In the following question, select the related number from the given alternatives. 198 : 66 :: ?
144 : 48
Understanding Number Analogy Problems
In number analogy questions, you are given a pair of numbers that have a specific relationship between them. You need to identify this relationship and then find another pair from the given options that shares the same relationship.
The question presents the analogy as 198 : 66 :: ?, where the '::' symbol means 'is to' or 'is analogous to'. So, 198 is related to 66 in the same way that the first number in the correct option is related to its second number.
Analyzing the Given Number Pair: 198 : 66
Let's examine the relationship between 198 and 66.
- Is there a simple difference? $198 - 66 = 132$. This doesn't seem like a common relationship pattern for simple number analogies unless it's a constant difference applied elsewhere.
- Is there a multiplicative or divisive relationship? Let's try dividing the first number by the second: $\frac{198}{66}$.
Performing the division:
This reveals a clear and simple relationship: The first number is 3 times the second number, or the second number is one-third ($\frac{1}{3}$) of the first number.
Finding the Related Pair from Options
We need to find an option pair (First Number : Second Number) where the First Number is 3 times the Second Number. Let's check each option provided.
Evaluating Each Option
We will test the relationship (First Number = 3 × Second Number) for each option:
| Option | First Number | Second Number | Calculation (First Number / Second Number) | Relationship Match (Is Ratio = 3?) |
|---|---|---|---|---|
| 1 | 146 | 46 | $\frac{146}{46} \approx 3.17$ | No |
| 2 | 144 | 48 | $\frac{144}{48} = 3$ | Yes |
| 3 | 142 | 42 | $\frac{142}{42} \approx 3.38$ | No |
| 4 | 148 | 44 | $\frac{148}{44} \approx 3.36$ | No |
Identifying the Correct Related Pair
From the evaluation table, only Option 2, the pair 144 : 48, satisfies the identified relationship. The first number, 144, is exactly 3 times the second number, 48 ($48 \times 3 = 144$).
Therefore, the pair 144 : 48 is related in the same way as 198 : 66.
Revision Table: Number Analogy Summary
| Given Analogy Pair | Identified Relationship | Matching Option Pair |
|---|---|---|
| 198 : 66 | First Number = 3 × Second Number | 144 : 48 |
Additional Information on Solving Number Analogies
Solving number analogies often requires looking for various possible relationships. Some common relationships include:
- Multiplication or Division: One number is a multiple or fraction of the other.
- Addition or Subtraction: There is a constant difference between the numbers.
- Squares, Cubes, or Roots: The numbers are related by squaring, cubing, or taking roots.
- Combinations of Operations: For example, multiply by a number and then add/subtract another number.
- Digital Sums: Relationships based on the sum of the digits of the numbers.
- Prime or Composite Numbers: Relationships based on the number properties.
It's helpful to systematically check for these common patterns when trying to solve number analogy problems.
Important Questions from Similarity
'Alone' is related to 'Unaccompanied' in the same way as 'Amount' is related to ______.
Select the option 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/deleting/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)
(4, 16, 64)
(7, 49, 343)
Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
97 : 2 :: 63 : ? :: 74 : 3
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(15, 135, 6)(12, 84, 5)
Select the option in which the numbers are related in the same way as are the numbers in the given set.
(146, 102, 58)
