Select the option that is related to the third number in the same way as the second number is related to the first number.
20
Solving the Number Analogy Question: 24 : 13 ∷ 38 : ?
This question asks us to find the relationship between the first pair of numbers (24 and 13) and then apply that same relationship to the third number (38) to find the fourth number.
Let's analyze the relationship between 24 and 13. We need to figure out what mathematical operation or pattern connects 24 to 13.
Analyzing the Relation Between 24 and 13
We can try different common relationships seen in number analogy problems:
- Addition/Subtraction: $24 - 13 = 11$. Is the difference 11?
- Multiplication/Division: How can we get close to 13 from 24 using multiplication or division? $24 \div 2 = 12$. This is close to 13.
- Combination of operations: What if we divide and then add or subtract? If we divide 24 by 2, we get 12. If we add 1 to 12, we get 13. Let's test this pattern: $n \rightarrow \frac{n}{2} + 1$.
Let's check if the pattern $\frac{n}{2} + 1$ works for the first pair (24 and 13):
For the first number, 24:
$$ \frac{24}{2} + 1 = 12 + 1 = 13 $$
Yes, this relationship holds true for the first pair 24 : 13.
Applying the Same Relation to 38
Now, we apply the exact same rule ($\frac{n}{2} + 1$) to the third number, 38, to find the missing fourth number.
For the third number, 38:
$$ \frac{38}{2} + 1 = 19 + 1 = 20 $$
So, the fourth number related to 38 by the same rule is 20.
Verifying the Answer
The calculated fourth number is 20. Let's check the given options:
- Option 1: 23
- Option 2: 17
- Option 3: 20
- Option 4: 25
Our calculated number, 20, matches Option 3.
The Rule Explained
The pattern in this number analogy is: The second number is obtained by dividing the first number by 2 and then adding 1 to the result.
| Pair | First Number (n) | Relationship | Second Number ($\frac{n}{2} + 1$) |
|---|---|---|---|
| First Pair | 24 | $\frac{24}{2} + 1$ | $12 + 1 = 13$ |
| Second Pair | 38 | $\frac{38}{2} + 1$ | $19 + 1 = 20$ |
Therefore, the number related to 38 in the same way that 24 is related to 13 is 20.
Revision Table: Number Analogy Patterns
| Pattern Type | Description | Example (using 24:13 pattern concept) |
|---|---|---|
| Basic Arithmetic | Addition, subtraction, multiplication, division. | $n \rightarrow n+k$, $n \rightarrow n-k$, $n \rightarrow n \times k$, $n \rightarrow n \div k$ |
| Combined Operations | Combining two or more basic operations. | $n \rightarrow n \div 2 + 1$ (as in this problem) |
| Squaring/Cubing | Using squares or cubes of numbers or related values. | $n \rightarrow n^2$, $n \rightarrow n^3$, $n \rightarrow n^2+k$ |
| Digit Operations | Using sum of digits, product of digits, etc. | $n \rightarrow$ sum of digits of $n$ |
Additional Information on Solving Number Analogy Questions
Number analogy questions are common in logical reasoning and quantitative aptitude tests. They require you to identify the underlying relationship or rule connecting two numbers and apply it to a third number.
Tips for solving number analogies:
- Look for simple relationships first (addition, subtraction, multiplication, division).
- Consider combinations of operations (like divide and add, multiply and subtract).
- Think about squares, cubes, and prime numbers.
- Sometimes the relationship involves the digits of the numbers.
- Systematically test potential rules on the first pair before applying to the second.
- Check the options to see which one fits the derived rule.
Practicing different types of number analogy problems helps in quickly identifying patterns.
Important Questions from Letter and Number Based
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 8, 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.
23 : 441 : : 28 : ?
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.
12 : 72 ∷ 18 : ? ∷22 : 242Select the option that is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 11 : ?
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
