co!rimes,

V."## $F DIVI#I'ILI!

1. Di-i*i)ilit ' 2 0 A number is diisible by 2, i$ its unit.s di#it is any o$ 0, 2, 4,

6, 8"

" 8432 is diisible by 2, w&ile 6535 is not"

2. Di-i*i)ilit ' 3 0 A number is diisible by 3, i$ t&e sum o$ its di#its is diisible

by 3"

".52482 is diisible by 3, since sum o$ its di#its )5 F F 2 F 4 F 8 F 2* 30,

w&ic& is diisible by 3"

Gut, 86432 is not diisible by 3, since sum o$ its di#its )8 F 6 F 4 F 3 F 2 F *

32, w&ic& is not diisible by 3"

3. Di-i*i)ilit ' 4 0 A number is diisible by 4, i$ t&e number $ormed by t&e last

two di#its is diisible by 4"

" 82648 is diisible by 4, since t&e number $ormed by t&e last two di#its is

48, w&ic& is diisible by 4"

Gut, 74282 is not diisible by 4, since t&e number $ormed by t&e last to di#its is


4. Di-i*i)ilit ' 5 0 A number is diisible by 5, i$ its unit.s di#it is eit&er 0 or 5" '&us, 20820 and 50345 are diisible by 5, w&ile 3034 and 4046 are not"

5. Di-i*i)ilit ' 6 0 A number is diisible by 6, i$ it is diisible by bot& 2 and 3"

" '&e number 35256 is clearly diisible by 2"

/um o$ its di#its )3 F 5 F 2 F 5 F 6* 21, w&ic& is diisible by 3" '&us, 35256 is

diisible by 2 as well as 3" Hence, 35256 is diisible by 6"

6. Di-i*i)ilit ' 8 0 A number is diisible by 8, i$ t&e number $ormed by t&e last

t&ree di#its o$ t&e #ien number is diisible by 8"

" 53360 is diisible by 8, since t&e number $ormed by last t&ree di#its is 360,

w&ic& is diisible by 8"

Gut, 52418 is not diisible by 8, since t&e number $ormed by last t&ree di#its is


7. Di-i*i)ilit ' 9 : A number is diisible by , i$ t&e sum o$ its di#its is diisible



by "

" 60732 is diisible by , since sum o$ di#its )6 F 0 F 7 F 3 F 2* 18, w&ic& is

diisible by "

Gut, 6856 is not diisible by , since sum o$ di#its )6 F 8 F F 5 F 6* 34,

w&ic& is not diisible by "

8. Di-i*i)ilit ' 1 0 A number is diisible by 10, i$ it ends wit& 0"

" 6410, 10480 are diisible by 10, w&ile 6375 is not"

9. Di-i*i)ilit ' 11 0 A number is diisible by 11, i$ t&e dierence o$ t&e sum o$

its di#its at odd !laces and t&e sum o$ its di#its at een !laces, is eit&er 0 or a

number diisible by 11"

". '&e number 4832718 is diisible by 11, since :

)sum o$ di#its at odd !laces* )sum o$ di#its at een !laces*

)8 F 7 F 3 F 4* )1 F 2 F 8* 11, w&ic& is diisible by 11"

1. Jiisibility Gy 12 A number is diisible by 12, i$ it is diisible by bot& 4 and

3"

". (onsider t&e number 34632"

)i* '&e number $ormed by last two di#its is 32, w&ic& is diisible by 4,

)ii* /um o$ di#its )3 F 4 F 6 F 3 F 2* 18, w&ic& is diisible by 3" '&us, 34632 isdiisible by 4 as well as 3" Hence, 34632 is diisible by 12"

11" Jiisibility Gy 14 : A number is diisible by 14, i$ it is diisible by 2 as well as 7"

12. Jiisibility Gy 15 : A number is diisible by 15, i$ it is diisible by bot& 3 and 5"

13. Jiisibility Gy 16 : A number is diisible by 16, i$ t&e number $ormed by t&elast4 di#its is diisible by

16"".757536 is diisible by 16, since t&e number $ormed by t&e last $our di#its is

7536, w&ic& is diisible by 16"

14. Di-i*i)ilit ' 24 0 A #ien number is diisible by 24, i$ it is diisible by bot&3

and 8"

15. Di-i*i)ilit ' 4 0 A #ien number is diisible by 40, i$ it is diisible by bot&

5 and 8"



16. Di-i*i)ilit ' 8 0 A #ien number is diisible by 80, i$ it is diisible by bot&

5 and 16"

Note 0 I$ a number is diisible by ! as well as >, w&ere ! and > are co!rimes, t&en

t&e #ien number is diisible by !>"

I$ ! arid > are not co!rimes, t&en t&e #ien number need not be diisible by !>,

een w&en it is diisible by bot& ! and >"

". 36 is diisible by bot& 4 and 6, but it is not diisible by )46* 24, since

4 and 6 are not co!rimes"

VI &%LIPLII$N '! #$( % &"$D#

1. &ultilication ' Di*tri)uti-e La 0

)i* a )b F c* a b F a c )ii* a)bc* a ba c"

". )i* 56758 56758 )100000 1*

56758 100000 56758 1 )5675800000 56758* 5675232042" )ii*

78 184 F 78 816 78 )184 F 816* 78 1000 78000"

2. &ultilication of a Num)er ' 5n 0 ut n eros to t&e ri#&t o$ t&e

multi!licand and diide t&e number so $ormed by 2n

" 75436 625 75436 54 754360000 6064760016

VII. '#I F$(&%L"

1" )a F b*2 a2 F b2 F 2ab 2" )a b*2 a2 F b2 2ab

3" )a F b*2 )a b*2 4ab 4" )a F b*2 F )a b*2 2 )a2 F b2*

5" )a2 b2* )a F b* )a b*

6" )a F b F c*2 a2 F b2 F c2 F 2 )ab F bc F ca*

7" )a3 F b3* )a Fb* )a2 ab F b2* 8" )a3 b3* )a b* )a2 F ab F b2*

" )a

3

F b

3

F c

3

3abc* )a F b F c* )a

2

F b

2

F c

2

ab bc ca*

10" I$ a F b F c 0, t&en a3 F b3 F c3 3abc"

VIII. DIVI#I$N L$(I& $( "%LID"N L$(I&

I$ we diide a #ien number by anot&er number, t&en :

Di-i/en/ : ;Di-i*or <uotient= > (emain/er





)1r*

Problems wit A!swers " E#$la!atio!

1. Which one of the following is not a prime number?

A. 31 B. 61

C. 71 D. 91

Answer: Option D

Explanation: 91 is divisible by 7. o! it is not a prime number.

". #11" $ %&' ( ?

A. 67))) B. 7))))

C. 76%)) D. 77"))

Answer: Option B

Explanation:

#11" $ %&' ( 11" $1) &

(11" $ 1)&

(11"))))

( 7))))" "& 16

3. *t is being given that #"3" + 1' is completely divisible by a whole number. Which of the

following numbers is completely divisible by this number?

A. #"16 + 1' B. #"16 , 1'

C. #7 $ ""3' D. #"96 + 1'

Answer: Option D

Explanation:

-et "

3"

( x

. hen! #"

3"

+ 1' ( # x

+ 1'.-et # x + 1' be completely divisible by the natural number /. hen!

#"96 + 1' ( 0#"3"'3 + 1 ( # x3 + 1' ( # x + 1'# x" , x + 1'! which is completely divisible by /!

since # x + 1' is divisible by /.



&. What least number must be added to 1)%6! so that the sum is completely divisible by "3 ?

A. " B. 3

C. 12 D. "1E. /one of these

Answer: Option A

Explanation:

"3' 1)%6 #&%

9"

,,,

136

11%

,,, "1

,,,

e4uired number ( #"3 , "1'

( ".

