A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘F’ can be represented by 12, 43 etc and ‘Z’ can be represented by 87, 98 etc. Similarly, you have to identify the set for the word ‘SOCK’. Matrix-I 0 1 2 3 4 0 A E E G H 1 I A F M D 2 E M A E H 3 I A C H B 4 D K H F E Matrix-II 5 6 7 8 9 5 Z P P Q S 6 V U S R N 7 U U N V X 8 N O Z V T 9 R W W Z N
67, 86, 32, 41
Understanding Matrix Coding and Decoding
This question asks us to decode the word ‘SOCK’ using two matrices where letters are represented by their row and column numbers. This is a typical matrix coding and decoding problem often found in reasoning sections of competitive exams. We are given two matrices, Matrix-I (rows/columns 0-4) and Matrix-II (rows/columns 5-9).
Analyzing the Provided Matrices
Let's look at the two matrices provided:
| Matrix-I | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 0 | A | E | E | G | H |
| 1 | I | A | F | M | D |
| 2 | E | M | A | E | H |
| 3 | I | A | C | H | B |
| 4 | D | K | H | F | E |
| Matrix-II | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|
| 5 | Z | P | P | Q | S |
| 6 | V | U | S | R | N |
| 7 | U | U | N | V | X |
| 8 | N | O | Z | V | T |
| 9 | R | W | W | Z | N |
As per the instructions, a letter is represented first by its row number and then by its column number. For example, ‘F’ can be represented by 12 (Row 1, Column 2 in Matrix-I) or 43 (Row 4, Column 3 in Matrix-I). ‘Z’ can be represented by 87 (Row 8, Column 7 in Matrix-II) or 98 (Row 9, Column 8 in Matrix-II).
Finding the Numerical Code for ‘SOCK’
We need to find the set of numbers that represent the word ‘SOCK’. Let’s find the possible codes for each letter in the word ‘SOCK’ individually by searching through both matrices.
- For the letter ‘S’:
- Looking at Matrix-I (0-4, 0-4), we do not find the letter ‘S’.
- Looking at Matrix-II (5-9, 5-9), we find ‘S’ at:
- Row 5, Column 9 → 59
- Row 6, Column 7 → 67
- For the letter ‘O’:
- Looking at Matrix-I (0-4, 0-4), we do not find the letter ‘O’.
- Looking at Matrix-II (5-9, 5-9), we find ‘O’ at:
- Row 8, Column 6 → 86
- For the letter ‘C’:
- Looking at Matrix-I (0-4, 0-4), we find ‘C’ at:
- Row 3, Column 2 → 32
- Looking at Matrix-II (5-9, 5-9), we do not find the letter ‘C’.
- Looking at Matrix-I (0-4, 0-4), we find ‘C’ at:
- For the letter ‘K’:
- Looking at Matrix-I (0-4, 0-4), we find ‘K’ at:
- Row 4, Column 1 → 41
- Looking at Matrix-II (5-9, 5-9), we do not find the letter ‘K’.
- Looking at Matrix-I (0-4, 0-4), we find ‘K’ at:
Based on our search, the valid codes for the letters in ‘SOCK’ are:
- S: 59, 67
- O: 86
- C: 32
- K: 41
Checking the Given Options
Now, let's examine each option to see which one provides a valid sequence of codes for S, O, C, and K in that specific order.
- Option 1: 14, 56, 10, 56
- 14: In Matrix-I, Row 1, Column 4 is ‘D’. This is not ‘S’. So, this option is incorrect.
- Option 2: 67, 86, 32, 41
- 67: In Matrix-II, Row 6, Column 7 is ‘S’. Correct.
- 86: In Matrix-II, Row 8, Column 6 is ‘O’. Correct.
- 32: In Matrix-I, Row 3, Column 2 is ‘C’. Correct.
- 41: In Matrix-I, Row 4, Column 1 is ‘K’. Correct.
- Option 3: 42, 59, 14, 78
- 42: In Matrix-I, Row 4, Column 2 is ‘H’. This is not ‘S’. So, this option is incorrect.
- Option 4: 21, 68, 22, 57
- 21: In Matrix-I, Row 2, Column 1 is ‘M’. This is not ‘S’. So, this option is incorrect.
Based on our verification, only Option 2 provides valid codes for the letters S, O, C, and K in the correct order.
