Questions with Answers: Character Puzzles

Basics for solution:
In this type of question, a figure or a matrix is given in which some numbers are filled according to a rule. A place is left blank. You have to find out a character (a number or a letter) from the given possible answers which may be filled in the blank space. Some examples are given below:
Example 1:
Which number will replace the question mark?

Solution:
Observe the rule: sum the three numbers inside the figure, then add 2 to that sum.
From Fig. a: 6 + 4 + 8 = 18
18 + 2 = 20
From Fig. b: 7 + 9 + 8 = 24
24 + 2 = 26
From Fig. c: 6 + 5 + 12 = 23
23 + 2 = 25
Hence the number 25 will replace the question mark.
Example 2:
Which number will replace the question mark?

Solution:
Here each figure shows the sum of the squares of the two given numbers.
From Fig. a: (3)² + (2)² = 9 + 4 = 13
From Fig. b: (4)² + (8)² = 16 + 64 = 80
From Fig. c: ? = (1)² + (5)² = 1 + 25 = 26
Hence the number 26 will replace the question mark.
Example 3:
Which number will replace the question mark?

Solution:
Each figure follows the rule: (first number) × (second number) + (third number).
From Fig. a: 7 × 6 + 3 = 42 + 3 = 45
From Fig. b: 5 × 4 + 6 = 20 + 6 = 26
From Fig. c: 7 × 3 + 8 = 21 + 8 = 29
Hence the number 29 will replace the question mark.
Example 4:
Which number will replace the question mark?

Solution:
Each figure shows the sum of the squares of four numbers.
From Fig. a: 9² + 8² + 7² + 6² = 81 + 64 + 49 + 36 = 230
From Fig. b: 6² + 7² + 3² + 4² = 36 + 49 + 9 + 16 = 110
From Fig. c: 9² + 6² + 5² + 4² = 81 + 36 + 25 + 16 = 158
Hence the number 158 will replace the question mark.
Example 5:
Which number will replace the question mark?

Solution:
Each figure gives the square of the sum of the two numbers shown.
(4 + 3)² = (7)² = 49
(8 + 5)² = (13)² = 169
(11 + 12)² = (23)² = 529
(10 + 9)² = (19)² = 361
Hence the number 361 will replace the question mark.
Example 6:
Which number will replace the question mark?

Solution:
Here each column shows that the product of the first two numbers divided by the third number gives the single result shown.
From column I: (9 × 5) ÷ 5 = 45 ÷ 5 = 9
From column II: (17 × 4) ÷ 4 = 68 ÷ 4 = 17
From column III: (16 × ?) ÷ 8 = 8 → (16 × ?) = 8 × 8 = 64 → ? = 64 ÷ 16 = 4
Hence the number 4 will replace the question mark.
Example 7:
Which number will replace the question mark?

Solution:
Each figure is the square of a single number shown in the small circle.
(5)² = 25
(6)² = 36
(4)² = 16
(7)² = 49
Hence the number 49 will replace the question mark.