%. 1397 $ 1397 ( ?

A. 19%16)9 B. 19217)9

C. 1236"619 D. ")31719

E. /one of these

Answer: Option A

Explanation:

1397 $ 1397 ( #1397'"

( #1&)) , 3'"

( #1&))'" + #3'" , #" $ 1&)) $ 3'

( 196)))) + 9 , 2&))



( 196)))9 , 2&))

( 19%16)9.

6. 5ow many of the following numbers are divisible by 13" ?

"6&! 396! &6"! 79"! 962! "172! %12&! 6336

A. & B. %

C. 6 D. 7

Answer: Option A

Explanation:

13" ( & $ 3 $ 11

o! if the number divisible by all the three number &! 3 and 11! then the number is divisible

by 13" also.

"6& 11!3!& #'396 11!3!& #'

&6" 11!3 #'79" 11!3!& #'

962 11!& #'

"172 11!3 #'

%12& 3!& #'6336 11!3!& #'

herefore the following numbers are divisible by 13" 8 "6&! 396! 79" and 6336.

e4uired number of number ( &.

7. #93%&"1 $ 6"%' ( ?

A. %7%6&21"% B. %2&6321"%

C. %2&6&91"% D. %2%6"21"%

n*er0 C!tion '"lanation0

35421 625 35421 54 35421

10

4

2

35421 104

354210000

24 16 584638125

2. he largest & digit number e$actly divisible by 22 is8

A. 99&& B. 9762



C. 9922 D. 2222

E. /one of these

Answer: Option A

Explanation:

-argest &,digit number ( 9999

22' 9999 #113

22 ,,,,

119

22

,,,, 319

"6&

,,,

%% ,,,

e4uired number ( #9999 , %%'

( 99&&.

9. Which of the following is a prime number ?

A. 33 B. 21

C. 93 D. 97

Answer: Option D

Explanation:

learly! 97 is a prime number.

1). What is the unit digit in :#637&'1793 $ #6"%'317 $ #3&1&91';?

A. ) B. "

C. 3 D. %

Answer & Explanation

Answer: Option A

Explanation:

<nit digit in #637&'1793 ( <nit digit in #&'1793

( <nit digit in 0#&"'296 $ &

( <nit digit in #6 $ &' ( &



<nit digit in #6"%'317 ( <nit digit in #%'317 ( %

<nit digit in #3&1'&91 ( <nit digit in #1'&91 ( 1

e4uired digit ( <nit digit in #& $ % $ 1' ( ).

11. 5358 x 51 = ?

A. 273258 B. 273268

C. 273348 D. 273358


Answer: Option A

Explanation:

5358 x51

= 5358 x (50 + 1)

= 5358 x 50 + 5358 x1

= 267900 + 5358

= 273258.

View Answer Workspace Report Discuss in Forum

12. The sum of fist fi!e pime num"es is#

A. 11 B. 18

C. 26 D. 28


Answer: Option D

Explanation:

$e%uie& sum = (2 + 3 + 5 + 7 + 11) = 28.

'ote# 1 is not pime num"e.

Definition: pime num"e (o pime) is ntu* num"e tht hs ext*, t-o &istint ntu*

num"e &i!isos# 1 n& itse*f.


http://www.indiabix.com/aptitude/numbers/discussion-29








13. The &iffeene of t-o num"es is 1365. On &i!i&in the *e num"e ", the sm**e/ -e et 6 s

%uotient n& the 15 s emin&e. ht is the sm**e num"e ?

A. 240 B. 270

C. 295 D. 360


Answer: Option B

Explanation:

et the sm**e num"e "e x . Then *e num"e = ( x + 1365).

x + 1365 = 6 x + 15

5 x = 1350

x = 270

m**e num"e = 270.


14. (12)3 x 64 432 = ?

A. 5184 B. 5060

C. 5148 D. 5084

E. 'one of these


Answer: Option A

Explanation:

i!en xp. =

(12)3 x 64

=

(12)3 x 64

= (12)

2

x 6

2

= (72)

2

= 5184432 12 x 62


15. 72519 x 9999 = ?









A. 725117481 B. 674217481

C. 685126481 D. 696217481

E. 'one of these


Answer: Option A

Explanation:

72519 x9999

= 72519 x (10000 1)

= 72519 x 10000 72519 x1

= 725190000 72519

= 725117481.


16. f the num"e 517 324 is omp*ete*, &i!isi"*e ", 3/ then the sm**est -ho*e num"e in the p*e

of -i** "e#

A. 0 B. 1

C. 2 D. 'one of these


Answer: Option C

Explanation:

um of &iits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x )/ -hih must "e &i!isi"*e ", 3.

x = 2.


17. The sm**est 3 &iit pime num"e is#

A. 101 B. 103

C. 109 D. 113










Answer: Option A

Explanation:

The sm**est 3&iit num"e is 100/ -hih is &i!isi"*e ", 2.

100 is not pime num"e.

101 11 n& 101 is not &i!isi"*e ", n, of the pime num"es 2/ 3/ 5/ 7/ 11.

101 is pime num"e.

:ene 101 is the sm**est 3&iit pime num"e.


18. hih one of the fo**o-in num"es is ext*, &i!isi"*e ", 11?

A. 235641 B. 245642

C. 315624 D. 415624


Answer: Option D

Explanation:

(4 + 5 + 2) (1 + 6 + 3) = 1/ not &i!isi"*e ", 11.

(2 + 6 + 4) (4 + 5 + 2) = 1/ not &i!isi"*e ", 11.

(4 + 6 + 1) (2 + 5 + 3) = 1/ not &i!isi"*e ", 11.

(4 + 6 + 1) (2 + 5 + 4) = 0/ o/ 415624 is &i!isi"*e ", 11.


19. (?) 19657 33994 = 9999

A. 63650 B. 53760

C. 59640 D. 61560

E. 'one of these










Answer: Option A

Explanation:

19657 Let x - 53651 = 9999

33994 Then, x = 9999 + 53651 = 63650

-----

53651

-----


20. The sum of fist 45 ntu* num"es is#

A. 1035 B. 1280

C. 2070 D. 2140


Answer: Option A

Explanation:

et n =(1 + 2 + 3 + ... + 45). This is n .;. in -hih =1/ & =1/ n = 45.

n =n

<2a + (n 1)d =45 x <2 x 1 + (45 1) x

1=

45x 46

= (45 x23)2 2 2

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

n =

n(n + 1)

=

45(45 + 1) =

1035.2 2View Answer Workspace Report Discuss in Forum

21. hih of the fo**o-in num"e is &i!isi"*e ", 24 ?

A. 35718 B. 63810

C. 537804 D. 3125736










Answer: Option D

Explanation:

24 = 3 x8/ -hee 3 n& 8 opime.

>*e*,/ 35718 is not &i!isi"*e ", 8/ s 718 is not &i!isi"*e ", 8.

imi**,/ 63810 is not &i!isi"*e ", 8 n& 537804 is not &i!isi"*e ", 8.

>i"su&e ot (&).

um of &iits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27/ -hih is &i!isi"*e ", 3.

*so/ 736 is &i!isi"*e ", 8.

3125736 is &i!isi"*e ", (3 x 8)/ i.e., 24.


22. 753 x 753 + 247 x 247 753 x 247

= ?753 x 753 x 753 + 247 x 247 x247

A.1

1000 B.

1

506

C.253

500 D. 'one of these


Answer: Option A

Explanation:

i!en xp. =

(a2 + b2 ab)

=

1

=

1

=

1

(a3 + b3) (a + b) (753 +

247)

1000


23. (?) + 3699 + 1985 2047 = 31111

A. 34748 B. 27474

C. 30154 D. 27574









E. 'one of these


Answer: Option B

Explanation:

x + 3699 + 1985 2047 = 31111

x + 3699 + 1985 = 31111 + 2047

x + 5684 = 33158

x = 33158 5684 = 27474.


