Select the set in which the numbers are related in the same way as are the numbers of the following set.
(8, 12, 24)

Question

Select the set in which the numbers are related in the same way as are the numbers of the following set.(8, 12, 24)

Prepp Team · Accepted Answer

Solving Number Analogy Problems

The question asks us to identify a set of numbers that share the same numerical relationship as the given set (8, 12, 24). To solve this number analogy problem, we first need to understand the relationship between the numbers in the original set.

Analyzing the Relationship in the Given Set (8, 12, 24)

Let's look at the numbers 8, 12, and 24. We can examine the relationship in various ways, such as differences, ratios, or multiplicative factors.

Difference between the first and second number: \(12 - 8 = 4\)
Difference between the second and third number: \(24 - 12 = 12\)

The differences are not constant (4 and 12), so a simple arithmetic progression is not the relationship.

Ratio between the first and second number: \(\frac{12}{8} = \frac{3}{2} = 1.5\)
Ratio between the second and third number: \(\frac{24}{12} = 2\)

This suggests a multiplicative relationship. The second number is 1.5 times the first, and the third number is 2 times the second.

Let the numbers be A, B, and C. The relationship appears to be:

\(B = \frac{3}{2} \times A\)
\(C = 2 \times B\)

Alternatively, we can look at the ratio between all three numbers: 8 : 12 : 24. Dividing all numbers by their greatest common divisor, 4, we get the simplified ratio 2 : 3 : 6.

So, the relationship is that the three numbers are in the ratio 2:3:6.

Checking the Options for the Same Number Relationship

We will now check each option to see which set of numbers follows the same relationship, i.e., the numbers are in the ratio 2:3:6 or follow the multiplicative rules \(B = \frac{3}{2} \times A\) and \(C = 2 \times B\).

Option Set	Numbers (A, B, C)	Check \(B = \frac{3}{2} \times A\)	Check \(C = 2 \times B\)	Simplified Ratio (A:B:C)	Matches (8, 12, 24) Relationship (2:3:6)?
1	(6, 9, 18)	\(9 = \frac{3}{2} \times 6 = \frac{18}{2} = 9\) (Yes)	\(18 = 2 \times 9 = 18\) (Yes)	6:9:18. Divide by 3: 2:3:6.	Yes
2	(6, 11, 18)	\(11 = \frac{3}{2} \times 6 = 9\) (No)	\(18 = 2 \times 11 = 22\) (No)	6:11:18. Cannot simplify to 2:3:6.	No
3	(9, 18, 27)	\(18 = \frac{3}{2} \times 9 = \frac{27}{2} = 13.5\) (No)	\(27 = 2 \times 18 = 36\) (No)	9:18:27. Divide by 9: 1:2:3.	No
4	(12, 20, 40)	\(20 = \frac{3}{2} \times 12 = \frac{36}{2} = 18\) (No)	\(40 = 2 \times 20 = 40\) (Yes)	12:20:40. Divide by 4: 3:5:10.	No

Based on the analysis, only the set (6, 9, 18) satisfies the same numerical relationship as the set (8, 12, 24).

Conclusion

The set (6, 9, 18) is related in the same way as the set (8, 12, 24) because in both sets, the numbers are in the ratio 2:3:6, or equivalently, the second number is 1.5 times the first, and the third number is 2 times the second.

Revision Table: Key Concepts in Number Analogy

Concept	Description	How it Applies Here
Number Analogy	Finding a relationship between a given set of numbers and applying that same relationship to find a matching set from options.	We found the relationship in (8, 12, 24) and applied it to the options.
Ratio Analysis	Expressing numbers in a set as a simplified ratio to understand their relative proportions.	The ratio 8:12:24 simplified to 2:3:6, which was a key to solving the problem.
Multiplicative Relationship	Identifying how numbers in a set are related through multiplication or division factors.	We found that \(B = 1.5 \times A\) and \(C = 2 \times B\) in the given set.

Additional Information: Solving Reasoning Questions

Number analogy questions are a common type of logical reasoning problem. They test your ability to identify patterns and relationships between numbers. Here are some tips for solving similar reasoning questions:

Look for basic arithmetic operations (addition, subtraction, multiplication, division).
Check for squares, cubes, or roots of the numbers.
Analyze the ratio between the numbers.
Consider prime numbers, composite numbers, odd or even sequences.
Look for patterns in the differences or ratios between consecutive numbers.
Try combining operations (e.g., multiply and then add).
Break down complex relationships into simpler steps.
Test your proposed relationship rigorously on the given set before applying it to the options.
Systematically check every option against the identified relationship.

Practicing various types of number series and analogy questions will help you become familiar with common patterns and improve your problem-solving speed.