Solving Number Set Analogy Problems

Number set analogy questions require us to find the relationship or pattern between the numbers in a given set and then identify the option that follows the same relationship. Let's analyze the provided set: (18, 24, 144).

Analyzing the Given Number Set (18, 24, 144)

Let the three numbers in the set be A, B, and C. So, for the given set, A = 18, B = 24, and C = 144.

We need to figure out how 18, 24, and 144 are related. Let's try some common arithmetic operations:

• Is C a direct sum or product of A and B?
• A + B = 18 + 24 = 42. This is not 144.
• A $\times$ B = 18 $\times$ 24. Let's calculate this:

So, A $\times$ B = 432. The third number is 144. How can we get 144 from 432? We can divide 432 by something to get 144.

$432 \div 144 = 3$.

This means that 144 is equal to 432 divided by 3. Since $432 = A \times B$, the relationship appears to be:

$$C = \frac{A \times B}{3}$$

Let's verify this rule with the given set:

$$ \frac{18 \times 24}{3} = \frac{432}{3} = 144 $$

The rule $C = (A \times B) / 3$ holds true for the given set (18, 24, 144).

Testing the Number Analogy Rule on Options

Now, we will apply this rule $C = (A \times B) / 3$ to each of the given options to find the set that follows the same pattern.

Option 1: (26, 15, 130)

Here, A = 26, B = 15, C = 130. Let's check if $(A \times B) / 3$ equals C:

$$ \frac{26 \times 15}{3} = \frac{390}{3} $$

Let's perform the division:

So, $(26 \times 15) / 3 = 130$. This matches the third number in the set (130). Thus, Option 1 follows the same number relationship as the given set.

Option 2: (22, 18, 246)

Here, A = 22, B = 18, C = 246. Let's check if $(A \times B) / 3$ equals C:

$$ \frac{22 \times 18}{3} = \frac{396}{3} $$

$$ 396 \div 3 = 132 $$

This does not match the third number in the set (246).

Option 3: (16, 12, 109)

Here, A = 16, B = 12, C = 109. Let's check if $(A \times B) / 3$ equals C:

$$ \frac{16 \times 12}{3} = \frac{192}{3} $$

$$ 192 \div 3 = 64 $$

This does not match the third number in the set (109).

Option 4: (18, 20, 137)

Here, A = 18, B = 20, C = 137. Let's check if $(A \times B) / 3$ equals C:

$$ \frac{18 \times 20}{3} = \frac{360}{3} $$

$$ 360 \div 3 = 120 $$

This does not match the third number in the set (137).

Conclusion on Number Set Relationship

Based on our analysis, only Option 1 (26, 15, 130) follows the same rule $C = (A \times B) / 3$ that was found in the given set (18, 24, 144).

Revision Table: Number Set Analogy

Additional Information on Number Set Patterns

Number set analogy questions are common in logical reasoning and quantitative aptitude tests. They can involve various types of patterns, not just the product/division pattern seen here. Some other common types of relationships include:

• Arithmetic Progression: Numbers increase or decrease by a constant difference.
• Geometric Progression: Numbers are multiplied or divided by a constant ratio.
• Squares and Cubes: Numbers might be squares, cubes, or related to squares/cubes of other numbers in the set.
• Sum/Difference/Product of Digits: The relationship might involve operations on the individual digits of the numbers.
• Combined Operations: A mix of different arithmetic operations. For example, $C = A^2 + B$, or $C = (A+B) \times k$.
• Prime or Composite Numbers: The numbers might follow a pattern related to their prime or composite nature.

To solve these problems effectively, it's helpful to try out different simple arithmetic operations and look for common mathematical relationships between the numbers.