Number Analogy: Identifying the Pattern

The question asks to find a set of numbers that follows the same relationship pattern as the given examples: (52, 100, 196) and (65, 126, 248). The rule applies to whole numbers without breaking them into digits.

Analyzing the Number Sets

Let's denote the numbers in a set as A, B, and C.

• Set 1: (52, 100, 196)
  • Calculate the difference between the second and first number: $B - A = 100 - 52 = 48$.
  • Calculate the difference between the third and second number: $C - B = 196 - 100 = 96$.
  • Observe the relationship between these differences: $96 = 2 \times 48$. So, $C - B = 2 \times (B - A)$.
• Set 2: (65, 126, 248)
  • Calculate the difference: $B - A = 126 - 65 = 61$.
  • Calculate the difference: $C - B = 248 - 126 = 122$.
  • Verify the relationship: $122 = 2 \times 61$. The pattern $C - B = 2 \times (B - A)$ holds true.

Testing the Options

We need to find the option that satisfies the condition $C - B = 2 \times (B - A)$.

• Option 1: (72, 140, 256)
  • $B - A = 140 - 72 = 68$
  • $C - B = 256 - 140 = 116$
  • Check: Is $116 = 2 \times 68$? $2 \times 68 = 136$. No.
• Option 2: (94, 184, 264)
  • $B - A = 184 - 94 = 90$
  • $C - B = 264 - 184 = 80$
  • Check: Is $80 = 2 \times 90$? $2 \times 90 = 180$. No.
• Option 3: (68, 132, 260)
  • $B - A = 132 - 68 = 64$
  • $C - B = 260 - 132 = 128$
  • Check: Is $128 = 2 \times 64$? $2 \times 64 = 128$. Yes. This set follows the pattern.
• Option 4: (56, 108, 202)
  • $B - A = 108 - 56 = 52$
  • $C - B = 202 - 108 = 94$
  • Check: Is $94 = 2 \times 52$? $2 \times 52 = 104$. No.

Conclusion

Option 3 is the only set that adheres to the identified number relationship pattern, where the difference between the second and first number, when doubled, equals the difference between the third and second number.