Solving Number Analogy Questions

Number analogy questions test your ability to identify the relationship between a pair of numbers and apply that same relationship to another number to find a missing term. The relationship can involve various mathematical operations like addition, subtraction, multiplication, division, squaring, cubing, or combinations of these.

Analyzing the Given Analogy: 6 : 18 :: 14 : ?

We are given the analogy 6 is to 18 as 14 is to an unknown number. Our task is to find the rule or relationship connecting 6 and 18 and then apply it to 14 to find the corresponding number.

Finding the Relationship Between 6 and 18

Let's look for a mathematical connection between the numbers 6 and 18:

• Is it addition? $6 + \text{something} = 18$. $6 + 12 = 18$. If we apply adding 12 to 14, we get $14 + 12 = 26$. This is not among the options.
• Is it multiplication? $6 \times \text{something} = 18$. $6 \times 3 = 18$. If we apply multiplying by 3 to 14, we get $14 \times 3 = 42$. This is not among the options.
• Is it related to squares or cubes? Let's consider the square of 6. $6^2 = 36$. How can we get 18 from 36? We can divide 36 by 2. $36 / 2 = 18$. This seems like a possible relationship: square the number and then divide by 2.

Testing the Relationship $x \to x^2 / 2$

Let's formalize the potential relationship as $x \to \frac{x^2}{2}$.

For the first pair (6 and 18):

Let $x = 6$. According to the relationship, the second term should be $\frac{6^2}{2}$.

$\frac{6^2}{2} = \frac{36}{2} = 18$.

This matches the given second term (18). So, this relationship seems correct.

Applying the Relationship to the Third Term (14)

Now, we apply the same relationship to the third term, 14, to find the missing fourth term.

Let $x = 14$. According to the relationship, the fourth term should be $\frac{14^2}{2}$.

$\frac{14^2}{2} = \frac{196}{2}$.

Now, we calculate the value:

$\frac{196}{2} = 98$.

Comparing the Result with Options

The calculated missing term is 98. Let's check the given options:

• Option 1: 64
• Option 2: 98
• Option 3: 108
• Option 4: 70

Our calculated value, 98, matches Option 2.

Step-by-Step Solution

Here is the step-by-step process followed to solve this number analogy:

1. Identify the first pair of numbers: 6 and 18.
2. Analyze the relationship between 6 and 18. We found the relationship $x \to x^2 / 2$.
3. Verify the relationship: For $x=6$, $\frac{6^2}{2} = \frac{36}{2} = 18$. The relationship holds for the first pair.
4. Identify the third number: 14.
5. Apply the same relationship to the third number: For $x=14$, calculate $\frac{14^2}{2}$.
6. Calculate the value: $\frac{14^2}{2} = \frac{196}{2} = 98$.
7. Select the option that matches the calculated value. The calculated value is 98, which matches Option 2.

Conclusion

The relationship between the first two terms (6 and 18) is that the second term is half the square of the first term ($x \to x^2/2$). Applying this same relationship to the third term (14), we find the missing term is 98.

Revision Table: Number Analogy Skills

Additional Information: Solving Analogy Questions

Analogy questions are common in reasoning tests. They can involve numbers, letters, words, or figures. For number analogies, always start by considering simple relationships like addition, subtraction, multiplication, and division. If these don't fit, look for more complex patterns involving squares, cubes, roots, digits of the number, or sequential relationships (like multiplying by the next number in a sequence). Sometimes, the relationship might involve a combination of operations or a pattern based on prime numbers, composite numbers, odd numbers, or even numbers. Practicing different types of number series and patterns can greatly improve your ability to solve analogy questions quickly and accurately.