Analyzing Number Set Relationships for Reasoning Questions

The problem asks us to identify a numerical relationship within a given set of numbers and find another set from the options that follows the same relationship. We are given two example sets: (5, 98, 9) and (10, 168, 14).

The rule is that operations should be performed on the whole numbers as given, not on their individual digits.

Finding the Relationship in the Given Sets

Let's examine the first set (5, 98, 9) and the second set (10, 168, 14). We need to find a pattern or relationship between the first, second, and third numbers in each set.

Let the first number be $A$, the second number be $B$, and the third number be $C$.

For the first set (5, 98, 9): $A=5$, $B=98$, $C=9$.

For the second set (10, 168, 14): $A=10$, $B=168$, $C=14$.

Let's try simple arithmetic operations involving $A$ and $C$ to arrive at $B$.

• Could $B$ be related to the sum of $A$ and $C$?
• Set 1: $A+C = 5+9 = 14$. How to get 98 from 14? $14 \times 7 = 98$.
• Set 2: $A+C = 10+14 = 24$. How to get 168 from 24? $24 \times 7 = 168$.

It appears the relationship is $(A+C) \times 7 = B$. Let's verify this rule.

• For set (5, 98, 9): $(5 + 9) \times 7 = 14 \times 7 = 98$. This holds true.
• For set (10, 168, 14): $(10 + 14) \times 7 = 24 \times 7 = 168$. This also holds true.

So, the established relationship is that the middle number is 7 times the sum of the first and third numbers.

Checking the Options

Now, we apply this rule $(A+C) \times 7 = B$ to each of the given options to find the set that follows the same pattern.

Option 1: (1, 28, 3)

• $A=1$, $B=28$, $C=3$.
• Calculate $(A+C) \times 7$: $(1 + 3) \times 7 = 4 \times 7 = 28$.
• The calculated value (28) matches the middle number ($B=28$) in this set.

This option follows the discovered relationship.

Option 2: (7, 108, 23)

• $A=7$, $B=108$, $C=23$.
• Calculate $(A+C) \times 7$: $(7 + 23) \times 7 = 30 \times 7 = 210$.
• The calculated value (210) does not match the middle number ($B=108$) in this set.

This option does not follow the relationship.

Option 3: (15, 248, 19)

• $A=15$, $B=248$, $C=19$.
• Calculate $(A+C) \times 7$: $(15 + 19) \times 7 = 34 \times 7 = 238$.
• The calculated value (238) does not match the middle number ($B=248$) in this set.

This option does not follow the relationship.

Option 4: (3, 88, 17)

• $A=3$, $B=88$, $C=17$.
• Calculate $(A+C) \times 7$: $(3 + 17) \times 7 = 20 \times 7 = 140$.
• The calculated value (140) does not match the middle number ($B=88$) in this set.

This option does not follow the relationship.

Conclusion

Based on our analysis, only Option 1: (1, 28, 3) follows the same numerical relationship as the given sets (5, 98, 9) and (10, 168, 14), which is $(A+C) \times 7 = B$.

Revision Table: Number Set Reasoning

Additional Information: Logical Reasoning Practice

Number set reasoning questions are common in competitive exams like SSC CGL. They test your ability to identify patterns and apply logical rules. To improve, practice with various types of number series, analogies, and set-based problems.

• Look for relationships between the first and last numbers to find the middle number, or vice versa.
• Consider sums, differences, products, quotients, powers, roots, and combinations of these operations.
• Sometimes the relationship might involve a constant factor (like '7' in this case) or a constant difference.
• Be systematic in checking potential rules against the given sets.
• Practice applying the identified rule quickly and accurately to the options.

Mastering logical reasoning helps improve problem-solving skills crucial for success in many exams.