24. f the num"e 481 673 is omp*ete*, &i!isi"*e ", 9/ then the sm**est -ho*e num"e in p*e of

-i** "e#

A. 2 B. 5

C. 6 D. 7

E. 'one of these


Answer: Option D

Explanation:

um of &iits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x)/ -hih must "e &i!isi"*e ", 9.

x = 7.


25. The &iffeene "et-een the *o* !*ue n& the fe !*ue of 7 in the nume* 32675149 is

A. 75142 B. 64851

C. 5149 D. 69993

E. 'one of these










Answer: Option D

Explanation:

(o* !*ue of 7) (e !*ue of 7) = (70000 7) = 69993


26. The &iffeene "et-een positi!e pope ftion n& its eipo* is 9@20. The ftion is#

A.3

5 B.

3

10

C.4

5 D.

4

3


Answer: Option C

Explanation:

et the e%uie& ftion "e x . Then1 x

=

9

x 20

1 x 2

=9

x 20

20 20 x 2 = 9 x

20 x 2 + 9 x 20 = 0

20 x 2 + 25 x 16 x 20 = 0

5 x (4 x + 5) 4(4 x + 5) = 0

(4 x + 5)(5 x 4) = 0

x =4

5View Answer Workspace Report Discuss in Forum

27. On &i!i&in num"e ", 56/ -e et 29 s emin&e. On &i!i&in the sme num"e ", 8/ -ht

-i** "e the emin&e ?

A. 4 B. 5

C. 6 D. 7










Answer: Option B

Explanation:

'o ns-e &esiption !i*"*e fo this %uestion. Let us discuss.


28. f n is ntu* num"e/ then (6n2 + 6n) is *-,s &i!isi"*e ",#

A. 6 on*, B. 6 n& 12 "oth

C. 12 on*, D. ", 18 on*,


Answer: Option B

Explanation:

(6n2 + 6n) = 6n(n + 1)/ -hih is *-,s &i!isi"*e ", 6 n& 12 "oth/ sine n(n + 1) is *-,s e!en.


29. 107 x 107 + 93 x 93 = ?

A. 19578 B. 19418

C. 20098 D. 21908

E. 'one of these


Answer: Option C

Explanation:

107 x 107 + 93 x93

= (107)2 + (93)2

= (100 + 7)2 + (100 7)2

= 2 x <(100)2 + 72 <Ref: (a + b)2 + (a - b)2 = 2(a2 + b2 )

= 20098















30. ht -i** "e emin&e -hen (6767 + 67) is &i!i&e& ", 68 ?

A. 1 B. 63

C. 66 D. 67


Answer: Option C

Explanation:

( x n + 1) -i** "e &i!isi"*e ", ( x + 1) on*, -hen n is o&&.

(6767 + 1) -i** "e &i!isi"*e ", (67 + 1)

(6767 + 1) + 66/ -hen &i!i&e& ", 68 -i** i!e 66 s emin&e.


31. On &i!i&in num"e ", 5/ -e et 3 s emin&e. ht -i** the emin&e -hen the s%ue of

the this num"e is &i!i&e& ", 5 ?

A. 0 B. 1

C. 2 D. 4


Answer: Option D

Explanation:

et the num"e "e x n& on &i!i&in x ", 5/ -e et k s %uotient n& 3 s emin&e.

x = 5A + 3

x 2 = (5A + 3)2

= (25k 2 + 30k + 9)

= 5(5k 2 + 6k + 1) + 4

On &i!i&in x 2 ", 5/ -e et 4 s emin&e.










32. :o- mn, 3&iit num"es e omp*ete*, &i!isi"*e 6 ?

A. 149 B. 150

C. 151 D. 166


Answer: Option B

Explanation:

3&iit num"e &i!isi"*e ", 6 e# 102/ 108/ 114/... / 996

This is n .;. in -hih a = 102/ d = 6 n& l = 996

et the num"e of tems "e n. Then t n = 996.

a + (n 1)& = 996

102 + (n 1) x 6 = 996

6 x (n 1) = 894

(n 1) = 149

n = 150

'um"e of tems = 150.


33. :o- mn, ntu* num"es e thee "et-een 23 n& 100 -hih e ext*, &i!isi"*e ", 6 ?

A. 8 B. 11

C. 12 D. 13

E. 'one of these


Answer: Option D

Explanation:

$e%uie& num"es e 24/ 30/ 36/ 42/ .../ 96







et the num"e of tems in it "e n.

Then tn = 96 a + (n 1)d = 96

24 + (n 1) x 6 = 96

(n 1) x 6 = 72

(n 1) = 12

n = 13

$e%uie& num"e of num"es = 13.


34. :o- mn, of the fo**o-in num"es e &i!isi"*e ", 3 "ut not ", 9 ?

2133/ 2343/ 3474/ 4131/ 5286/ 5340/ 6336/ 7347/ 8115/ 9276

A. 5 B. 6



Answer: Option B

Explanation:

BAin (@) those -hih e e &i!isi"*e ", 3 ", not ", 9 n& the othes ", (C)/ ", tAin the

sum of &iits/ -e et#s

2133 9 (C)

2343 12 (@)

3474 18 (C)

4131 9 (C)

5286 21 (@)

5340 12 (@)






6336 18 (C)

7347 21 (@)

8115 15 (@)

9276 24 (@)

$e%uie& num"e of num"es = 6.


35. (963 + 476)2 + (963 476)2

= ?(963 x 963 + 476 x 476)

A. 1449 B. 497

C. 2 D. 4

E. 'one of these


Answer: Option C

Explanation:

i!en xp. =

(a + b)2 + (a b)2

=

2(a2 + b2) = 2

(a2 + b2) (a2 + b2)View Answer Workspace Report Discuss in Forum

36. :o- mn, 3 &iit num"es e &i!isi"*e ", 6 in ** ?

A. 149 B. 150

C. 151 D. 166


Answer: Option B

Explanation:

$e%uie& num"es e 102/ 108/ 114/ ... / 996










et the num"e of tems "e n. Then/

a + (n 1)d = 996

102 + (n 1) x 6 = 996

6 x (n 1) = 894

(n 1) = 149

n = 150.


37. 3&iit num"e 4a3 is &&e& to nothe 3&iit num"e 984 to i!e 4&iit num"e 13b7/

-hih is &i!isi"*e ", 11. Then/ (a + b) = ?

A. 10 B. 11

C. 12 D. 15


Answer: Option A

Explanation:

4 a 3 |

9 8 4 } ==> a + 8 = b ==> b - a = 813 b 7 |

*so/ 13 b7 is &i!isi"*e ", 11 (7 + 3) (b + 1) = (9 b)

(9 b) = 0

b = 9

(b = 9 n& a = 1) (a + b) = 10.


38. 8597 ? = 7429 4358

A. 5426 B. 5706

C. 5526 D. 5476









E. 'one of these


Answer: Option C

Explanation:

7429 Let 8597 - x = 3071

-4358 Then, x = 8597 - 3071

---- = 5526

3071

----


39. The sm**est pime num"e is#

A. 1 B. 2

C. 3 D. 4


Answer: Option B

Explanation:

The sm**est pime num"e is 2.


40. (12345679 x 72) = ?

A. 88888888 B. 888888888

C. 898989898 D. 9999999998


Answer: Option B

Explanation:

12345679 x72

= 12345679 x (70 +2)

= 12345679 x 70 + 12345679 x2









= 864197530 + 24691358

= 888888888


41. On &i!i&in num"e ", 357/ -e et 39 s emin&e. On &i!i&in the sme num"e 17/ -ht -i**

"e the emin&e ?

