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
65, 12, 32, 24
Finding the Matrix Representation for "NAME"
In this question, we are given two matrices, Matrix-I and Matrix-II, containing letters of the alphabet. Each letter can be represented by a pair of numbers indicating its row and column index in the matrices. Matrix-I uses rows and columns numbered 0 to 4, while Matrix-II uses rows and columns numbered 5 to 9. We need to find the set of numbers that represents the word "NAME". The representation for a letter is given by writing the row number first, followed by the column number.
Analyzing the Matrices
Let's look at the provided matrices:
| 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 |
| 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 |
Finding Representations for "NAME"
We need to find representations for each letter in the word "NAME":
- N: Look for 'N' in the matrices. 'N' is found in Matrix-II.
- Row 6, Col 5: 65
- Row 7, Col 5: 75
- Row 8, Col 7: 87
- A: Look for 'A' in the matrices. 'A' is found in Matrix-I.
- Row 0, Col 4: 04
- Row 1, Col 2: 12
- Row 4, Col 2: 42
- Row 4, Col 4: 44 (Note: 'A' is at (4,2) and 'E' is at (4,4). Let's double check the question example: K is 23 (Row 2, Col 3) and 41 (Row 4, Col 1). P is 59 (Row 5, Col 9) and 67 (Row 6, Col 7). This confirms row then column. Let's check 'A' again: (0,4) -> A, (1,2) -> A, (4,2) -> A. There is no A at (4,4); it is E. So possible codes for A are 04, 12, 42.)
- M: Look for 'M' in the matrices. 'M' is found in Matrix-I.
- Row 1, Col 0: 10
- Row 2, Col 0: 20
- Row 3, Col 2: 32
- E: Look for 'E' in the matrices. 'E' is found in Matrix-I.
- Row 0, Col 3: 03
- Row 1, Col 1: 11
- Row 2, Col 4: 24
- Row 3, Col 4: 34
- Row 4, Col 4: 44
Checking the Options
Now, let's examine each option to see which one provides a valid representation for "NAME" using the possible codes we found:
- 24, 59, 30, 99
- 24: E (Matches the last letter, but should be N) - Incorrect start.
- 65, 12, 32, 24
- 65: N (Matches the first letter) - Correct.
- 12: A (Matches the second letter) - Correct.
- 32: M (Matches the third letter) - Correct.
- 24: E (Matches the fourth letter) - Correct.
This set of numbers represents "NAME".
- 10, 68, 14, 95
- 10: M (Matches the third letter, but should be N) - Incorrect start.
- 30, 85, 44, 75
- 30: D (Does not match N) - Incorrect start.
Based on the analysis of the options, only the set 65, 12, 32, 24 correctly represents the word "NAME" according to the given matrix encoding rules.
Revision Table: Matrix Coding
| Letter | Matrix | Row | Column | Code (Row, Column) | Possible Codes |
|---|---|---|---|---|---|
| N | Matrix-II | 6, 7, 8 | 5, 5, 7 | 65, 75, 87 | 65, 75, 87 |
| A | Matrix-I | 0, 1, 4 | 4, 2, 2 | 04, 12, 42 | 04, 12, 42 |
| M | Matrix-I | 1, 2, 3 | 0, 0, 2 | 10, 20, 32 | 10, 20, 32 |
| E | Matrix-I | 0, 1, 2, 3, 4 | 3, 1, 4, 4, 4 | 03, 11, 24, 34, 44 | 03, 11, 24, 34, 44 |
Comparing these possible codes with the options, only option 2 (65, 12, 32, 24) contains a valid code for each letter of "NAME" in the correct order.
Additional Information: Matrix Reasoning Concepts
Matrix reasoning questions involving letter coding are common in various aptitude and reasoning tests. Understanding how letters are mapped to numerical pairs based on their position (row and column) is key. Here are some related concepts:
- Coordinate System: Similar to plotting points on a graph, each letter is located at a specific coordinate (row, column) within the matrix.
- Multiple Representations: Often, a single letter might appear in multiple places within the matrix, meaning it can have several possible numerical codes.
- Word Encoding: To encode a word, you need to find a valid sequence of codes, one for each letter of the word, in the correct order, by selecting from the possible codes for each letter.
- Decoding: The reverse process involves taking a sequence of numbers and using the matrix to find the letter represented by each number pair to form a word.
- Matrix Types: Matrices can vary in size and numbering schemes (e.g., starting from 0, starting from 1, using alphabets for rows/columns). Always check the rules given for the specific matrices in the question.
These types of questions test your ability to follow rules and locate information quickly within a structured format like a matrix.
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 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
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 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
