To solve the analogy question 256 : 4096 :: 225 : ?, we need to identify the mathematical relationship between the pairs of numbers provided.
Let's start by analyzing each part of the analogy:
- The first pair is 256 : 4096: Here, 256 and 4096 have a specific relationship.
To find this relationship, observe that:
- \(256 = 4^4\)
- \(4096 = 4^6\)
Thus, it seems that the second number in the pair is the cube (or higher power) of the base taken for the first number.
- Now let's consider the second pair 225 : ?: We must find a number which holds a similar relationship with 225 as 4096 does with 256.
Given that:
- \(225 = 15^2\)
Applying a similar process for the number 225:
- Calculate the cube of 15:
- \(15^3 = 3375\)
Thus, the missing number that completes the analogy is 3375.
Now, let us verify this by ruling out the other options:
- 3125: This is \(5^5\), which does not seem relevant as 225 relates to 15.
- 4225: This is \(65^2\), unrelated directly to 225.
- 4096: Already used in pairing with 256, unsuitable here.
Therefore, the correct answer is 3375.
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: $8 : 27 :: 64 : ?$
- 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 : ?
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)