A. 0 B. 3

C. 5 D. 11


Answer: Option C

Explanation:

et x "e the num"e n& y "e the %uotient. Then/

x = 357 x y + 39

= (17 x 21 x y ) + (17 x 2) + 5

= 17 x (21y + 2) + 5)

$e%uie& emin&e = 5.


42. f the po&ut 4864 x 9 ; 2 is &i!isi"*e ", 12/ then the !*ue of ; is#

A. 2 B. 5

C. 6 D. 8

E. 'one of these


Answer: Option E

Explanation:

>*e*,/ 4864 is &i!isi"*e ", 4.









o/ 9;2 must "e &i!isi"*e ", 3. o/ (9 + ; + 2) must "e &i!isi"*e ", 3.

; = 1.


43. hih one of the fo**o-in is the ommon fto of (4743 + 4343) n& (4747 + 4347) ?

A. (47 43) B. (47 + 43)

C. (4743 + 4343) D. 'one of these


Answer: Option B

Explanation:

hen n is o&&/ ( x n + an) is *-,s &i!isi"*e ", ( x + a).

h one of (4743 + 4343) n& (4747 + 4343) is &i!isi"*e ", (47 + 43).


44. 84 x 29 + 365 = ?

A. 2436 B. 2801

C. 2801 D. 2071

E. 'one of these


Answer: Option D

Explanation:

i!en xp. = 84 x (30 1) + 365

= (84 x 30) + 84 +365

= 2520 + 449

= 2071













45. num"e -hen &i!i&e& ", 296 *e!es 75 s emin&e. hen the sme num"e is &i!i&e& ", 37/

the emin&e -i** "e#

A. 1 B. 2

C. 8 D. 11


Answer: Option A

Explanation:

et x = 296q + 75

= (37 x 8q + 37 x 2) + 1

= 37 (8q + 2) + 1

Thus/ -hen the num"e is &i!i&e& ", 37/ the emin&e is 1.


46. n &i!i&in num"e ", 585/ stu&ent emp*o,e& the metho& of shot &i!ision. :e &i!i&e& the

num"e suessi!e*, ", 5/ 9 n& 13 (ftos 585) n& ot the emin&es 4/ 8/ 12 espeti!e*,. f

he h& &i!i&e& the num"e ", 585/ the emin&e -ou*& h!e "een

A. 24 B. 144

C. 292 D. 584


Answer: Option D

Explanation:

5 | x z = 13 x 1 + 12 = 25

--------------

9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233

--------------

13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169

--------------

| 1 -12

585) 1169 (1

585

---

584

---






Therefore, on d!dn" the n#$%er %& 585, re$'nder = 584


47. n &i!ision sum/ the &i!iso is 10 times the %uotient n& 5 times the emin&e. f the emin&e

is 46/ -ht is the &i!i&en& ?

A. 4236 B. 4306

C. 4336 D. 5336

E. 'one of these


Answer: Option D

Explanation:

Di!iso = (5 x 46) = 230

10 x Euotient = 230 =230

= 2310

Di!i&en& = (Di!iso x Euotient) + $emin&e

= (230 x 23) + 46

= 5290 + 46

= 5336.


48. 4500 x ? = 3375

A.2

5 B.

3

4

C.1

4 D.

3

5

E. 'one of these


Answer: Option B

Explanation:









4500 x x = 3375 x =337575

=3

4500100 4View Answer Workspace Report Discuss in Forum

49. ht sm**est num"e shou*& "e &&e& to 4456 so tht the sum is omp*ete*, &i!isi"*e ", 6 ?

A. 4 B. 3

C. 2 D. 1

E. 'one of these


Answer: Option C

Explanation:

6) 4456 (742

42

---

25

24 Therefore, e*#red n#$%er = (6 - 4) = 2

---

16

12

---

4


50. ht *est num"e must "e su"tte& fom 13601/ so tht the emin&e is &i!isi"*e ", 87 ?

A. 23 B. 31

C. 29 D. 37

E. 49


Answer: Option C

Explanation:

87) 13601 (156

87

----

490

435

----

551









522

---

29

---

Therefore, the re*#red n#$%er = 29


51. 476 0 is &i!isi"*e ", "oth 3 n& 11. The nonFeo &iits in the hun&e&Gs n& tenGs p*es e

espeti!e*,#

A. 7 n& 4 B. 7 n& 5

C. 8 n& 5 D. 'one of these


Answer: Option C

Explanation:

et the i!en num"e "e 476 xy 0.

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y ) must "e &i!isi"*e ", 3.

n&/ (0 + x + 7) (y + 6 + 4) = ( x y 3) must "e eithe 0 o 11.

x y 3 = 0 y = x 3

(17 + x + y ) = (17 + x + x 3) = (2 x + 14)

x = 2 o x = 8.

x = 8 n& y = 5.



-i** "e#

A. 3 B. 2

C. 1 D. 5

E. 'one of these


Answer: Option A









Explanation:

i!en num"e = 97215 x 6

(6 + 5 + 2 + 9) ( x + 1 + 7) = (14 x)/ -hih must "e &i!isi"*e ", 11.

x = 3


53. (112 + 122 + 132 + ... + 202) = ?

A. 385 B. 2485

C. 2870 D. 3255


Answer: Option B

Explanation:

(112 + 122 + 132 + ... + 202) = (12 + 22 + 32 + ... + 202) (12 + 22 + 32 + ... + 102)

Ref: (12 + 22 + 32 + ... + n2) =1

n(n + 1)(2n + 1)6

=

20 x 21 x41

10 x 11 x21

6 6

= (2870 385)

= 2485.


54. f the num"e 5 2 is &i!isi"*e ", 6/ then = ?

A. 2 B. 3

C. 6 D. 7


Answer: Option A

Explanation:









6 = 3 x 2. >*e*,/ 5 2 is &i!isi"*e ", 2. $ep*e ", x .

Then/ (5 + x + 2) must "e &i!isi"*e ", 3. o/ x = 2.


55. hih of the fo**o-in num"es -i** omp*ete*, &i!i&e (4915 1) ?

A. 8 B. 14

C. 46 D. 50


Answer: Option A

Explanation:

( x n 1) -i** "e &i!isi"*, ", ( x + 1) on*, -hen n is e!en.

(4915 1) = H(72)15 1I = (730 1)/ -hih is &i!isi"*e ", (7 +1)/ i.e./ 8.


56.9 +

3+ 7 +

2 9 +

1= ?

4 17 15

A. 7 +

719

1020 B. 9 +

817

1020

C. 9 +719

1020 D. 7 +

817

1020

E. 'one of these


Answer: Option D

Explanation:

i!en sum

= (9 + 7 9) +3

+2

1

4 17 15

= 9 + 3 + 7 + 2 9 + 1

4 17 15









= 7 +

765 + 120 68

1020

= 7 +817

1020


57.1

1+ 1

2+ 1

3+ ... up to n tems = ?

n n n

A.1n

2 B.

1(n 1)

2

C.1n(n 1)

2 D. 'one of these


Answer: Option B

Explanation:

i!en sum

= n n + 1

2

=1

(n 1)2


58. On &i!i&in 2272 s -e** s 875 ", 3&iit num"e '/ -e et the sme emin&e. The sum of the

&iits of ' is#

A. 10 B. 11

C. 12 D. 13


Answer: Option A

= (1 + 1 + 1 + ... to n tems) 1

+2

+3

+ ... to n temsn n n

= n n 1

+ 1 < Ref # nth tems = (n @n) = 1

2 n









Explanation:

>*e*,/ (2272 875) = 1397/ is ext*, &i!isi"*e ", '.

