The question asks to find the missing number in the given analogy: 14 : 2758 :: 16 : ?. We need to identify the mathematical relationship between 14 and 2758 and apply the same relationship to 16.
Finding the Number Pattern
Let the first number be $n$. We examine the relationship between $n=14$ and the second number, 2758.
- Calculate the cube of 14: $14^3 = 14 \times 14 \times 14 = 2744$.
- Compare the cube with the second number: $2758 - 2744 = 14$.
- The pattern observed is $n^3 + n$.
Let's verify this pattern:
For $n=14$, $14^3 + 14 = 2744 + 14 = 2758$. The pattern holds true.
Applying the Pattern
Now, we apply the same pattern ($n^3 + n$) to the second number, where $n=16$.
- Calculate the cube of 16: $16^3 = 16 \times 16 \times 16 = 4096$.
- Add $n$ to the cube: $16^3 + 16 = 4096 + 16 = 4112$.
Determining the Missing Number
The calculated missing number is 4112.
This corresponds to Option 1.
Similar Questions
Solve:
DF : GI :: KM : ?- Choose the number that fits the analogy: $3 : 24 :: 5 : ?$
- Find the missing number:
$100 : 1000 :: 64 : ?$ - Find the missing number: 12 : 441 :: 13 : ?
- Solve:
AB : CD :: EF : ? - Find the missing number: $8 : 27 :: 64 : ?$
- Solve:
BG : DJ :: FM : ? - Find the missing number: 10 : 21 :: 12 : ?
- Find the missing number: 21 : 3 :: 574 : ?
- Find the missing number: 256 : 4096 :: 225 : ?
Important Questions from Analogy
Select the related word pair from the given alternatives. Teeth : Cut :: ____ : ______.
Select the related word pair from the given alternatives. Celsius : Temperature :: ______ : ____.
Select the option that is related to the third term in the same way as the second term is related to the first term.
0.24 : 0.0024 :: 3.03 : ?
Select the option in which the numbers are related in the same way as are the numbers in the given set.
(11, 13, 17)
Select the option that is related to the third number in the same way as the second number is related to the first number.
154 : 10 :: 261 : ?
