Solving Number Set Relation Reasoning Questions

This question asks us to identify the set of numbers that shares the same mathematical relationship as the two given sets: (5, 60, 70) and (9, 108, 126). The rule is that operations should be performed on the whole numbers themselves, not on their individual digits.

Analyzing the Given Number Sets

Let's look closely at the two given sets and try to find a consistent pattern relating the three numbers in each set. We can denote the numbers in a set as A, B, and C.

For the first set (5, 60, 70):

• The first number is 5.
• The second number is 60. Let's see how 60 relates to 5. $60 = 5 \times 12$.
• The third number is 70. Let's see how 70 relates to 5. $70 = 5 \times 14$.

The relationship seems to be that the second number is 12 times the first number, and the third number is 14 times the first number.

Let's check if this pattern holds true for the second given set (9, 108, 126):

• The first number is 9.
• The second number is 108. Let's see how 108 relates to 9. $108 = 9 \times 12$. This matches the pattern.
• The third number is 126. Let's see how 126 relates to 9. $126 = 9 \times 14$. This also matches the pattern.

The consistent pattern observed in both given sets is:

• Second Number = First Number $\times$ 12
• Third Number = First Number $\times$ 14

Applying the Pattern to the Options

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

Option 1: (7, 84, 98)

• First number = 7
• Check the second number: $7 \times 12 = 84$. This matches the second number in the set.
• Check the third number: $7 \times 14 = 98$. This matches the third number in the set.

Option 1 follows the established pattern.

Option 2: (4, 48, 52)

• First number = 4
• Check the second number: $4 \times 12 = 48$. This matches the second number in the set.
• Check the third number: $4 \times 14 = 56$. This does not match the third number (52) in the set.

Option 2 does not follow the pattern.

Option 3: (6, 72, 74)

• First number = 6
• Check the second number: $6 \times 12 = 72$. This matches the second number in the set.
• Check the third number: $6 \times 14 = 84$. This does not match the third number (74) in the set.

Option 3 does not follow the pattern.

Option 4: (8, 84, 112)

• First number = 8
• Check the second number: $8 \times 12 = 96$. This does not match the second number (84) in the set.
• Check the third number: $8 \times 14 = 112$. This matches the third number in the set, but the second number does not fit the pattern.

Option 4 does not follow the pattern.

Based on the analysis, only Option 1 follows the same mathematical relationship as the given sets.

Conclusion

The set (7, 84, 98) is related in the same way as the given sets (5, 60, 70) and (9, 108, 126), where the second number is 12 times the first, and the third number is 14 times the first.

Revision Table - Number Set Pattern

Additional Information - Reasoning Concepts

Number set relation questions are common in logical reasoning and aptitude tests. They assess your ability to identify patterns and relationships between numbers. These relationships can involve various mathematical operations like addition, subtraction, multiplication, division, squares, cubes, or a combination of these.

Key strategies for solving such problems include:

• Look for patterns: Examine the relationship between the first and second numbers, first and third numbers, and second and third numbers.
• Consider operations: Test simple operations like addition, subtraction, multiplication, or division.
• Check for consistent rules: The pattern must apply consistently across all given examples.
• Apply to options: Once a potential rule is found, apply it to each option to see which one fits.

These types of questions help improve analytical thinking and problem-solving skills needed for various competitive exams.