'o-/ 1397 = 11 x 127

The e%uie& 3&iit num"e is 127/ the sum of -hose &iits is 10.


59. "o, mu*tip*ie& 987 ", etin num"e n& o"tine& 559981 s his ns-e. f in the ns-e

"oth 98 e -on n& the othe &iits e oet/ then the oet ns-e -ou*& "e#

A. 553681 B. 555181

C. 555681 D. 556581


Answer: Option C

Explanation:

987 = 3 x 7 x 47

o/ the e%uie& num"e must "e &i!isi"*e ", eh one of 3/ 7/ 47

553681 (um of &iits = 28/ not &i!isi"*e ", 3)

555181 (um of &iits = 25/ not &i!isi"*e ", 3)

555681 is &i!isi"*e ", 3/ 7/ 47.


60. :o- mn, pime num"es e *ess thn 50 ?

A. 16 B. 15

C. 14 D. 18


Answer: Option B

Explanation:

;ime num"es *ess thn 50 e#









2/ 3/ 5/ 7/ 11/ 13/ 17/ 19/ 23/ 29/ 31/ 37/ 41/ 43/ 47

Thei num"e is 15


61. hen num"e is &i!i&e& ", 13/ the emin&e is 11. hen the sme num"e is &i!i&e& ", 17/

then emin&e is 9. ht is the num"e ?

A. 339 B. 349

C. 369 D. Dt in&e%ute


Answer: Option B

Explanation:

x = 13 p + 11 n& x = 17q + 9

13 p + 11 = 17q + 9

17q 13 p = 2

q=

2 +13 p

17

The *est !*ue of p fo -hih q

=

2 +

13 p is -ho*e num"e is p = 2617

x = (13 x 26 + 11)

= (338 + 11)

= 349


62.(51 + 52 + 53 + ... + 100) = ?

A. 2525 B. 2975

C. 3225 D. 3775










Answer: Option D

Explanation:

n = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) (1 + 2 + 3 + ... + 50)

=100 x (1 + 100)

50x (1 + 50)

2 2

= (50 x 101) (25 x 51)

= (5050 1275)

= 3775.


63. (800 64) x (1296 36) = ?

A. 420 B. 460

C. 500 D. 540

E. 'one of these


Answer: Option E

Explanation:

i!en xp. =800

x1296

= 45064 36


64. hih ntu* num"e is neest to 8485/ -hih is omp*ete*, &i!isi"*e ", 75 ?

A. 8475 B. 8500

C. 8550 D. 8525

E. 'one of these


Answer: Option A









Explanation:

n d!dn", e "et

75) 8485 (113

75 ---

98

75

----

235

225

---

10

---

e*#red n#$%er = (8485 - 10) .e/'#e 10 (75 - 10)

= 8475


65. f the num"e 42573 is ext*, &i!isi"*e ", 72/ then the minimum !*ue of is#

A. 4 B. 5

C. 6 D. 7

E. 8


Answer: Option C

Explanation:

72 = 9 x8/ -hee 9 n& 8 e opime.

The minimum !*ue of x fo -hih 73 x fo -hih 73 x is &i!isi"*e ", 8 is/ x = 6.

um of &iits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27/ -hih is &i!isi"*e ", 9.

$e%uie& !*ue of is 6.


66. hih of the fo**o-in num"es is &i!isi"*e ", eh one of 3/ 7/ 9 n& 11 ?

A. 639 B. 2079

C. 3791 D. 37911









E. 'one of these


Answer: Option B

Explanation:

639 is not &i!isi"*e ", 7

2079 is &i!isi"*e ", eh of 3/ 7/ 9/ 11.


67. hih ntu* num"e is neest to 9217/ -hih is omp*ete*, &i!isi"*e ", 88 ?

A. 9152 B. 9240

C. 9064 D. 9184

E. 'one of these


Answer: Option B

Explanation:

n d!dn" e "et,

88) 9217 (104

88

----

417

352

----

65

----

Therefore, e*#red n#$%er = 9217 + (88 - 65) .e/'#e (88 - 65) 65

= 9217 + 23

= 9240


68. (4300731) ? = 2535618

A. 1865113 B. 1775123

C. 1765113 D. 1675123









E. 'one of these


Answer: Option C

Explanation:

et 4300731 x = 2535618

Then x / = 4300731 2535618 = 1765113


69. n is -ho*e num"e -hih -hen &i!i&e& ", 4 i!es 3 s emin&e. ht -i** "e the emin&e

-hen 2n is &i!i&e& ", 4 ?

A. 3 B. 2

C. 1 D. 0


Answer: Option B

Explanation:

et n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.

Thus/ -hen 2n is &i!i&e& ", 4/ the emin&e is 2.


70. (489 + 375)2 (489 375)2

= ?(489 x 375)

A. 144 B. 864

C. 2 D. 4

E. 'one of these


Answer: Option D

Explanation:









i!en xp. = (a + b)2 (a b)2=

4a

b= 4

ab ab


71. 397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

A. 250001 B. 251001

C. 260101 D. 261001


Answer: Option B

Explanation:

i!en xp. = (397)2 + (104)2 + 2 x 397 x 104

= (397 + 104)2

= (501)2 = (500 + 1)2

= (5002) + (1)2 + (2 x 500 x 1)

= 250000 + 1 + 1000

= 251001


72. (35423 + 7164 + 41720) (317 x 89) = ?

A. 28213 B. 84307

C. 50694 D. 56094

E. 'one of these


Answer: Option D

Explanation:

35423 317 x 89 = 317 x (90 -1 )

+ 7164 = (317 x 90 - 317)

+ 41720 = (28530 - 317)

----- = 28213

84307









- 28213

-----

56094

-----


73. ( x n an) is omp*ete*, &i!isi"*e ", ( x a)/ -hen

A. n is n, ntu* num"e B. n is n e!en ntu* num"e

C. n is n& o&& ntu* num"e D. n is pime


Answer: Option A

Explanation:

o e!e, ntu* num"e n/ ( x n an) is omp*ete*, &i!isi"*e ", ( x a).


74. hih one of the fo**o-in num"es is omp*ete*, &i!isi"*e ", 45?

A. 181560 B. 331145

C. 202860 D. 2033555

E. 'one of these


Answer: Option C

Explanation:

45 = 5 x 9/ -hee 5 n& 9 e opimes.

Jnit &iit must "e 0 o 5 n& sum of &iits must "e &i!isi"*e ", 9.

mon i!en num"es/ suh num"e is 202860.


75. hih of the fo**o-in num"es -i** omp*ete*, &i!i&e (325 + 326 + 327 + 328) ?

A. 11 B. 16

C. 25 D. 30













Answer: Option D

Explanation:

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

= 324 x 3 x 4 x 10

= (324 x 4 x 30)/ -hih is &i!isi"*e ",30.


76. num"e -hen &i!i&e ", 6 *e!es emin&e 3. hen the s%ue of the num"e is &i!i&e& ", 6/

the emin&e is#

A. 0 B. 1

C. 2 D. 3


Answer: Option D

Explanation:

et x = 6q + 3.

Then/ x 2 = (6q + 3)2

= 36q2 + 36q + 9

= 6(6q2 + 6q + 1) + 3

Thus/ -hen x 2 is &i!i&e& ", 6/ then emin&e = 3.


77. The sum of the t-o num"es is 12 n& thei po&ut is 35. ht is the sum of the eipo*s of

these num"es ?

A.12

35 B.

1

35

C.35

8 D.

7

32










Answer: Option A

Explanation:

et the num"es "e a n& b. Then/ a + b = 12 n& ab = 35.

a +b = 12 1 + 1 = 12

ab 35 b a 35

um of eipo*s of i!en num"es =12

35View Answer Workspace Report Discuss in Forum

78. ht -i** "e emin&e -hen 17200 is &i!i&e& ", 18 ?

