Identifying the Different Number Pattern

The question asks us to find the number set among the given options that follows a different pattern compared to the others. We need to examine the relationship between the three numbers in each option.

Let's denote the three numbers in each option as A : B : C.

Analyzing the Number Patterns in Each Option

Option 1: 34 : 102 : 204

• Relationship between the first and second number: Is B related to A?
• Calculate the ratio of the second number to the first number: $\frac{102}{34} = 3$.
• So, the second number (102) is 3 times the first number (34): $102 = 34 \times 3$.
• Relationship between the second and third number: Is C related to B?
• Calculate the ratio of the third number to the second number: $\frac{204}{102} = 2$.
• So, the third number (204) is 2 times the second number (102): $204 = 102 \times 2$.
• Pattern observed in Option 1: A : $A \times 3$ : $(A \times 3) \times 2$, which is also A : B : $B \times 2$.

Option 2: 24 : 72 : 144

• Relationship between the first and second number: Is B related to A?
• Calculate the ratio: $\frac{72}{24} = 3$.
• So, $72 = 24 \times 3$.
• Relationship between the second and third number: Is C related to B?
• Calculate the ratio: $\frac{144}{72} = 2$.
• So, $144 = 72 \times 2$.
• Pattern observed in Option 2: A : $A \times 3$ : $(A \times 3) \times 2$, or A : B : $B \times 2$. This pattern is the same as in Option 1.

Option 3: 21 : 63 : 126

• Relationship between the first and second number: Is B related to A?
• Calculate the ratio: $\frac{63}{21} = 3$.
• So, $63 = 21 \times 3$.
• Relationship between the second and third number: Is C related to B?
• Calculate the ratio: $\frac{126}{63} = 2$.
• So, $126 = 63 \times 2$.
• Pattern observed in Option 3: A : $A \times 3$ : $(A \times 3) \times 2$, or A : B : $B \times 2$. This pattern is the same as in Options 1 and 2.

Option 4: 17 : 51 : 106

• Relationship between the first and second number: Is B related to A?
• Calculate the ratio: $\frac{51}{17} = 3$.
• So, $51 = 17 \times 3$.
• Relationship between the second and third number: Is C related to B?
• Calculate the ratio: $\frac{106}{51}$. This does not result in a whole number (approximately 2.078).
• Let's check if $106 = 51 \times 2$. $51 \times 2 = 102$. $106 \neq 102$.
• Pattern observed in Option 4: A : $A \times 3$. However, the third number is not 2 times the second number.

Conclusion: Identifying the Different Pattern

From the analysis, we can see that Options 1, 2, and 3 all follow the same pattern where the second number is 3 times the first number, and the third number is 2 times the second number (A : $A \times 3$ : $(A \times 3) \times 2$).

Option 4 follows the pattern where the second number is 3 times the first number (17 : $17 \times 3$), but the third number (106) is not 2 times the second number (51). $51 \times 2 = 102$, not 106.

Therefore, the number set 17 : 51 : 106 is different from the others because it does not follow the C = B $\times$ 2 pattern.

Revision Table: Number Pattern Analysis

Additional Information: Number Analogy and Pattern Recognition

Questions like this test your ability to identify mathematical or logical relationships between numbers. These are common in reasoning and quantitative aptitude tests. To solve them, you should look for common relationships such as:

• Arithmetic progression (adding or subtracting a constant)
• Geometric progression (multiplying or dividing by a constant)
• Squares, cubes, or other powers
• Sum or difference of digits
• Prime numbers, composite numbers, etc.
• Combinations of these operations

In number analogy problems like this, you usually find a consistent rule applied across several sets of numbers, and one set deviates from that rule. The key is to systematically test simple operations first, like multiplication or addition, between the numbers in each set.