Gi
Gi
.
Hence, the correct answer is (d)
y,1. 5 6
4
2 3 7
81 439 9
1 8 3
21 98. ?
16 64
(a) 16 (b) 73 (c) 76 (d) 94 (e) 102
~ ) 8107 (d) 789
(:i) 871 0 (b) 1078
of the triangle are the 2
So l. Numbers placed along the ~ides Sol. ( 4)2 + (2)2 +. (1) == 21
sq.uar · · s of the number at the centre of the
es 0 f th e ct 1g1t
· · ' · 2
tn;ingle. cs)2 + (3) + (8)2 == 98
( 4)2 = 16 ' (3)2== 9, (9) 2
= 81
2 2
tre' would be (64 = 8 . (6) + ( 4) + (3)2 == 94
Therefore, the number at the cen '
l 00 = 10 , 49 -- 7) . 8107. Hence, the correct answer is (c). Hence, the correct ans we r is (d)
.
_ I 1 I s I I s l 21 l 1211: 1 J
Ex 2.
0 @] -EJ
(a) 4 (b) 8 (c) 20 ' ~ 14
Sol. ?_ ~ = 6 S + 21 21 +7
2 ' =1 3, . -:Z - ==14
Sol . {(5 )2 + (4) 2}- {(3 ) 2 + (2)2} 2
5 + 16)-( 9+ 4) =4 1-1 3= 28
= c2_ Hence , the correct answer is (d) ..'.
-! -
l ··"")11~.fT
•·'I 120 45 ?
C4 E6 I I
A2
(a) 15 (b) 16 (c) 17 (d) 18
G3 15 ?
of
M5 09 014 9. Which one number can be placed at the sign
interrog ation ?
(b) KlS (c) K8 (d) JlS
(a) L10 67
I- 93 27 79
2,
K7 L4 M10
I
L8 M5 K12
M9 L6 ?
IBIB 51 7 ~?5
(b) OQ40 (c) NP49 (d) PQ6s
5 4 5 4
C1s B21
D1s A24 (d) 47
(a) 35 ,--Bi) 37 (c) 45
? H3
Fs . Gs ► Direct ions for Q. No. 11 to 13 : The numbers in
(a) E31 (b) E12 (c) F12 (d) H 8 following questions have been arranged according to an
s. Find out the missing number in the following : identical pattern. Find out the missing numbers.
1 3 7 11. 17 41
5 12 14 ~ -
32 83 11
25 ? 28 /
26 ? 31
125 192 56
/
I
11 , --/•,' i':
I.
t ':,· /,•//, J\l '/ /1,(
- --
r,
•/ lf( , ( /U/1 .\ .
8 ?
16/\ 9 9/\36
~ ~
-
~l 3 13
-- 1 ?
10 14 1
(a) 38 (b) 64 Cc) 4 (d) 1
6
\ .1) I l (b) 9 (c ) 7 (d) 5
- 22 . Find the missing number in the following question :
15 . I )
2 3 5
9 17 33 cq_JIJ ~~ . (~l
~-
6J 129 7
-
[ITTI c&tJ OJtJ
( , 1) 228 (b) 199 (\) 257 (d) 209 (a) 4 (b) 5 (c) 1 (d) 3
1(j, 23 b · boxes given below follow the ,
111 (al
25 4 57 ' Num ers
an-angement.
Yo_ur task is to find out the r,} ·\
••1is •
11
9 71 6 numbers : 1 ~O·
<rill
52 7 23
, pir
49 24. Find out the missing number.
foU'
? 1 4 I ,
1)1~
9 25 16
I
~
(a) 2 (b) 3 (c) 5 (d) 4
- -
18.
64
1 4 6
31
4 ? 36 (a) 16 (b) 9 (c) 85 (d) 112
25. Find out the missing number. 31
(c1) 32 (IJ) 30 (c) 28 (d) 40
J 9.
64 3:
ti
4 6
? 36
(c) 4
3 9, Le tJ = 1, I<= 2, L = '.:i , M = 7, N = 11,0 = 13, P= 17.
