Finding the Different Number Pair

In this type of question, we are given a set of pairs, and we need to find the pattern or relationship between the numbers in each pair. Three pairs will follow a similar pattern, while one will be different. Our goal is to identify the pair that doesn't fit the common rule.

Analyzing the Number Pairs

Let's examine each given number pair:

• Pair 1: 17 - 54
• Pair 2: 19 - 60
• Pair 3: 15 - 48
• Pair 4: 14 - 42

We need to look for a mathematical relationship between the first number and the second number in each pair. Common relationships include addition, subtraction, multiplication, division, or a combination of these operations.

Discovering the Pattern

Let's test some common relationships on the first pair, 17 - 54. If we try multiplication, $17 \times 3 = 51$. The second number is 54, which is $51 + 3$. So, a possible pattern is to multiply the first number by 3 and then add 3.

Let's see if this pattern, $n \times 3 + 3$, applies to the other pairs:

• Pair 1: $17 \times 3 + 3 = 51 + 3 = 54$. This matches the given pair 17 - 54.
• Pair 2: $19 \times 3 + 3 = 57 + 3 = 60$. This matches the given pair 19 - 60.
• Pair 3: $15 \times 3 + 3 = 45 + 3 = 48$. This matches the given pair 15 - 48.

So far, the first three pairs follow the pattern: Multiply the first number by 3 and add 3 to get the second number.

Identifying the Different Pair

Now let's check the fourth pair, 14 - 42, using the same pattern:

• Pair 4: $14 \times 3 + 3 = 42 + 3 = 45$.

According to the pattern, the second number should be 45, but the given second number is 42. This pair does not follow the $n \times 3 + 3$ pattern.

Let's look at the relationship in the fourth pair, 14 - 42, directly. We can see that $14 \times 3 = 42$. This pair simply follows the pattern of multiplying the first number by 3.

Since the first three pairs follow the rule $n \times 3 + 3$, and the fourth pair follows the rule $n \times 3$, the pair 14 - 42 is different from the others.

Conclusion

The pairs 17-54, 19-60, and 15-48 follow the pattern where the second number is obtained by multiplying the first number by 3 and adding 3 ($n \times 3 + 3$). The pair 14-42 follows a different pattern where the second number is obtained by simply multiplying the first number by 3 ($n \times 3$). Therefore, 14 - 42 is the pair that is different.

Revision Table: Number Pair Analysis

Additional Information: Odd One Out Questions

Questions asking to find the "odd one out" or the "different" item are common in reasoning tests. They can involve various types of items, such as:

• Numbers (like in this question, looking for patterns, divisibility, prime/composite, etc.)
• Letters (looking for position in the alphabet, vowels/consonants, sequence patterns)
• Words (looking for categories, meanings, synonyms/antonyms, word structure)
• Figures (looking for shapes, rotations, number of sides, shading, symmetry)

The key to solving these questions is to systematically look for a consistent rule or pattern that applies to most of the given items and then identify the one item that does not follow that rule.

Sometimes, there might be more than one potential pattern. It's important to test a hypothesis across all options before concluding the answer. Simple arithmetic patterns like addition, subtraction, multiplication, and their combinations are frequently used in number-based questions.