A. 17 B. 16

C. 1 D. 2


Answer: Option C

Explanation:

hen n is e!en. ( x n an) is omp*ete*, &i!isi"*, ", ( x + a)

(17200

1200

) is omp*ete*, &i!isi"*e ", (17 + 1)/ i.e., 18.

(17200 1) is omp*ete*, &i!isi"*e ", 18.

On &i!i&in 17200 ", 18/ -e et 1 s emin&e.


79. f 1400 x x = 1050. Then/ x = ?

A.1

4 B.

3

5

C.2

3 D.

3

4

E. 'one of these










Answer: Option D

Explanation:

1400 x x = 1050 x =

1050

=

3


80. (12 + 22 + 32 + ... + 102) = ?

A. 330 B. 345

C. 365 D. 385


Answer: Option D

Explanation:

e Ano- tht (12 + 22 + 32 + ... + n2) =1

n(n + 1)(2n + 1)6

;uttin n = 10/ e%uie& sum =1 x 10 x 11 x

21= 385

6


81. The &iffeene of the s%ues of t-o onseuti!e e!en intees is &i!isi"*e ", -hih of the

fo**o-in intees ?

A. 3 B. 4

C. 6 D. 7


Answer: Option B

Explanation:

et the t-o onseuti!e e!en intees "e 2n n& (2n + 2). Then/

(2n + 2)2 = (2n + 2 + 2n)(2n + 2 2n)

= 2(4n + 2)









= 4(2n + 1)/ -hih is &i!isi"*e ", 4.


82. hih one of the fo**o-in is pime num"e ?

A. 119 B. 187

C. 247 D. 551

E. 'one of these


Answer: Option E

Explanation:

551 K 22

** pime num"es *ess thn 24 e # 2/ 3/ 5/ 7/ 11/ 13/ 17/ 19/ 23.

119 is &i!isi"*e ", 7L 187 is &i!isi"*e ", 11L 247 is &i!isi"*e ", 13 n& 551 is &i!isi"*e ", 19.

o/ none of the i!en num"es is pime.


83. The sum ** e!en ntu* num"es "et-een 1 n& 31 is#

A. 16 B. 128

C. 240 D. 512


Answer: Option C

Explanation:

$e%uie& sum = (2 + 4 + 6 + ... + 30)

This is n .;. in -hih a = 2/ d = (4 2) = 2 n& l = 30.










tn = 30 a + (n 1)d = 30

2 + (n 1) x 2 = 30

n 1 = 14

n = 15

n =n(a + l ) =

15x (2 + 30) = 240.


84. The &iffeene "et-een the p*e !*ue n& the fe !*ue of 6 in the nume* 856973 is

A. 973 B. 6973



Answer: Option C

Explanation:

(;*e !*ue of 6) (e !*ue of 6) = (6000 6) = 5994


85. f a n& b e o&& num"es/ then -hih of the fo**o-in is e!en ?

A. a + b B. a + b + 1

C. ab D. ab + 2

E. 'one of these


Answer: Option A

Explanation:

The sum of t-o o&& num"e is e!en. o/ + " is e!en.


86. hih one of the fo**o-in num"es is omp*ete*, &i!isi"*e ", 99?












A. 3572404 B. 135792

C. 913464 D. 114345

E. 'one of these


Answer: Option D

Explanation:

99 = 11 x 9/ -hee 11 n& 9 e opime.

M, hit n& ti*/ -e fin& tht 114345 is &i!isi"*e", 11 s -e** s 9. o/ it is &i!isi"*e ", 99.


87. The sum of ho- mn, tems of the seies 6 + 12 + 18 + 24 + ... is 1800 ?

A. 16 B. 24

C. 20 D. 18

E. 22


Answer: Option B

Explanation:

This is n .;. in -hih a = 6/ d = 6 n& n = 1800

Then/n<2a + (n 1)d = 1800

2

n <2 x 6 + (n 1) x 6 =

18002

3n (n + 1) = 1800

n(n + 1) = 600

n2 + n 600 = 0

n2 + 25n 24n 600 = 0






n(n + 25) 24(n + 25) = 0

(n + 25)(n 24) = 0

n = 24

'um"e of tems = 24.


88. (51+ 52 + 53 + ... + 100) = ?

A. 2525 B. 2975

C. 3225 D. 3775


Answer: Option D

Explanation:

This is n .;. in -hih a = 51/ l = 100 n& n = 50.

um =n(a + l ) =

50x (51 + 100) = (25 x 151) = 3775.


89. 1904 x 1904 = ?

A. 3654316 B. 3632646

C. 3625216 D. 3623436

E. 'one of these


Answer: Option C

Explanation:

1904 x1904

= (1904)2

= (1900 + 4)2









= (1900)2 + (4)2 + (2 x 1900 x 4)

= 3610000 + 16 + 15200.

= 3625216.


90. ht is the unit &iit in(795 358)?

A. 0 B. 4

C. 6 D. 7


Answer: Option B

Explanation:

Jnit &iit in 795 = Jnit &iit in <(74)23 x 73

= Jnit &iit in <(Jnit &iit in(2401))23 x (343)

= Jnit &iit in (123 x 343)

= Jnit &iit in (343)

= 3

Jnit &iit in 358 = Jnit &iit in <(34)14 x 32

= Jnit &iit in <Jnit &iit in (81)14 x 32

= Jnit &iit in <(1)14 x 32

= Jnit &iit in (1 x 9)

= Jnit &iit in (9)

= 9

Jnit &iit in (795 358) = Jnit &iit in (343 9) = Jnit &iit in (334) = 4.

o/ Option M is the ns-e.


91. hih one of the fo**o-in is pime num"e ?

A. 161 B. 221

C. 373 D. 437

E. 'one of these










Answer: Option C

Explanation:

437 K 22

** pime num"es *ess thn 22 e # 2/ 3/ 5/ 7/ 11/ 13/ 17/ 19.

161 is &i!isi"*e ", 7/ n& 221 is &i!isi"*e ", 13.

373 is not &i!isi"*e ", n, of the "o!e pime num"es.

373 is pime.


92. The sm**est 6 &iit num"e ext*, &i!isi"*e ", 111 is#

A. 111111 B. 110011

C. 100011 D. 110101

E. 'one of these


Answer: Option C

Explanation:

The $'et 6-d"t n#$%er 100000

111) 100000 (900

999

-----

100

---

e*#red n#$%er = 100000 + (111 - 100)

= 100011


93. The *est 5 &iit num"e ext*, &i!isi"*e ", 91 is#

A. 99921 B. 99918

C. 99981 D. 99971









E. 'one of these


Answer: Option B

Explanation:

L'r"et 5-d"t n#$%er = 99999

91) 99999 (1098

91

---

899

819

----

809

728

---

81

---

e*#red n#$%er = (99999 - 81)

= 99918


94. 768 x 768 x 768 + 232 x 232 x232 = ?

768 x 768 768 x 232 + 232 x 232

A. 1000 B. 536

C. 500 D. 268

E. 'one of these


Answer: Option A

Explanation:

i!en xp. =

(a3 + b3)

= (a + b) = (768 + 232) = 1000(a2 ab + b2)View Answer Workspace Report Discuss in Forum

95. The sm**est 5 &iit num"e ext*, &i!isi"*e ", 41 is#

A. 1004 B. 10004









C. 10045 D. 10025

E. 'one of these


Answer: Option B

Explanation:

The $'et 5-d"t n#$%er = 10000

41) 10000 (243

82

---

180

164

----

160 123

---

37

---

e*#red n#$%er = 10000 + (41 - 37)

= 10004


96. :o- mn, tems e thee in the .;. 3/ 6/ 12/ 24/ ... / 384 ?

