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.
Similar Questions
In the question, 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 in two matrices given below. The columns and rows of Matrix I 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, e.g., G can be represented by 03, 12, etc., and 'L' can be represented by 57, 65, etc. Similarly you have to identify the set for the word 'DATE'
Identify the correct set of numbers representing the word "GOOD" from the matrix provided.
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 Matrix-I are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can by represented first by its row and next by its column, for example, ‘ O’ can be represented by 30, 23, etc, and ‘D’ can be represented by 76, 88, etc. Similarly, you have to identify the set for the word “POND”.
Matrix - I Matrix - II 0 1 2 3 4 5 6 7 8 9 0 P G H L O 5 N T D S U 1 L O P G H 6 S U N T D 2 G H L O P 7 T D S U N 3 O P G H L 8 U N T D S 4 H L O P G 9 D S U N T A word is represented by only one set of numbers as given in any one of the alternative. 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 numbered from 0 to 4 and that of Matrix-II are numbered for 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 14, 03 etc. and ‘Z’ can be represented by 58. 69 etc. similarly, you have to identify the set for the word ‘KIJL’.
Matrix I Matrix II 0 1 2 3 4 5 6 7 8 9 0 I C L K J 5 U N N Z S 1 C J I I K 6 S O U T Z 2 H F E I A 7 W T P V O 3 F I L H B 8 V Y U Y P 4 D G G B D 9 T R V Z 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 represented 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 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 ‘K’ can be represented by 41, 34 etc. and ‘Z’ can be represented by 75, 86 etc. Similarly, you have to identify the set for the word ‘PAWN’.
Matrix – I
Matrix – II
0
1
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A word is represented by only one set of numbers as gives 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 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 ‘Z’ can be represented by 87, 99 etc. and ‘T’ be represented by 69, 95 etc. Similarly, you have to identify the set for the word ‘MAZE’.
Matrix - I
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1
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Matrix - II
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Z
A word is represented by only one set of numbers as gives 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 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 ‘R’ can be represented by 23, 31 etc. and ‘O’ be represented by 75, 98 etc. Similarly, you have to identify the set for the word ‘TRAY’.
Matrix - I Matrix - II 0 1 2 3 4 5 6 7 8 9 0 T Z Y B R 5 A O U E I 1 Y B R T Z 6 U E I A O 2 Z T B R Y 7 O A E I U 3 B R Z Y T 8 E I O U A 4 R Y T Z B 9 I U A O E A word is represented by only one set of numbers as gives 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 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, ‘K’ can be represented by 33, 43 etc. and ‘Z’ be represented by 65, 59 etc. similarly, you have to identify the set for the word ‘SIZE ’.
Matrix – I Matrix – II 0 1 2 3 4 5 6 7 8 9 0 E M E J H 5 U V U V Z 1 I H F G A 6 Z O X S P 2 E H D A I 7 P P R V N 3 C B M K L 8 Q S N S W 4 F L G K D 9 S X T N S 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 Matrix - I 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 ‘K’ can be represented by 40, 24 etc. and ‘Z’ can be represented by 98, 67 etc. Similarly, you have to identify the set for the word ‘OXEN’.
Matrix - I Matrix - II 0 1 2 3 4 5 6 7 8 9 0 G B I K C 5 Z X S R T 1 L H H H G 6 O N Z P T 2 L H I A K 7 U R Q Z W 3 A D M G B 8 V Q X Y V 4 K J E L F 9 Y O X Z N A word is represented by only one set of numbers as given in any of the alternatives. The sets of numbers given in the alternatives represented by two classes of alphabets as show in the given two matrices. The columns and rows of Matrix-I 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 ‘K’ can be represented by 20, 34 etc. and ‘Z” can be represented by 67, 88 etc. Similarly, you have to identify the set for the word ‘PURE’.
Matrix – I Matrix – II 0 1 2 3 4 5 6 7 8 9 0 G K D D G 5 Q T V U R 1 A J F E J 6 Q U Z Y T 2 K F H F A 7 V Y X Q N 3 D G M C K 8 Y R X Z P 4 C L H J B 9 N U Y U O
Important Questions from Matrix
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 Matrix-I 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, ‘E’ can be represented by 32, 12 etc and ‘X’ can be represented by 87, 79 etc. Similarly, you have to identify the set for the word ‘MYTH’.
Matrix-I
Matrix-Ii
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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 in two matrices given below. The columns and rows of Matrix I 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, e.g., ‘M’ can be represented by 01, 14, etc., and ‘S’ can be represented by 58, 77 etc., and ‘S’ can be represented by 58, 77 etc. Similarly, you have to identify the set for the word ‘ROHAN’.
Matrix I
Matrix II
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A word is represented by only one set of number 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 numbered from 0 to 4 and that of Matrix-II are numbered form 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example ‘U’ can be represented by 30, 41 etc and ‘E’ can be represented by 85, 67 etc. Similarly, you have to identify the set for the word ‘SWORD’.
Matrix I
Matrix II
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NEST
FAITH