Revision Table: Matrix Coding Concepts
| Concept | Description | Application in ‘SOCK’ Example |
|---|---|---|
| Matrix Coding | Representing letters using coordinates (row and column numbers) from a grid/matrix. | Letters like S, O, C, K are given numerical codes from Matrix-I and Matrix-II. |
| Decoding | Finding the original letters corresponding to a given set of numerical codes. | Checking if numerical codes in options (e.g., 67, 86) represent the target letters (S, O). |
| Multiple Codes | A single letter might appear at multiple positions in the matrix/matrices, thus having multiple possible codes. | ‘S’ can be 59 or 67. The correct option uses one of these valid codes. |
| Order Matters | The sequence of numbers must correspond to the sequence of letters in the word. | The first number is for ‘S’, the second for ‘O’, and so on for ‘SOCK’. |
Additional Information: Letter and Number Coding Techniques
Matrix coding is a specific type of coding-decoding question. Coding-decoding puzzles test a candidate's ability to decipher rules and patterns in coded messages. They are common in reasoning tests.
- Types of Coding:
- Letter Coding: Letters are replaced by other letters based on a pattern (e.g., shifting letters in the alphabet).
- Number Coding: Letters are replaced by numbers or sequences of numbers. Our matrix coding problem falls under this category.
- Symbol Coding: Letters are replaced by symbols.
- Mixed Coding: A combination of letters, numbers, and/or symbols is used.
- Solving Strategy:
- Identify the letters in the word to be coded/decoded.
- Analyze the provided coding pattern (e.g., the matrices and the row-column rule).
- Find the codes for each letter individually based on the pattern.
- Combine the individual codes in the correct order to get the code for the word.
- Alternatively, when given options, check each option against the pattern to see if it correctly represents the target word.
- Key Skills:
- Attention to detail: Carefully reading row and column numbers.
- Systematic searching: Checking all relevant cells in the matrices.
- Logical deduction: Applying the coding rule consistently.
- Option elimination: Quickly ruling out incorrect options saves time.
Important Questions from Matrix
Find the missing number from the below options.
\(\begin{array}{*{20}{c}} 6&{24}&{96}\\ 7&{28}&{112}\\ {13}&{52}&? \end{array}\)
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matri×-I are numbered from 0 to 4 and that of Matri×-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and ne×t by its column, for e×ample ‘C’ can be represented by 21, 34 etc and ‘T’ can be represented by 97, 89 etc. Similarly, you have to identify the set for the word ‘MAZE’.
Matrix- I
0
1
2
3
4
0
E
F
H
E
I
1
E
G
E
M
M
2
K
C
H
G
L
3
L
J
G
G
C
4
J
A
M
J
J
Matrix- II
5
6
7
8
9
5
N
W
P
V
S
6
R
W
Q
Y
N
7
P
Z
P
U
U
8
N
Q
U
R
T
9
R
V
T
Q
O
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are resented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that a Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘K’ can be represented by 23, 41, etc., and ‘P’ can be represented by 59, 67, etc. Similarly, you have to identify the set for the word “NAME”.
Matrix-I
0
1
2
3
4
0
H
H
C
E
A
1
M
E
A
B
I
2
M
L
G
K
E
3
D
H
M
L
E
4
C
K
A
B
E
Matrix-II
5
6
7
8
9
5
O
S
Z
O
P
6
N
W
P
X
W
7
N
S
R
Q
Q
8
O
P
N
X
V
9
V
Z
S
S
T
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘A’ can be represented by 23, 41 etc and ‘U’ can be represented by 86, 97 etc. Similarly, you have to identify the set for the word ‘GONE’.
Matrix-I
0
1
2
3
4
0
G
G
K
A
G
1
D
K
E
E
L
2
K
B
E
A
J
3
L
M
G
J
K
4
K
A
G
L
B
Matrix-II
5
6
7
8
9
5
N
Q
W
S
O
6
O
Q
V
R
R
7
W
O
N
T
Y
8
T
U
Y
R
V
9
N
X
U
S
Q
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are resented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that a Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘D’ can be represented by 24, 41 etc., and ‘T’ can be represented by 96, 87 etc. Similarly, you have to identify the set for the word ‘ GASH’.
Matrix-I
0
1
2
3
4
0
C
G
D
K
M
1
I
B
L
H
B
2
K
B
L
B
D
3
I
A
C
D
E
4
L
D
G
A
E
Matrix-II
5
6
7
8
9
5
P
Q
U
W
R
6
P
Z
V
P
W
7
U
X
Q
X
V
8
V
O
T
N
R
9
P
T
U
S
Y