I
Find the lette r to be inserted in t:he box in the re lation
the fo llowin ) (d) 16 / ' given below . (IGNOU MAT 2006)
~
(a) L (b) p (c) J (d) 0
40 . The power a nd squa re root places in the equatio n below
~ - I,.<'' ~ 9
require num bers to be inserted :
(d) 3
~
below foll 0 1v th I (b) 16 (c) 32 (d) 24 Pl+ ✓?- (2)2 = 10
co trnd o uc e ..,, 11) I 2 (a) 2, 4 (b) 5, 81 (c) 4 , 16 (d) 2, 25
the fll i.11,--.; . the missing num er.
b
41. In the followin g equation find out the starting number.
f1nd . t
,o 21 51
?[;:]4 [±] 4G:]9 = 54
J 2 22 53 19 17 ? 48 (a) 72 (c) 4
(b) 8 (d) 24
► Directions For Q. No. 42 to 43 : In the following
0 15 13
questions '?' mark can be replaced by one of the four
)3. 24, 63 ta) 25 (b) 129 (c) 7 (d) 49 alternatives. Choose the correct one. (MAT 2006)
i1, 25, 6 1 ·recdons for Q. No. 31 to 34 : Numbers in all the 42. 8 128 2
I i~,figllres given below follow a similar pattern. Find out the 4 1 64
? 32 256
~i§ingnumb£e,,.?
J / ? (IGNOUMAT20061
13 2 (d) 17
(a) 14 (b) 15 (c) 16
£ F~ 1
9 11
Fig. 2
Fig. 4
43. A2
G3
M5
(a) LlO
C4
15
09
E6
?
014
2y9
Directions for Q. No. 44 to 47 : Find the missing
(d) 112 ►
32. The missing number in figure 2 is : number from the responses given below. (SSC 2005)
(a) 16 (b) 22 (c) 7
lJ. The 111issing number in figure 3 is :
(d) 8
(d) 24
44. 16y12 10
"" /
?
45.&
(a) 12 (b) 14 (c) 35 (d) 34
I, Direction (a) - 21 (b) 12 (c) 32 (d) 22
rhw s i~r Q . No. 35 to 40 : Some questwns
. are
t · ihon the basis of a certain system. On the same basis, find
·~.t t ecorrec t answer from amongst the four alternatives for 916
g & \\
~ ~
(d) 49 • each question.
· tn
l• Ull.!o1vedequ at10n (SSC 2006)
.
S, lf 7X 3.:. 8 . . for 80, then 8 7 2 x 9 will 3 4
Numbers in iht · stands stand for
sing a particulaJ
1
\Vhat?
(a) 625 (b) 255 (c) 22 5 <Cd) 125
l (aJ 9o (b) 25 (c) 19 (d) 40
46. 11 6 8
I, 2• 6• 8
==43664 17 12 ?
3t 4* 7
'= 91649
5' 7* 9:=? 25 34 19
(a) 2516 · 19 28 11
81 (b) 121614 (c) 356345 (d) 254981
(d)•75 (a) 13 (b) 15 (c) 16 (d) 9
VERBAL REASONING
22 0INumoor Puzzles
47. 3 4 2 51.
2 3
2
6 24 (1
ii~
~)
~
nw:11>,·1· /rr m .111:01~~·' ' rile gi,·i-11 o/rernatives at the place of (a) 20 (b) 23 (c) 25
,,.~n,,, il llr rr,'_1/ t!Ci , i11 ( .11. (LIC ADO 2006) (d)
52, 3 I I , ~)
2
-
I
4 5 0
,1c)
3 4 421
(c) 49
7
6 4 4 5 22
--
5 5 I ?
-
9 6
-
498 -: {:}
(b) 42 (c) 44
(a) 34 (d) 45
6-- 8 6
l::i) 10 (b)l5 (c) 20 (d) 25
50 .
(d)
~-~
picl
~xercise 16.1
Number ~...
l (c) In each block alphabet occurs skip~ _ng_f ne alphabet, 6 (b} nd in 3rd column. = 2 x 1st block .nllillllCJ
and numeric i.n the last row in each l:> ~ is the sum of 3 x 2 block number. Hence, the missing number ul
numerics in l5 1 & 2 nd block. Hence, the missing number Number
. in . 1st row = 7 x number
7 (c} . _m· 2nd row. I~)
wil l be K 8. Number m the 3rd row= 2 x nu m·ber m . th c , th row.
