Question

Select the odd group of numbers.

• A. $13 - 159$
• B. $9 - 71$
• C. $5 - 31$
• D. $17 - 279$

Hint:

When solving number pair classification problems, always check the squares or cubes of the smaller number first.
If the larger number is close to a perfect square, write down the difference to quickly identify the rule.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The objective of this question is to analyze the relationship between the two numbers in each group and identify which group does not follow the established mathematical pattern.

Step 2: Key Formula or Approach:
Let the pair of numbers in each group be represented as $(x, y)$.
We will test standard algebraic relationships such as $y = ax + b$, $y = x^2 \pm c$, or other common series relations to find a consistent logic.

Step 3: Detailed Explanation:
Let us analyze each option step-by-step:

• Analyzing Option (A): For the pair $13 - 159$, we have $x = 13$ and $y = 159$.
Let us evaluate the square of $x$: $13^2 = 169$.
Subtracting $10$ from the square gives: $169 - 10 = 159$.
This satisfies the relation $y = x^2 - 10$.

• Analyzing Option (B): For the pair $9 - 71$, we have $x = 9$ and $y = 71$.
Let us evaluate the square of $x$: $9^2 = 81$.
Subtracting $10$ from the square gives: $81 - 10 = 71$.
This also satisfies the relation $y = x^2 - 10$.

• Analyzing Option (D): For the pair $17 - 279$, we have $x = 17$ and $y = 279$.
Let us evaluate the square of $x$: $17^2 = 289$.
Subtracting $10$ from the square gives: $289 - 10 = 279$.
This satisfies the same relation $y = x^2 - 10$.

• Analyzing Option (C): For the pair $5 - 31$, we have $x = 5$ and $y = 31$.
Applying the established rule: $5^2 - 10 = 25 - 10 = 15$.
However, the given value is $31$, which does not match $15$.
Thus, this group does not conform to the pattern of the other three.

Step 4: Final Answer:
The group $5 - 31$ is the odd group of numbers because it does not follow the general mathematical rule $y = x^2 - 10$ observed in the other options.