Find the missing number from the below options. \(\begin{array}{*{20}{c}} 6&{24}&{96}\\ 7&{28}&{112}\\ {13}&{52}&? \end{array}\)
208
Finding the Missing Number in the Patterned Matrix
The problem asks us to identify the missing number in a given 3x3 matrix based on a specific pattern or rule governing the numbers in each row or column.
The given matrix is:
| Column 1 | Column 2 | Column 3 |
|---|---|---|
| 6 | 24 | 96 |
| 7 | 28 | 112 |
| 13 | 52 | ? |
Analyzing the Pattern in the Matrix Rows
Let's examine the relationship between the numbers in each row.
- Row 1: 6, 24, 96
- Let's see if there's a multiplicative relationship.
- Is the second number a multiple of the first? ${24}/{6} = 4$. Yes, ${24} = 6 \times 4$.
- Is the third number a multiple of the second? ${96}/{24} = 4$. Yes, ${96} = 24 \times 4$.
- So, the pattern in Row 1 appears to be: Second Number = First Number $\times 4$, and Third Number = Second Number $\times 4$.
- Row 2: 7, 28, 112
- Let's check if the same pattern holds.
- Is the second number a multiple of the first? ${28}/{7} = 4$. Yes, ${28} = 7 \times 4$.
- Is the third number a multiple of the second? ${112}/{28} = 4$. Yes, ${112} = 28 \times 4$.
- The pattern identified in Row 1 is also true for Row 2. Each number is obtained by multiplying the previous number in the row by 4.
Applying the Pattern to Find the Missing Number
Now, let's apply the established pattern to the third row to find the missing number.
- Row 3: 13, 52, ?
- Based on the pattern from the first two rows, the second number should be the first number multiplied by 4. Let's check: ${13 \times 4} = 52$. This is correct.
- The missing number (the third number) should be the second number multiplied by 4.
- Missing Number = ${52 \times 4}$
- Let's calculate: ${52 \times 4 = 208}$.
Conclusion
The pattern in the matrix is that each number in a row is 4 times the number preceding it in the same row. Applying this pattern to the third row, we find that the missing number is 208.
The missing number is 208.
Revision Table: Checking the Pattern
| Row | First Number | Second Number | Third Number | Relation 1 to 2 | Relation 2 to 3 |
|---|---|---|---|---|---|
| 1 | 6 | 24 | 96 | ${24 \div 6 = 4}$ | ${96 \div 24 = 4}$ |
| 2 | 7 | 28 | 112 | ${28 \div 7 = 4}$ | ${112 \div 28 = 4}$ |
| 3 | 13 | 52 | ? | ${52 \div 13 = 4}$ | ${? \div 52 = 4}$ |
From the table, the pattern holds true for the first two rows. Applying ${? \div 52 = 4}$ to the third row gives ${? = 52 \times 4 = 208}$.
Additional Information: Types of Number Patterns
Number pattern questions in matrices or series can follow various rules. Understanding common types helps in solving these problems:
- Arithmetic Progression: Numbers increase or decrease by a constant difference (e.g., 2, 5, 8, 11...).
- Geometric Progression: Numbers increase or decrease by a constant ratio (e.g., 3, 6, 12, 24...). This was the pattern in our problem (ratio of 4).
- Squares or Cubes: Numbers are squares (${1^2, 2^2, 3^2...}$) or cubes (${1^3, 2^3, 3^3...}$) or derived from them.
- Fibonacci Sequence: Each number is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5, 8...).
- Mixed Operations: A combination of operations (e.g., multiply by 2 then add 1).
- Row-wise or Column-wise Logic: The pattern applies horizontally across rows or vertically down columns. Sometimes it involves operations between rows/columns.
To solve these, it's helpful to look for differences, ratios, squares, cubes, or sums between consecutive numbers or numbers in corresponding positions in different rows/columns.
Important Questions from Matrix
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 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