2 (c) 1' consists of alphabets K,L and M. The Hence, the missing number is 123.
difl l:1~nce in numeric of 3rd column is 2. Hence, the
8 (b} Number in 3rd row= (Number of 2nd row) 2 _ (d)
missing number is K 14.
Each block comprises rwo alphabets and a numeric. 1
3 (c) (Number of l5 row (a)
Alp habe ts occur in pa irs with a gap of one alphabet in Hence, the missing number is 16.
(a)
rnc block ;:ind l 51 alpha bet of 3rd column is the next 9 (d} 93 - (27 + 63) = 3
rd
;,il prui bet of 2nd alphabet of 2nd block. Numeric in 3nd 79 - (38 + 37) = 4 (a)
st
1-ilrJ('k of each row is 2 more than the sum of 1 & 2 67 - (16 + 42) = 9
r)l,,tl numeric. Hence, NP49 is the correct answer.
10 (b} 39 = 3 X 3 + 6 x 5
.'.'.ph.ib->t occurs in anticlockwise direction and the 51 = 4 X 4 t 5 X 7
4 (b J
nurr. t rtr i'> 1he rnulriple of 3 in clockwise direction. 37 = 4 X 3 t 5 x 5 ll(a)
r Ir: nu·, 1h1~(_1Jrrec1 answer is Ei 2. Number at the centre is th
11 (a} , 11.
Tl.t· s<:que111 t cl numbe r in rhe first col umn is x 5 i.e., and column. e sum of numbers in the ro
S (bJ
I / S :.: 5, S / 5 = 7.5, 25 x 5 = 125. The sequence
(d)
ul 11umht 1 In 1. 11 <.l < ril umn i•, Y 4, i.e., 3 x 4 = 12, 12 (b) Same as in Q. No. 11.
12 ,, ~ = '1 ' ,. '1 'J ,, 4 I 1n I ltnC'e , rhe misslng number 13 (~) Same as in Q. No. J 1.
is 413 .
(e)
p
VERBAL REASONING I221
Numh9r Puulos
rl : r I
,c row and column totals are 86 •
, tlll 1t11lII 11 . 36 (d}
3 :: I
, (II) 4 -
{dJ (
6)2 + (2) 2 = 40 r r
,(li) (5 + 1)2 = 36
Similarly, 5 x S = 25, 7 x 7 = 49, 9 x 9 = 81
2 ~ 7 = 14, 7 X 9 = 63 , 9 x 15 = 135
i (c) JS )( 2:: 30, _ Hence , the correct answer would be 254981
Hence, the nussmg number is 135.
37 (a) 28 +O (4 + 3) = 4
(c) Clearly the numbers along the sides of triangle are
the
squares of digits of numbers at the centre .
33 to
c4 + 7) = 3
72 +O ( 4 + 8) = 6
2
(1)2 = 1, (4) 2 = 16, (3) = 9
38 (C) }2 - 5 ⇒ }2 X 7 = 84
2 2
(2)2 = 4, (3) = 9, (6) = 36
10-5 ⇒ 10 x5=50
Hence, the correct answer is (c) . 8-5 ⇒ 8x 3=24
! (b) {(4)2 + (5)2}- {(6)2 + (1)2}= 4 6-5 ⇒ 6x 1 =6
2 2
((10) 2 + (3)2}- {(8) +(4) }= 9 39 (a) (N x? + M) O+ K = 31 ⇒ (11 x ? + 7) +O 2 = 31
2 2 2
{(7) 2 + (2) }- {(3) + (5) }= 19 ⇒ 11?+7=31 x 2
2 =5 ⇒ 3(?) + ✓? = 10 + 4
I (c) (1) 2 + (2)
(5)2 + (4) 2 = 41 · ⇒ i+ ..fis =14⇒ 9+ 5=14
(6)2 + (7)2 = 85
41 (a) ? + 4 + 4 X 9 = 54
i (a) 26 + 13 = 39
⇒ ? +4=5 4-36= 18
11 + 24 = 35
⇒ ? =18 x 4=72
25 + 9 = 34
7 + 28 = 35 42 (c) The numbers follow certain pattern i.e., x x 2
Total of the numbers are on the opposite side.
