3 18 11 12 24 18 ? 12 14
Solving the Number Pattern Puzzle
The question presents a number sequence: 3, 18, 11, 12, 24, 18, ?, 12, 14. We need to identify the pattern to find the missing number.
Analyzing the Pattern
Let's group the numbers into triplets (X, Y, Z):
- Triplet 1: (3, 18, 11)
- Triplet 2: (12, 24, 18)
- Triplet 3: (?, 12, 14)
We look for a relationship between X, Y, and Z within each triplet.
Identifying the Relationship
Let's test the relationship Y = AX + BZ, where A and B are constants.
- For Triplet 1 (3, 18, 11): $18 = A \cdot 3 + B \cdot 11$
- For Triplet 2 (12, 24, 18): $24 = A \cdot 12 + B \cdot 18$
Solving these simultaneous equations:
- From Equation 1: Multiply by 4 => $72 = 12A + 44B$
- Equation 2: $24 = 12A + 18B$
Subtract Equation 2 from the modified Equation 1:
$72 - 24 = (12A + 44B) - (12A + 18B)$ $48 = 26B$ $B = \frac{48}{26} = \frac{24}{13}$Substitute B back into Equation 2:
$24 = 12A + 18 \cdot \frac{24}{13}$ $24 = 12A + \frac{432}{13}$ $24 - \frac{432}{13} = 12A$ $\frac{24 \cdot 13 - 432}{13} = 12A$ $\frac{312 - 432}{13} = 12A$ $\frac{-120}{13} = 12A$ $A = \frac{-120}{13 \cdot 12} = \frac{-10}{13}$So, the relationship is $Y = -\frac{10}{13}X + \frac{24}{13}Z$
Calculating the Missing Number
Now, apply this relationship to Triplet 3 (?, 12, 14), where X is the missing number:
$12 = -\frac{10}{13} \cdot X + \frac{24}{13} \cdot 14$ $12 = -\frac{10X}{13} + \frac{336}{13}$Multiply the entire equation by 13:
$12 \cdot 13 = -10X + 336$ $156 = -10X + 336$ $10X = 336 - 156$ $10X = 180$ $X = \frac{180}{10}$ $X = 18$The missing number is 18.
Similar Questions
Study the given pattern carefully and select the number from among the given options that can replace the question mark (?) in it.
- Study the given grid carefully and select the option from among the given options that can replace the question mark (?).
$B_{3}$ $E_{4}$ $H_{7}$ $K_{8}$ $N_{9}$ ? $T_{11}$ $W_{13}$ $Z_{24}$ - Study the given pattern carefully and select the number from among the given options that can replace the question mark (?).
4 7 13 5 7 13 6 9 ? - Study the given pattern carefully and select the number that can replace the question mark (?) in it.
3 ? 4 7 121 8 6 9 5 Study the given pattern carefully and select the number from among the given options that can replace the question mark (?).
Study the given pattern carefully and select the letter from among the given options that can replace the question mark (?).
- Study the given pattern carefully and select the number that can replace the question mark (?) in it.
48 64 80 24 ? 40 12 16 20 Study the given pattern carefully and select the number that can replace the question mark (?) in it.
- Select the number from among the given options that can replace the question mark (?) in the given table.
5 8 15 6 11 ? 35 96 210 - Find the missing number.
48 24 8 55 20 11 63 ? 9
Important Questions from Missing Number in Matrix
Select the missing number from the given responses:
1
216
343
8
125
512
27
64
?
35
401
1575
Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?) accordingly.
7B 10A 3C 3C 9B 6A 10A 13C ? Study the given pattern carefully and select the number that can replace the question mark (?) in it.
116 160 ? 3 8 13 7 4 2 Find the missing number from the given responses in the following question.
9 6 8 5 8 4 7 4 ? 11 2 7 In the following question, from the given alternatives, select the number that comes in place of the question mark (?).
16
8
13
17
12
23
21
15
19
162
105
?
