16 is related to 30 following a certain logic. Following the same logic, 81 is related to 110. To which of the following is 49 related, following the same logic?

Question

Accepted Answer

Step 1: Analyze the given pairs:
- 16 is related to 30
- 81 is related to 110

Step 2: Try to find a relation between the numbers without breaking them into digits.

Check if the second number is related to the first number by some arithmetic operation:

For 16 and 30:
- 16 * 2 = 32 (close to 30)
- 16 + 14 = 30
- 16 + 16 - 2 = 30

For 81 and 110:
- 81 + 29 = 110
- 81 * 1.35 = 109.35 (close to 110)

Step 3: Try to find a pattern in the difference:
- Difference between 30 and 16 = 14
- Difference between 110 and 81 = 29

Step 4: Check if the difference relates to the original number:
- 14 is close to sqrt(16) * 3.5 = 4 * 3.5 = 14
- 29 is close to sqrt(81) * 3.5 = 9 * 3.5 = 31.5 (close but not exact)

Step 5: Try another approach:
- 16 * 2 - 2 = 32 - 2 = 30
- 81 * 2 - 52 = 162 - 52 = 110 (not consistent)

Step 6: Try adding the square root multiplied by 3.5:
- 16 + (4 * 3.5) = 16 + 14 = 30
- 81 + (9 * 3.5) = 81 + 31.5 = 112.5 (close to 110)

Step 7: Since the second number is approximately the first number plus 3.5 times its square root, apply this to 49:
- sqrt(49) = 7
- 49 + (7 * 3.5) = 49 + 24.5 = 73.5 (closest option is 72)

Step 8: Check options for closest match:
- 64 (too low)
- 60 (too low)
- 72 (closest to 73.5)
- 90 (too high)

Step 9: However, the problem states operations on whole numbers without breaking digits, so the logic might be simpler:

Try this:
- 16 * 2 - 2 = 30
- 81 * 2 - 52 = 110 (not consistent)

Try adding the number and its half:
- 16 + 14 = 30
- 81 + 29 = 110

Notice 14 is 16 - 2, 29 is 81 - 52 (no clear pattern)

Step 10: Another approach is to add the number and its square root multiplied by 3.5 rounded down:
- For 16: 16 + 4*3.5 = 16 + 14 = 30
- For 81: 81 + 9*3.5 = 81 + 31.5 = 112.5 (close to 110)

Step 11: For 49:
- 49 + 7*3.5 = 49 + 24.5 = 73.5 (closest option 72)

Step 12: Since 72 is an option and closest to 73.5, select 72.

Final answer: 72

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