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 option that is related to the third number in the same way as the second number is related to the first number.
12 : 60 :: 16 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
16 : 144 :: 28 : ?
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding / subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
(42, 18, 3)
(36, 14, 4)
Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster.
ABILITY : LIBAYTI : : CHRONIC : ORHCCIN : : HEAVILY : ?
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
(4, 50, 6)
(13, 128, 3)
