Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(16, 4, 8)
(12, 2, 12)

Question

Select the set in which the numbers are related in the same way as are the numbers of the following sets.(16, 4, 8)(12, 2, 12)

Prepp Team · Accepted Answer

Finding the Number Relationship in Sets

The question asks us to identify the numerical relationship within two given sets of numbers and then find the option set that shares the same relationship. The given sets are (16, 4, 8) and (12, 2, 12).

Analyzing the Given Number Sets

Let's examine the relationship between the numbers in the first set: (16, 4, 8).

If we divide the first number by the second: \(16 \div 4 = 4\).
If we look at the third number, 8, how does it relate to 4? \(4 \times 2 = 8\) or \(8 \div 2 = 4\).

This suggests a potential relationship involving division and multiplication or a ratio.

Let's test a potential rule based on this observation: Is (First Number / Second Number) related to (Third Number / 2)?

For set (16, 4, 8): \(16 \div 4 = 4\). And \(8 \div 2 = 4\). The values are equal.
This suggests the relationship might be: \( \frac{\text{First Number}}{\text{Second Number}} = \frac{\text{Third Number}}{2} \)

Now, let's check if this rule holds for the second set: (12, 2, 12).

Using the rule: \( \frac{12}{2} = 6 \).
And \( \frac{12}{2} = 6 \). The values are equal.

The relationship \( \frac{\text{First Number}}{\text{Second Number}} = \frac{\text{Third Number}}{2} \) holds true for both given sets.

We can rearrange this rule to make it easier to test options. Multiplying both sides by \(2 \times \text{Second Number}\) gives:

\( 2 \times \text{First Number} = \text{Second Number} \times \text{Third Number} \)

Applying the Relationship to Options

Now we will test each option set using the identified rule: \( 2 \times \text{First Number} = \text{Second Number} \times \text{Third Number} \)

Option Set	\(2 \times \text{First Number}\)	\( \text{Second Number} \times \text{Third Number} \)	Relationship Holds?
(20, 2, 8)	\(2 \times 20 = 40\)	\(2 \times 8 = 16\)	\(40 \neq 16\) (No)
(18, 8, 3)	\(2 \times 18 = 36\)	\(8 \times 3 = 24\)	\(36 \neq 24\) (No)
(28, 7, 8)	\(2 \times 28 = 56\)	\(7 \times 8 = 56\)	\(56 = 56\) (Yes)
(32, 3, 10)	\(2 \times 32 = 64\)	\(3 \times 10 = 30\)	\(64 \neq 30\) (No)

The analysis shows that only the set (28, 7, 8) satisfies the established relationship \( 2 \times \text{First Number} = \text{Second Number} \times \text{Third Number} \).

Therefore, the set (28, 7, 8) is related in the same way as the given sets (16, 4, 8) and (12, 2, 12).

Revision Table: Key Relationships

Set	First Num	Second Num	Third Num	\(2 \times \text{First Num}\)	\( \text{Second Num} \times \text{Third Num} \)	Matches Rule?
(16, 4, 8)	16	4	8	32	32	Yes
(12, 2, 12)	12	2	12	24	24	Yes
(28, 7, 8)	28	7	8	56	56	Yes

Additional Information: Number Analogy Reasoning

Number analogy questions are a common type of logical reasoning problem. They require you to find a specific rule or relationship that connects the numbers in a given set (or pairs of sets) and then apply that same rule to new options to find the matching one.

Strategies for solving number analogy problems often involve:

Looking for basic arithmetic operations (addition, subtraction, multiplication, division) between the numbers.
Checking for relationships between the position of the numbers (first, second, third).
Considering powers, roots, or other mathematical functions.
Testing simple ratios or proportions between the numbers.
Sometimes, the relationship might involve digits of the numbers or other less obvious patterns.

Practice is key to becoming proficient in identifying these patterns quickly.