This document contains 7 slides with math problems and their solutions. The problems involve finding missing numbers in sequences, determining patterns in matrices, and performing calculations. For example, one problem finds the missing number in the sequence 72, 15, 31, ?, 127 by noting each term is the previous multiplied by 2 and added 1. The solutions are provided and range from simple arithmetic to more complex algebraic steps.

1. Slide 1 of 7
Type - 1
Sol. (d).
We have : 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, 31 × 2 + 1
= 63, 63 × 2 + 1 = 127.
1.
(a) 190 (b) 221 (c) 236 (d) 255
Sol. (c).
Moving clockwise, we have :
594 ÷ 3 = 198 ; 198 ÷ 3 = 66.
So, missing number = 66 ÷ 3 = 22.
2.
(a) 11 (b) 12 (c) 22 (d) 33
Directions :
Find the missing character in each of the following :
72
15
31
?
127
63
? 66
594 198

2. Slide 2 of 7
Sol. (d).
We have :
149 + 26 = 175, 175 + 28 = 203.
So, missing number = 203 + 30 = 233.
5.
(a) 148 (b) 208 (c) 213 (d) 233
Sol. (c).
Moving clockwise, the terms are :
23
, 33
, 43
, 53
, 63
, 73
.
3.
(a) 4 (b) 305 (c) 343 (d) 729
Sol. (a).
The two ends of each line segment contain a number and its
square.
So, missing number = 12
= 1.
4.
(a) 1 (b) 2 (c) 3 (d) 4
? 8
125 64
27216
25
? 2
4 1
5
64 8
? 203
149 175

3. Slide 3 of 7
Sol. (b).
1.
(a) 21 (b) 25 (c) 35 (d) 45
Sol. (b).
2.
(a) 12 (b) 21 (c) 24 (d) 35
Directions :
In each of the following questions, a set of figures carrying certain characters, is given. Assuming that the characters in
each set follow a similar pattern, find the missing character in each case.
We have : 4 9 6, 9 16 12.
Let, the missing number be . Then,
16 20 5 25.
x
x x x
× = × =
× = ⇒ = ⇒ =
4 9
6
9 16
12
16 ?
20
27 54
9
22 24
43
26 27
?
27 54 42 84
We have : 9 ; 9.
9 14
Let, the missing number be . Then,
42
9 21.
7
x
x
x
+ +
= =
+
= ⇔ =

4. Slide 4 of 7
Sol. (c).
We have : 5 × 3 + 4 = 19 ; 6 × 4 + 5 = 29.
So, missing number = 7 × 5 + 6 = 41.
10.
(a) 25 (b) 37 (c) 41 (d) 47
Sol. (c).
We have : 42
× 32
= 144, (11)2
× 92
= 9801.
So, missing number = (15)2
× 62
= 8100.
8.
(a) 1216 (b) 2250 (c) 8100 (d) 11036
Sol. (b).
The above three numbers are multiples of the number at the
bottom.
Clearly, 36, 18 and 27 are all multiples of 9. So, the missing
number is 9.
9.
(a) 6 (b) 9 (c) 12 (d) 18
4 3
144
11 9
9801
15 6
?
12 30
144
16 40
8
36 27
?
18 32 18
19
35
4
?
57
6
29
46
5

5. Slide 5 of 7
Sol. (b).
In the first column, 6 × 5 × 4 = 120.
In the second column, 6 × 7 × 3 = 126.
Let, the missing number be x. Then, in the third column, we
have :
11.
(a) 4 (b) 8 (c) 12 (d) 16
Sol. (c).
In the first column, (1 + 4 + 2)2
= 49.
In the second column, (4 + 2 + 2)2
= 64.
Let, the missing number be x. Then, in the third column, we
have :
(x + 5 + 3)2
= 169 = (13)2
⇔ x + 5 + 3 = 13
⇔ x = 5.
12.
(a) 3 (b) 4 (c) 5 (d) 6
Directions :
In each of the following questions, a matrix of certain characters is given. These characters follow a certain trend, row-
wise or column-wise. Find out this trend and choose the missing character from the given alternatives.
320
8 5 320 8.
40
x x× × = ⇔ = =
6 6 8
5 7 5
4 3 ?
120 126 320
1 4 ?
4 2 5
2 2 3
49 64 169

6. Slide 6 of 7
Sol. (a).
13.
(a) 10 (b)12 (c) 13 (d) 20
5 2 8
In the first column, 40.
2
5 4 3
In the second column, 30
2
2 1 10
Missing number = 10.
2
× ×
=
× ×
=
× ×
∴ =
5 5 2
2 4 1
8 3 10
40 30 ?
Sol. (a).
In the first column, (6 + 7) × 5 = 65.
In the second column, (3 + 2) × 4 = 20.
Let, the missing number be x. Then,
(4 + x) × 9 = 45 ⇔ 4 + x = 5 ⇔ x = 1.
14.
(a) 1 (b) 2 (c) 3 (d) 4
5 4 9
6 3 ?
7 2 4
65 20 45

7. Slide 7 of 7
Sol. (b).
In the first column, (5 × 9) + (3 × 100) = 345.
In the second column, (6 × 10) + (4 × 100) = 460.
∴ Missing number = (7 × 11) + (5 × 100) = 577.
15.
(a) 535 (b) 577 (c) 755 (d) 775
5 6 7
3 4 5
9 10 11
345 460 ?