Finding the Different Number Pair Using Pattern Analysis

This question asks us to identify the number pair that does not follow the same rule or pattern as the other three pairs. To solve this, we need to examine each pair and try to find a mathematical relationship between the first number and the second number.

Analyzing the Given Number Pairs

The four number pairs are:

• 82 : 236
• 36 : 98
• 54 : 152
• 68 : 196

Discovering the Pattern

Let's try to find a consistent rule connecting the first number (let's call it A) and the second number (let's call it B) in each pair. A common approach in such problems is to look for multiplication and addition/subtraction operations.

Let's examine the first pair: 82 and 236. How can we get 236 from 82?

We can see that 236 is roughly three times 82 (82 * 3 = 246). The difference is 246 - 236 = 10. So, a possible pattern could be multiplying the first number by 3 and then subtracting 10.

Let's test this potential rule: $$B = A \times 3 - 10$$

Testing the Pattern on Each Pair

Now, we will apply this rule to each of the given number pairs to see if it holds true.

Identifying the Different Pair

As shown in the table above, the first three pairs (82:236, 36:98, and 54:152) all follow the rule $$B = A \times 3 - 10$$.

However, for the fourth pair (68:196), applying the rule gives $$68 \times 3 - 10 = 204 - 10 = 194$$. The given second number is 196, which is different from the expected number 194.

Therefore, the number pair 68 : 196 is the one that does not follow the pattern observed in the other three pairs.

Conclusion

The number pair that is different from the others is 68 : 196 because it does not fit the pattern where the second number is obtained by multiplying the first number by 3 and subtracting 10.

Revision Table: Number Pattern Analysis

Additional Information on Number Patterns

Number pattern questions are common in logical reasoning and aptitude tests. They assess your ability to observe, identify rules, and apply them. Patterns can involve various mathematical operations:

• Addition or subtraction of a constant.
• Multiplication or division by a constant.
• Operations based on position in the sequence.
• Operations on the digits of the numbers.
• Combinations of operations (like $$A \times m \pm c$$ or $$A/m \pm c$$).
• Sequences involving squares, cubes, prime numbers, etc.

To solve such problems, start by looking for simple relationships. Calculate differences, ratios, or try simple multiplicative factors combined with addition/subtraction. Test your hypothesized rule on all given examples to confirm its validity before identifying the element that breaks the pattern.