$100 : 1000 :: 64 : ?$
Analogy Pattern Identification
The question presents a number analogy: $100 : 1000 :: 64 : ?$. We need to find the relationship between the first pair of numbers (100 and 1000) and apply it to the second pair (64 and the missing number).
Finding the Mathematical Relationship
Observe the relationship between 100 and 1000:
- $100 = 10^2$ (10 squared)
- $1000 = 10^3$ (10 cubed)
The pattern appears to be $x^2 : x^3$. In the first pair, $x=10$.
Applying the Pattern
Now, let's apply this $x^2 : x^3$ pattern to the second pair, starting with 64:
- $64 = 8^2$ (8 squared)
Here, $x=8$. Following the pattern, the missing number should be $x^3$.
Calculating the Missing Number
Calculate $8^3$:
$ 8^3 = 8 \times 8 \times 8 = 64 \times 8 = 512 $
Conclusion
The missing number is 512. This corresponds to Option C.
Similar Questions
Solve:
DF : GI :: KM : ?- Choose the number that fits the analogy: $3 : 24 :: 5 : ?$
- Find the missing number: 12 : 441 :: 13 : ?
- Solve:
AB : CD :: EF : ? - Find the missing number: $8 : 27 :: 64 : ?$
- Find the missing number: $14 : 2758 :: 16 : ?$
- 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)
