Select the number that is related to the third number in the same way as the second number is related to the first number. 12 : 36 :: 18 : ?
81
Understanding Number Analogy Questions
Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find a missing term. In this question, we are given the relationship 12 : 36 and asked to find the number that relates to 18 in the same way: 18 : ?
Analyzing the Relationship Between 12 and 36
We need to figure out the rule or pattern that transforms 12 into 36. Let's explore a few possibilities:
- Multiplication: $12 \times 3 = 36$. If this is the rule, then for 18, it would be $18 \times 3 = 54$. However, 54 is not among the given options.
- Squaring: Is 36 related to the square of 12? $12^2 = 144$. No direct relation here. What about the square of half of 12? $(12/2)^2 = 6^2 = 36$. This matches!
- Digit Operations: Could it involve the digits of 12? $1+2=3$. $12 \times 3 = 36$. This works for the first pair. Let's apply it to 18: $1+8=9$. $18 \times 9 = 162$. 162 is not an option.
The pattern $(First\ number / 2)^2 = Second\ number$ seems to be the most likely relationship that fits the first pair and potentially leads to one of the options for the second pair.
Applying the Analogy Pattern to 18
Using the pattern we identified from the first pair (12 : 36), which is $(First\ number / 2)^2 = Second\ number$, let's apply it to the number 18 to find the missing term in the analogy 18 : ?
According to the pattern, the missing number should be $(18 / 2)^2$.
Let's calculate this value:
- First, divide 18 by 2: $18 / 2 = 9$.
- Next, square the result: $9^2 = 9 \times 9 = 81$.
So, the missing number in the analogy 18 : ? is 81.
Identifying the Correct Option
We found that applying the relationship $(Number / 2)^2$ to 18 results in 81. Let's look at the given options:
- 64
- 81
- 68
- 83
The calculated value, 81, is present as one of the options.
Final Answer Determination
The relationship $12 \to 36$ is explained by $(12/2)^2 = 6^2 = 36$. Applying the same logic, the number related to 18 is $(18/2)^2 = 9^2 = 81$. Therefore, the number that completes the analogy 18 : ? is 81.
Revision Table: Number Analogy Rule
| First Number | Rule Applied | Calculation | Second Number |
|---|---|---|---|
| 12 | $(Number / 2)^2$ | $(12 / 2)^2 = 6^2$ | 36 |
| 18 | $(Number / 2)^2$ | $(18 / 2)^2 = 9^2$ | 81 |
Additional Information: Understanding Number Relationships
Number analogy questions often involve common mathematical operations or patterns. Recognizing these patterns is key to solving such problems. Some common types of relationships include:
- Arithmetic operations (addition, subtraction, multiplication, division)
- Squares and cubes
- Operations involving digits of the number (sum of digits, product of digits, etc.)
- Combinations of operations
Practicing different types of number analogy problems helps improve pattern recognition skills, which are valuable in various reasoning tests.
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