Select the set in which the number are related in the same way as are the numbers of the following sets.
(NOTE: Operation should be performed on whole number; without breaking down the numbers into their constituent digits. E.g. 13 - Operation on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operation on 1 and 3 is not allowed.)
(162, 9, 18)
(231, 11, 21)

Question

Select the set in which the number are related in the same way as are the numbers of the following sets.

(NOTE: Operation should be performed on whole number; without breaking down the numbers into their constituent digits. E.g. 13 - Operation on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operation on 1 and 3 is not allowed.)

(162, 9, 18)

(231, 11, 21)

Prepp Team · Accepted Answer

Understanding Number Set Analogy Questions

Number set analogy questions ask you to find the relationship between numbers in a given set and then identify another set from the options that follows the same relationship. The key rule here is that operations must be performed on the whole numbers themselves, not on their individual digits.

Analyzing the Given Number Sets

We are given two sets of numbers:

Set 1: (162, 9, 18)
Set 2: (231, 11, 21)

Let's look for a relationship between the numbers in these sets. Let the numbers in a set be represented as (A, B, C).

In Set 1, we have A = 162, B = 9, and C = 18.

Let's test common mathematical operations:

Is there a relationship between B and C that results in A?
Can we multiply B and C? \(9 \times 18\). \(9 \times 10 = 90\), \(9 \times 8 = 72\). \(90 + 72 = 162\).
So, \(9 \times 18 = 162\). This fits the pattern \(A = B \times C\).

Let's test this relationship with Set 2, where A = 231, B = 11, and C = 21.

Is \(A = B \times C\)? Is \(231 = 11 \times 21\)?
\(11 \times 21 = 11 \times (20 + 1) = (11 \times 20) + (11 \times 1) = 220 + 11 = 231\).
Yes, \(11 \times 21 = 231\). This confirms the relationship \(A = B \times C\) holds for the given sets.

The relationship connecting the numbers in the given sets is that the first number is the product of the second and third numbers.

Relationship: \(A = B \times C\)

Checking the Options based on the Number Relationship

Now, we need to check each option to find which set follows the same \(A = B \times C\) relationship.

Option Set (A, B, C)	Calculate \(B \times C\)	Compare with A	Relationship Holds?
(336, 28, 12)	\(28 \times 12\) = \(28 \times (10 + 2)\) = \(280 + 56\) = 336	336 = 336	Yes (\(A = B \times C\))
(270, 12, 23)	\(12 \times 23\) = \(12 \times (20 + 3)\) = \(240 + 36\) = 276	276 ≠ 270	No
(314, 19, 16)	\(19 \times 16\) = \(19 \times (10 + 6)\) = \(190 + 114\) = 304	304 ≠ 314	No
(296, 21, 14)	\(21 \times 14\) = \(21 \times (10 + 4)\) = \(210 + 84\) = 294	294 ≠ 296	No

Based on the analysis, only the set (336, 28, 12) follows the established number relationship where the first number is the product of the second and third numbers.

Conclusion

The set (336, 28, 12) exhibits the same numerical relationship (\(A = B \times C\)) as the given sets (162, 9, 18) and (231, 11, 21).

Revision Table: Number Set Analogy Tips

Step	Description
Analyze Given Sets	Examine the numbers in the provided sets to identify a pattern or relationship (addition, subtraction, multiplication, division, squares, cubes, etc.).
Formulate Relationship	Express the identified pattern as a rule or formula (e.g., \(A = B + C\), \(A = B \times C\), \(A = B^2 - C\)).
Test the Rule	Ensure the rule holds true for all the given example sets.
Apply to Options	Check each option one by one to see which set of numbers fits the established rule.
Verify the Answer	Double-check the calculation for the option that seems correct.

Additional Information: Types of Number Relationships in Analogies

Number set analogy problems can involve various types of relationships between the numbers. Some common types include:

Arithmetic Operations: Addition, subtraction, multiplication, division (as seen in this problem).
Squares and Cubes: Relationships involving squares or cubes of the numbers (e.g., \(A = B^2 + C\), \(A = C^3 - B\)).
Ratios and Proportions: The numbers might be in a specific ratio (e.g., \(A:B = C:D\)).
Sequences: The numbers might follow a specific sequence or progression.
Combinations of Operations: More complex rules involving multiple operations.

Always remember the instruction to treat the numbers as whole numbers unless explicitly stated otherwise. Practice with different types of number set analogy problems helps in quickly identifying the pattern.