A. 8 B. 9

C. 10 D. 11

E. 7


Answer: Option A

Explanation:

:ee a = 3 n& r = 6 = 2. et the num"e of tems "e n.3

Then/ tn = 384 ar n1 = 384

3 x 2n 1 = 384






2n1 = 128 = 27

n 1 = 7

n = 8

'um"e of tems = 8.


97. f x n& y e positi!e intees suh tht (3 x + 7y ) is mu*tip*e of 11/ then -hih of the fo**o-in

-i** "e &i!isi"*e ", 11 ?

A. 4 x + 6y B. x + y + 4

C. 9 x + 4y D. 4 x 9y


Answer: Option D

Explanation:

M, hit n& ti*/ -e put x = 5 n& y = 1 so tht (3 x + 7y ) = (3 x 5 + 7 x 1) = 22/ -hih is

&i!isi"*e ", 11.

(4 x + 6y ) = ( 4 x 5 + 6 x 1) = 26/ -hih is not &i!isi"*e ", 11L

( x + y + 4 ) = (5 + 1 + 4) = 10/ -hih is not &i!isi"*e ", 11L

(9 x + 4y ) = (9 x 5 + 4 x 1) = 49/ -hih is not &i!isi"*e ", 11L

(4 x 9y ) = (4 x 5 9 x 1) = 11/ -hih is &i!isi"*e ", 11.


98. 9548 + 7314 = 8362 + (?)

A. 8230 B. 8410

C. 8500 D. 8600

E. 'one of these


Answer: Option C









Explanation:

9548 16862 = 8362 + x

+ 7314 x = 16862 - 8362

----- = 8500

16862 -----


99. n &i!ision sum/ the emin&e is 0. s stu&ent mistooA the &i!iso ", 12 inste& of 21 n&

o"tine& 35 s %uotient. ht is the oet %uotient ?

A. 0 B. 12

C. 13 D. 20


Answer: Option D

Explanation:

'um"e = (12 x 35)

>oet Euotient = 420 21 = 20


100. 2 + 22 + 23 + ... + 29 = ?

A. 2044 B. 1022



Answer: Option B

Explanation:

This is .;. in -hih a = 2/ r = 2

2

= 2 n& n = 9.2

n =a(r n 1)

=2 x (29 1)

= 2 x (512 1) = 2 x 511 = 1022.(r 1) (2 1)













101. The sum of e!en num"es "et-een 1 n& 31 is#

A. 6 B. 28

C. 240 D. 512


Answer: Option C

Explanation:

et n = (2 + 4 + 6 + ... + 30). This is n .;. in -hih a = 2/ d = 2 n& l = 30


a + (n 1)d = 30

2 + (n 1) x 2 = 30

n = 15.

n =n

(a + l ) =15 x (2 + 30) = (15 x 16) =



-i** "e#

A. 1 B. 2

C. 3 D. 4

E. 'one of these


Answer: Option C

Explanation:

Then num"e 6 x 2 must "e &i!isi"*e ", 8.

x = 3/ s 632 is &i!isi"*e 8.


103. 2056 x 987 = ?









A. 1936372 B. 2029272

C. 1896172 D. 1926172

E. 'one of these


Answer: Option B

Explanation:

2056 x 987 = 2056 x (1000 13)

= 2056 x 1000 2056 x13

= 2056000 26728

= 2029272.


104. On mu*tip*,in num"e ", 7/ the po&ut is num"e eh of -hose &iits is 3. The sm**est

suh num"e is#

A. 47619 B. 47719

C. 48619 D. 47649


Answer: Option A

Explanation:

M, hit n& ti*/ -e fin& tht

47619 x 7 = 333333.


105.f 60N of

3of num"e is 36/ then the num"e is#

5

A. 80 B. 100

C. 75 D. 90










Answer: Option B

Explanation:

et the num"e "e x . Then

60N of 3

of x = 365

60x

3x x = 36

100 5

x = 36 x25

= 1009

$e%uie& num"e = 100


106. f x n& y e the t-o &iits of the num"e 653 xy suh tht this num"e is &i!isi"*e ", 80/

then x + y = ?

A. 2 o 6 B. 4

C. 4 o 8 D. 8

E. 'one of these


Answer: Option A

Explanation:

80 = 2 x 5 x 8

ine 653 xy is &i!isi"*e ", 2 n& 5 "oth/ so y = 0.

'o-/ 653 x0 is &i!isi"*e ", 8/ so 3 x 0 shou*& "e &i!isi"*e ", 8.

This hppens -hen x = 2 o 6.

x + y = (2 + 0) = 2 <o x + y = (6 + 0) = 6.


107. The &iffeene of the s%ues of t-o onseuti!e o&& intees is &i!isi"*e ", -hih of the

fo**o-in intees ?









A. 3 B. 6

C. 7 D. 8


Answer: Option D

Explanation:

et the t-o onseuti!e o&& intees "e (2n + 1) n& (2n + 3). Then/

(2n + 3)2 (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 2n 1)

= (4n + 4) x 2

= 8(n + 1)/ -hih is &i!isi"*e ", 8.


108. ht is the unit &iit in (4137)754?

A. 1 B. 3

C. 7 D. 9


Answer: Option D

Explanation:

Jnit &iit in (4137)754 = Jnit &iit in H<(4137)4188 x (4137)2I

=Jnit &iit in H 292915317923361 x 17114769 I

= (1 x 9) = 9


109. 587 x 999 = ?

A. 586413 B. 587523

C. 614823 D. 615173










Answer: Option A

Explanation:

587 x

999 = 587 x (1000 1)

= 587 x 1000 587 x1

= 587000 587

= 586413.


110. num"e -s &i!i&e& suessi!e*, in o&e ", 4/ 5 n& 6. The emin&es -ee espeti!e*, 2/ 3

n& 4. The num"e is#

A. 214 B. 476

C. 954 D. 1908


Answer: Option A

Explanation:

4 | x z = 6 x 1 + 4 = 10

-----------

5 | y -2 y = 5 x z + 3 = 5 x 10 + 3 = 53

-----------

6 | z - 3 x = 4 x y + 2 = 4 x 53 + 2 = 214

-----------

| 1 - 4

en/e, re*#red n#$%er = 214


111. f (64)2 (36)2 = 20 x x / then x = ?

A. 70 B. 120

C. 180 D. 140









E. 'one of these


Answer: Option D

Explanation:

20 x x = (64 + 36)(64 36) = 100 x 28

x =100 x 28

= 14020


112. hih one of the fo**o-in nGt "e the s%ue of ntu* num"e ?

A. 32761 B. 81225

C. 42437 D. 20164

E. 'one of these


Answer: Option C

Explanation:

The s%ue of ntu* num"e ne!e en&s in 7.

42437 is not the s%ue of ntu* num"e.


113. (22 + 42 + 62 + ... + 202) = ?

A. 770 B. 1155

C. 1540 D. 385 x 385


Answer: Option C

Explanation:

(22 + 42 + 62 + ... + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + ... + (2 x 10)2









= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)

= 22 x <12 + 22 + 32 + ... + 102

Ref: (12 + 22 + 32 + ... + n2) =

1

n(n + 1)(2n + 1)6

= 4 x1 x 10 x 11 x

216

= (4 x 5 x 77)

= 1540.


114. 854 x 854 x 854 276 x 276 x 276= ?854 x 854 + 854 x 276 + 276 x

276

A. 1130 B. 578

C. 565 D. 1156

E. 'one of these


Answer: Option B

Explanation:

i!en xp. =(a3 b3)

= (a b) = (854 276) = 578(a2 + ab + b2)


115. 35 + 15 x 1.5 = ?