I x 2=2,2 x 2=4,4 x 2=8, 8 x 2=16a ndsoo n.
, (b) The pattern used for arrangement of numbers
is as
43 (c) The letters in each row are even numbered:
below :
8 + 5 = 13 13 X (8-5) = 39
13X4 =52 A ~ C ~ E
'(d) 20 x 4 = 80 11 + 9 = 20 20 X (11 - 9) = 40
G~I~K
l (a) 35 X4=1 40 18+1 7=35 3Sx( 18-1 7)=3 5
In each column, the lowermost numbe r is the sum of
I (a) 12 X4 = 48 = 12
9+3 12 X (9- 3) = 72
the upper two numbers.
l(a) (16-6) 2 + (5-2) 2 = (10)2 + (3)2 = 109
44(d) 16+1 2=28 LJ+2= 14
(22-15 ) 2 + (21-1 9) = (7)2 + (2)2 = 53
2
21+9=30 +□ 2=15
2 2 2
07-13 ) 2 t (51 -48) = (4) + (3) = 25 (10 + X) 0+ 2 = 16 ⇒ X = 32 - 10 = 22
· (a) The number at the top = Sum of the first and third 45 (d) As, (3)2 (4)2 ⇒ 916
and (2) 2 (6) ⇒ 436,
2
numbers in the bottom row.
18 + 7 = 25
we have (1) (5) ⇒ 125
2 2
_r
VERBAL REASOl'llt~G \
. · /e. ·•
Nurntw r Pua e 223
4 6 3 8
l· 2 8 4 (a) 8 (b)4
4 (c) 'L,
6 5 ? (d) 6
10 (e) None of lhest:
,,·11ich on e number can be placed at the sign of ► Directi ons for Q. No. 8 to 41. : Fine/ 1/-i <: mi:., tn g
. ....-og,iuon in the above
1nte•• . number table? (Read number in rnclt set -up of th e fol/owi11g q11 cs1io11s:
Ro'".w1se) 8.
()3 (b)6 (c)2 10 12 14 16
~) 7 (e) None of these 12 14 16 18
(. d the missing number. (Read column-wise) 8 10 12 14
Z· f,111 2
1 3 14 ? 18 20
4 5 6
6 8 10 12
7 8 9
27 38 ? (a) 10 (b) 16 (c) 12
(a) 49 (b) 50 (c) 51 (d) 18 (e) None of th ese
(d) 52 (e) None of these :
9. 6 7 4 15
oi.rections for <?· .No. 3 to 7 : In the following 7 15 25 28
,
qui;.S11,.;ans, select tile missing numbers from the responses given · 8 13 ? 20
3, 11 77 21 87 41 ? 3 5 7 9
(a) 14 (b) 22 (c) 18
(d) 20 (e) None of these
10. 5 7 6 10
(a) 107 (b) 97 (c) 189 8 11 13 rn
(d) 67 (e) None of these 14 19 27 ?
4. 26 35 55 66
(a) 34 (b) 36 (c) 30
(d) 38 (e) None of these
11.
1 7 6
(a) 32 (b) 54 (c) 100 3 3 ?
(d) 57 (e) None of these
5 4 8
s.
35 74 104
25 49
(a) 1 (b)2 (c)3
(d) 4 (e) None of these
121 ? 12.
7 11 14
8 ? 10
(a) 64 (b) 81 (c) 100
(d) 125 9 10 16
(e) None of these
6. 6 7 3
6 I
10 I 8 I
3 7 ? (a) 8 (b) 10 (c) 9
3 2 5 (d) 11 (e) None of these
54 102 50 13. 2 5 15
(a) 4 (b) 5 (c) 6
(d) 10 6 7 27
(e) None of these
7. 7 5 ? 5 7 ?
4 3 4 2 G 17
2 3 5
-- (a) 12 (b) 32 le) 54
56 45 40 (d) 25 (e) None of th ese
VERBAL REASONING
224 INumbe1 Puzzles
14. 6 8 6 !J 21.
