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: 4 : 49 :: 6 : 81 :: 8 :?

1. A. 176
2. B. 145
3. C. 187
4. D. 121 (Correct answer)

Correct Answer

Option D — 121

Detailed Solution & Explanation

The correct answer is 121.

Key Points

• Check the rule against both given pairs:
  • 4 → 49 is (4 + 3)² = 7² ✓
  • 6 → 81 is (6 + 3)² = 9² ✓
• The rule is (n + 3)², so for 8:
  • (8 + 3)² = 11² = 121

Additional Information

• Squares worth instant recall: 49, 64, 81, 100, 121, 144, 169, 196, 225 — recognising 49 and 81 as 7² and 9² is what reveals the "+3 then square" structure.
• Note that both outputs are odd squares, and 8 + 3 = 11 keeps that pattern, which is a useful sanity check.
• Test any candidate rule on both worked pairs; "n² + 33" fits 4 → 49 but fails 6 → 81 at once.
• Where an analogy links a small number to a much larger one, try squaring or cubing an adjusted value before considering multi-step arithmetic.