Find the missing term in the given pattern: 12 : 36 :: 15 : ?
45
Understanding the Pattern Analogy: 12 : 36 :: 15 : ?
The problem asks us to find the missing term in the given pattern analogy: 12 : 36 :: 15 : ?. This type of problem requires us to identify the relationship between the first pair of numbers (12 and 36) and then apply the same relationship to the first number of the second pair (15) to find the missing term.
Analyzing the Relationship between 12 and 36
Let's examine the connection between 12 and 36. We can look for simple mathematical operations that relate these two numbers.
- Is it addition? $12 + x = 36 \implies x = 36 - 12 = 24$. So, adding 24.
- Is it subtraction? $12 - x = 36$ (doesn't work as 36 is larger).
- Is it multiplication? $12 \times x = 36$. Dividing 36 by 12 gives $x = \frac{36}{12} = 3$. So, multiplying by 3.
- Is it division? $12 \div x = 36$ (doesn't work as 36 is larger).
Multiplying the first number (12) by 3 gives the second number (36). Let's see if this rule applies to the second pair.
Applying the Pattern to Find the Missing Term
If the rule is to multiply the first number by 3, we apply this rule to 15:
Missing Term = $15 \times 3$
Missing Term = $45$
So, the missing term is 45.
Checking the Options
Let's compare our calculated missing term with the given options:
- 99
- 45
- 39
- 60
Our calculated term, 45, matches option 2.
Therefore, the missing term in the pattern 12 : 36 :: 15 : ? is 45.
| First Number | Relationship | Second Number |
|---|---|---|
| 12 | $\times 3$ | 36 |
| 15 | $\times 3$ | ? (45) |
Revision Table: Understanding Number Pattern Analogies
| Concept | Explanation | Example |
|---|---|---|
| Analogy | Finding a relationship between a pair of items and applying the same relationship to another item to find a missing one. | Apple : Fruit :: Carrot : Vegetable |
| Number Pattern | A sequence of numbers that follows a specific rule or relationship. | 2, 4, 6, 8, ... (Add 2 each time) |
| Number Analogy Pattern | Applying a number pattern relationship found in one pair to another pair. | 3 : 9 :: 5 : ? (Relationship: square the number. $3^2 = 9$, $5^2 = 25$. Missing term is 25) |
Additional Information: Types of Number Relationships
Number analogy problems can involve various relationships. Here are some common types:
- Arithmetic Operations: Addition, subtraction, multiplication, division. (e.g., 5 : 10 :: 7 : 14 - multiply by 2)
- Squaring or Cubing: Squaring the number or cubing the number. (e.g., 4 : 16 :: 6 : 36 - square the number)
- Square Root or Cube Root: Taking the root of the number. (e.g., 25 : 5 :: 49 : 7 - take the square root)
- Combinations of Operations: A sequence of operations. (e.g., 3 : 10 :: 4 : 13 - multiply by 3 then add 1, $3 \times 3 + 1 = 10$, $4 \times 3 + 1 = 13$)
- Digit Operations: Operations based on the digits of the number. (e.g., 12 : 3 :: 24 : 6 - sum of digits, $1+2=3$, $2+4=6$)
- Prime or Composite Numbers: Relationships based on the number being prime or composite, or its position in a series.
Solving these problems requires careful observation and testing different possible relationships between the numbers in the first pair.
Important Questions from Ratio and Proportion
Choose the correct option for the missing term: 27 : 18 :: 102 : ?
Divide 243 kg weight into three parts such that half of the first part, one-third of the second part, and one-fourth of the third part are equal.
If 5A = 4B, 7B = 3C, and 2C = 7D, then A:D is:
The ratio between two numbers is 2:3. If each number is increased by 2, then the ratio becomes 3:4. Find the sum of the original numbers.
P is directly proportional to Q and Q = 7 when P = 15. Find P when Q = 14.
