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
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Important Questions from Missing Number in Matrix
Study the given pattern carefully and select the number from among the given options that can replace the question mark (?) in it.
24
36
32
6
3
?
12
2
24
12
54
24
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
3 5 7 23 27 31 69 135 ? Study the given matrix carefully and select the number from among the given options that can replace the question mark(?) in it.
13 6 75 15 8 ? 18 4 70 Study the given pattern carefully and select the number from among the given options that can replace the question mark (?) in it.
15 81 12 18 99 15 17 120 ? Study the given pattern carefully and select the number from among the given options that can replace the question mark (?) in it.
18 24 19 7 8 9 8 11 14 17 ? 14