A. 85 B. 51.5

C. 57.5 D. 5.25

E. 'one of these


Answer: Option C









Explanation:

i!en xp. = 35 + 15 x3

= 35 +45

= 35 + 22.5 = 57.52 2


116. The sum of fist 45 ntu* num"es is#

A. 1035 B. 1280

C. 2070 D. 2140


Answer: Option A

Explanation:

et n = (1 + 2 + 3 + ... + 45)

This is n .;. in -hih a = 1/ d = 1/ n = 45 n& l = 45

n =n(a + l ) =

45x (1 + 45) = (45 x 23) = 1035

2 2

$e%uie& sum = 1035.


117. 666 6 3 = ?

A. 37 B. 333

C. 111 D. 84

E. 'one of these


Answer: Option A

Explanation:

i!en xp. = 666 x1

x1

= 376 3













118. The sum of ** t-o &iit num"es &i!isi"*e ", 5 is#

A. 1035 B. 1245

C. 1230 D. 945

E. 'one of these


Answer: Option D

Explanation:

$e%uie& num"es e 10/ 15/ 20/ 25/ .../ 95

This is n .;. in -hih a = 10/ d = 5 n& l = 95.

tn = 95 a + (n 1)d = 95

10 + (n 1) x 5 = 95

(n 1) x 5 = 85

(n 1) = 17

n = 18

$e%uuie& um =n(a + l ) =

18 x (10 + 95) = (9 x 105) =


119. The &iffeene "et-een the p*e !*ues of t-o se!ens in the nume* 69758472 is

A. 0 B. 6993



Answer: Option C

Explanation:

$e%uie& &iffeene = (700000 70) = 699930


120. On &i!i&in num"e ", 68/ -e et 269 s %uotient n& 0 s emin&e. On &i!i&in the sme









num"e ", 67/ -ht -i** the emin&e ?

A. 0 B. 1

C. 2 D. 3


Answer: Option B

Explanation:

#$%er = 269 x 68 + 0 = 18292

67) 18292 (273

134

----

489

469

---- 202

201

---

1

---

Therefore, e*#red re$'nder = 1


121. ht is the unit &iit in the po&ut (365 x 659 x 771)?

A. 1 B. 2

C. 4 D. 6


Answer: Option C

Explanation:

Jnit &iit in 34 = 1 Jnit &iit in (34)16 = 1

Jnit &iit in 365 = Jnit &iit in < (34)16 x 3 = (1 x 3) = 3

Jnit &iit in 659 = 6

Jnit &iit in 74 Jnit &iit in (74)17 is 1.






Jnit &iit in 771 = Jnit &iit in <(74)17 x 73 = (1 x 3) = 3

$e%uie& &iit = Jnit &iit in (3 x 6 x 3) = 4.


122. 3251 + 587 + 369 ? = 3007

A. 1250 B. 1300

C. 1375 D. 1200

E. 'one of these


Answer: Option D

Explanation:

3251 Let 4207 - x = 3007

+ 587 Then, x = 4207 - 3007 = 1200

+ 369

----

4207

----


123. 7589 ? = 3434

A. 4242 B. 4155

C. 1123 D. 11023

E. 'one of these


Answer: Option B

Explanation:

et 7589 x = 3434

Then/ x = 7589 3434 = 4155















Explanation:

90 = 10 x 9

>*e*,/ 653 xy is &i!isi"*e ", 10/ so y = 0

'o-/ 653 x 0 is &i!isi"*e ", 9.

o/ (6 + 5 + 3 + x + 0) = (14 + x ) is &i!isi"*e ", 9. o/ x = 4.

:ene/ ( x + y ) = (4 + 0) = 4.


127. 3897 x 999 = ?

A. 3883203 B. 3893103

C. 3639403 D. 3791203

E. 'one of these


Answer: Option B

Explanation:

3897 x 999 = 3897 x (1000 1)

= 3897 x 1000 3897 x1

= 3897000 3897

= 3893103.


128. ht is the unit &iit in 7105 ?

A. 1 B. 5

C. 7 D. 9


Answer: Option C









Explanation:

Jnit &iit in 7105 = Jnit &iit in < (74)26 x 7

Mut/ unit &iit in (74)26 = 1

Jnit &iit in 7105 = (1 x 7) = 7


129. hih of the fo**o-in num"es -i** omp*ete*, &i!i&e (461 + 462 + 463 + 464) ?

A. 3 B. 10

C. 11 D. 13


Answer: Option B

Explanation:

(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85

= 460 x (4 x 85)

= (460 x 340)/ -hih is &i!isi"*e ", 10.


130. 106 x 106 94 x 94 = ?

A. 2400 B. 2000

C. 1904 D. 1906

E. 'one of these


Answer: Option A

Explanation:

106 x 106 94 x94

= (106)2 (94)2









= (106 + 94)(106 94) <Ref: (a2 - b2 ) = (a + b)(a - b)

= (200 x 12)

= 2400.


131. num"e -hen &i!i&e& suessi!e*, ", 4 n& 5 *e!es emin&es 1 n& 4 espeti!e*,. hen it

is suessi!e*, &i!i&e& ", 5 n& 4/ then the espeti!e emin&es -i** "e

A. 1/ 2 B. 2/ 3

C. 3/ 2 D. 4/ 1


Answer: Option B

Explanation:

4 | x y = (5 x 1 + 4) = 9

--------

5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37

--------

| 1 -4

o, 37 hen d!ded #//e!e& %& 5 'nd 4, e "et

5 | 37 ---------

4 | 7 - 2

---------

| 1 - 3

ee/t!e re$'nder 're 2 'nd 3


132. 8796 x 223 + 8796 x 77 = ?

A. 2736900 B. 2638800

C. 2658560 D. 2716740

E. 'one of these










Answer: Option B

Explanation:

8796 x 223 + 8796 x

77 = 8796 x (223 + 77) <Ref: By Distributie !a"

= (8796 x 300)

= 2638800


133. 8988 8 4 = ?

A. 4494 B. 561.75

C. 2247 D. 280.875

E. 'one of these


Answer: Option D

Explanation:

i!en xp. = 8988 x1

x1

=2247 =

280.875

8 4 8View Answer Workspace Report Discuss in Forum

134. 287 x 287 + 269 x 269 2 x 287 x 269 = ?

A. 534 B. 446

C. 354 D. 324

E. 'one of these


Answer: Option D

Explanation:

i!en xp. = a2 + b2 2ab/ -hee a = 287 n& b = 269

= (a - b)2 = (287 269)2









= (182)

= 324


135. 3 + 33 + 333 + 3.33 = ?

A. 362.3 B. 372.33

C. 702.33 D. 702

E. 'one of these


Answer: Option B

Explanation:

3

+ 33

+ 333

+ 333

------

37233

------


136. hih one of the fo**o-in nGt "e the s%ue of ntu* num"e ?

A. 30976 B. 75625

C. 28561 D. 143642

E. 'one of these


Answer: Option D

Explanation:

The s%ue of ntu* num"e ne!e en&s in 2.

143642 is not the s%ue of ntu* num"e.


137. (1000)9 1024 = ?












A. 10000 B. 1000

C. 100 D. 10

E. 'one of these


Answer: Option B

Explanation:

i!en xp. =(1000)9

=(103)9

=(10)27

= 10(2724) = 103 = 10001024 1024 1024


138. H(476 + 424)2

4 x 476 x 424I = ?

A. 2906 B. 3116

C. 2704 D. 2904

E. 'one of these


Answer: Option C

Explanation:

i!en xp. = <(a + b)2 4ab/ -hee a = 476 n& b = 424

= <(476 + 424)2 4 x 476 x 424

= <(900)2 807296

= 810000 807296

= 2704.








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