Analyzing the Number Relationships

The question asks us to find an option where the numbers share the same relationship as the numbers in the given sets. We are provided with two sets: (1056, 11, 16) and (480, 10, 8). We need to discover the mathematical rule or pattern connecting the three numbers in each set. The note specifies that operations must be performed on the whole numbers themselves, not on their constituent digits.

Identifying the Pattern in the Given Sets

Let's examine the first set: (1056, 11, 16).

We need to find a relationship between 1056, 11, and 16. Let's try simple operations involving the second and third numbers (11 and 16) to see if they relate to the first number (1056).

• Addition: $11 + 16 = 27$. $1056 / 27$ is not a whole number.
• Subtraction: $16 - 11 = 5$. Not directly related to 1056.
• Multiplication: $11 \times 16 = 176$.

Now let's see how 176 relates to 1056. Let's divide 1056 by 176:

$$ \frac{1056}{176} = 6 $$

This suggests a possible relationship: The first number is 6 times the product of the second and third numbers. Let's write this as: First number = $6 \times$ (Second number $\times$ Third number).

Let's verify this rule with the first set (1056, 11, 16):

$$ 1056 = 6 \times (11 \times 16) $$ $$ 1056 = 6 \times 176 $$ $$ 1056 = 1056 $$

The rule holds for the first set.

Now let's verify the same rule with the second set: (480, 10, 8).

According to the rule, the first number (480) should be 6 times the product of the second (10) and third (8) numbers.

$$ 480 = 6 \times (10 \times 8) $$ $$ 480 = 6 \times 80 $$ $$ 480 = 480 $$

The rule also holds for the second set. So, the established relationship is: First number = $6 \times$ (Second number $\times$ Third number).

Applying the Pattern to the Options

Now we will apply this rule to each of the given options to find the set that follows the same pattern.

Step-by-Step Option Analysis

Checking Option 1: (88, 2, 7)

Second number $\times$ Third number = $2 \times 7 = 14$.

According to the rule, the first number should be $6 \times 14$.

$$ 6 \times 14 = 84 $$

The given first number is 88. Since $88 \neq 84$, this option does not follow the rule.

Checking Option 2: (110, 3, 6)

Second number $\times$ Third number = $3 \times 6 = 18$.

According to the rule, the first number should be $6 \times 18$.

$$ 6 \times 18 = 108 $$

The given first number is 110. Since $110 \neq 108$, this option does not follow the rule.

Checking Option 3: (384, 8, 4)

Second number $\times$ Third number = $8 \times 4 = 32$.

According to the rule, the first number should be $6 \times 32$.

$$ 6 \times 32 = 192 $$

The given first number is 384. Since $384 \neq 192$, this option does not follow the rule.

Checking Option 4: (90, 3, 5)

Second number $\times$ Third number = $3 \times 5 = 15$.

According to the rule, the first number should be $6 \times 15$.

$$ 6 \times 15 = 90 $$

The given first number is 90. Since $90 = 90$, this option follows the rule.

Based on the analysis, Option 4 (90, 3, 5) is the set where the numbers are related in the same way as the numbers in the given sets.

Revision Table: Number Analogy Practice

Understanding number analogy patterns is crucial for logical reasoning questions. Reviewing different types of relationships helps in quickly identifying the rule in exam scenarios. Common relationships include multiplication, division, addition, subtraction, squares, cubes, or combinations of these operations.

Additional Information on Number Series and Analogy

Number analogy problems are a common type of question in competitive exams designed to test logical reasoning and pattern recognition skills. They require you to find the relationship between a given pair or set of numbers and then apply that same relationship to another pair or set to find a missing number or identify a matching set. These problems can involve various mathematical operations and sometimes multiple steps. Practice with different types of number analogies helps improve the ability to quickly spot patterns.