Select the option that is related to the fifth number in the same way as the second number is related to the first number and the…

Question

Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number: 3 : 30 :: 4 : 68 :: 5 :?

1. A. 145
2. B. 130 (Correct answer)
3. C. 126
4. D. 175

Correct Answer

Option B — 130

Detailed Solution & Explanation

The correct answer is 130.

Key Points

• Test the relationship on both worked pairs:
  • 3 → 30 is 3³ + 3 = 27 + 3 ✓
  • 4 → 68 is 4³ + 4 = 64 + 4 ✓
• The rule is n³ + n, so for 5:
  • 5³ + 5 = 125 + 5 = 130

Additional Information

• Validate a candidate rule on every given pair before applying it. A rule such as "×10" fits 3 → 30 but fails 4 → 68 immediately, and that is precisely how the distractors are built.
• Cubes worth instant recall: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
• The form n³ + n factors as n(n² + 1), which some find quicker: 5 × 26 = 130.
• When outputs grow far faster than inputs, test cubes before squares — 30 from 3 is a tenfold jump, too large for a square-based rule.