Understanding Number Analogy Questions

Number analogy questions ask you to find a relationship between two numbers and then apply that same relationship to a third number to find a fourth, missing number. These questions test your ability to recognize patterns and mathematical operations.

In the given question, we have the analogy: 18 ∶ 10 ∶∶ 24 ∶ ?

We need to find the relationship between the first number, 18, and the second number, 10. Once we identify this relationship, we will apply it to the third number, 24, to find the missing fourth number.

Finding the Relationship between 18 and 10

Let's explore possible mathematical relationships between 18 and 10.

• Could it be a simple subtraction? $18 - 8 = 10$. If we subtract 8 from 24, we get $24 - 8 = 16$. Is 16 an option? No.
• Could it involve division? Let's try dividing 18 by a number. $18 \div 2 = 9$. How can we get from 9 to 10? By adding 1: $9 + 1 = 10$.

So, the potential relationship is: divide the first number by 2, and then add 1.

Let's verify this rule with the first pair (18 and 10):

$$ \frac{18}{2} + 1 $$

$$ 9 + 1 = 10 $$

This relationship holds true for the first pair of numbers.

Applying the Relationship to 24

Now, we apply the same rule to the third number, 24, to find the missing number.

We need to calculate: $\text{(24 divided by 2)} + 1$.

$$ \frac{24}{2} + 1 $$

$$ 12 + 1 = 13 $$

The result is 13.

Checking the Options

Now let's look at the given options:

1. 13
2. 17
3. 12
4. 29

Our calculated number, 13, is one of the options.

Conclusion

The relationship between the first pair of numbers (18 and 10) is dividing the first number by 2 and adding 1. Applying this same relationship to the third number (24) gives us 13. Therefore, the missing number in the analogy 24 ∶ ? is 13.

The complete analogy is: 18 ∶ 10 ∶∶ 24 ∶ 13.

Revision Table: Number Analogy

Understanding the relationship between numbers is key to solving number analogy problems.

Additional Information: Solving Analogy Problems

Number analogy questions often involve basic arithmetic operations, squares, cubes, roots, or digit-based manipulations. Here are some common approaches to finding the relationship:

• Arithmetic Operations: Look for addition, subtraction, multiplication, or division. Sometimes a combination of these is used.
• Squares and Cubes: The numbers might be squares or cubes, or related to them (e.g., one more or less than a square).
• Digit Operations: The relationship might involve the sum of digits, product of digits, or other manipulations of the digits themselves.
• Prime or Composite Numbers: The pattern might relate to properties like being prime or composite.
• Sequence Patterns: Although less common in simple analogies, sometimes there's an underlying sequence.

To solve these problems effectively, practice identifying common patterns and perform calculations carefully.