5 3 9 (3
,e·
3 4 7 ? @-
3'.I d4 105 GO
1
(b) :1
lc) None of these
(c) 2
(b) 11
(c) 10
(3\3
(e) None of these (dl
--
15. 6 9 11 27
- 22. ,9'
2 4 5 12
13 7 4 25
(31 18
20 25 7 ? @ (dl is
\.,) ~.: (b)52 (c) 53
t J) b'1 (e)Noneof these 30·
2
16. (b) 450 (c) 70
2 7 10 26 (a) 210
(e) None of these
4 8 15 7 (d) 150 (al 76
5 6 12 ? 2 7 (dl s6
12 22 38 34
31·
(a) 1 (b) O (c) 6
(d) 5 (e) None of these
17. 2 (b) 25
1 6 (a) 26 • (c) 27
(e) None of these (al 0
3 7 ? (d) 30 (d) 4
4 8 2 24. 5 . 4 7
24 56 48
(a) 4 (b) 3 (c) 2
(d) 5 (e) None of these
27 53
) 8. 4 7 6 9 7
(a) 20 (b) 22 (c) 18 (a) 9
(d) 21 (e) None of these (d) 11
25. · 36
19Ej-@
t
(d) 55
14
(e) None of these
26.
(a) 7
(d) 10
11
(b) 9
(e) None of these
3 12
(c) 6
(a) 30
(d) 0
r-;/ 9 9 34,
~ rt 4 2
?
9
{ a) 5 (b) 7 (c) 4 16 10 15
(d J 6 (e) None of these (a) 11
(b) 12 (c) 13
20. (d) 14
(e) None of these
~
I
1, (a)
1 11 , lb)
21 , la)
ll, (c)
(b) 141 (c) 144 41. Id)
(a) 23 5
(e) None of these (b)? c)B
(d) 188
(e) None of these
: VERBAL REASONING \
225
h
Numbor Puzzle s
l
..i--+----::-.J
(a) 55
lb) 45 le) 56
Y--+--3-+-~ (d) 26
le) None o f the se
5 6
35,~
$$
(b) 2
l"" (c) 1
'-'Se 0 (e) None of these (c) S
45
g
9
27
3
?
36
9
5
12
15
27
~ (a) 1 (b) 0 (c) 2
(,1) JB
(b) 25
(c) 16
~ /4!/4!
( e) None of these
(d) 15 _--,--r-
5 20 15 200
(c) 7o I1 ., 3 4 5 18
9 6 9 ?
(a) 15 Cb) 14 (c) 20
5 (b) 66 (c) 56
(a) 76 (d) 12 (e) None of these
(e) None of these
(d) 86
0 2 I 4
- 37. 637 (S) 498
123 (?) 912
2 6 3 (a) 4 Cb) 6 (c) S
(d) 7 (e) None of these
3 ? 5
38. 15
35 225 216 70 45 60
8 95 23 ?
(b) 2 (c) 1
(a) 0 19 200 41 90
(e) None of these
) (d) 4 9 40 20 45 I
8 6 7
(a) 35 Cb) 40 (c) 45
3 7 5 (d) 30 (e) None of these
I 14 12 13 39. 1
4 8 12 I
I 9 J 13 I ? 5 7 9 11
(b) 7 (c) 13 8 16 24 ?
(a) 9
(d) 11
(e) None of these (a) 16 (b) 12 (c) 10
(d) 1 (e) None of these
(i
33, 4 7 8 ? 40. 42 22 28 100
8 7 2
36 ? 35 49
8 1 7 5
60 7 55 79
v 144
4
42
2
100
3 7
36
45 29 105 43 I
~swers
1 7. (cl 8. tb) 9. \0) 10, \C
1, /o) 4. (6) 5. (6) 6. (al
2. (a) 3. (a) 17. (al 18. tb) 19, \C) 20, \l
~ 1, lb)
1 14. (a) 15. (6) 16. (bl
12. (c) 13. (d) 27. (bl 28. ta) 29. td) 30. \
21, /a) 25. (d) 26. (b)
22. (c) 23. (a) 24. (6) 38. td) 39. ta) 40.
31, /c) 35. (d) 36. (bl 37. (b)
32. !d) 33. (c) 34. (a)
41, /d)