40 is related to 53 following certain logic. Following the same logic, 8 is related to 13. To which of the following numbers is 68 related, following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

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Accepted Answer

Step 1: Analyze the given pairs:
- 40 is related to 53
- 8 is related to 13

Step 2: Check the difference between the pairs:
- 53 - 40 = 13
- 13 - 8 = 5

Step 3: The difference is not consistent, so check other operations.

Step 4: Check if the second number is the first number plus a prime number:
- 40 + 13 = 53 (13 is prime)
- 8 + 5 = 13 (5 is prime)

Step 5: The logic seems to be: The second number is the first number plus a prime number.

Step 6: Now, for 68, find the prime number added to 68 to get the related number.

Step 7: Check options:
- 84 - 68 = 16 (not prime)
- 85 - 68 = 17 (prime)
- 83 - 68 = 15 (not prime)
- 73 - 68 = 5 (prime)

Step 8: Both 85 and 73 are possible if the prime number added is 17 or 5.

Step 9: Check the pattern of prime numbers added:
- For 40, prime added is 13
- For 8, prime added is 5

Step 10: The prime numbers added are decreasing: 13, 5, so next prime could be 17 or 5 again.

Step 11: Since 17 is larger than 13, and 5 is smaller, the pattern is not strictly increasing or decreasing.

Step 12: Another approach: Check if the prime number added is the difference between the digits of the first number.
- For 40: digits 4 and 0, difference 4, but prime added is 13, no match.
- For 8: single digit, no difference.

Step 13: Since the problem states no breaking digits, this is invalid.

Step 14: Another approach: Check if the prime number added is the difference between the first number and the second number's digits sum.
- Sum of digits of 53 = 5 + 3 = 8
- 40 + 13 = 53
- Sum of digits of 13 = 1 + 3 = 4
- 8 + 5 = 13

Step 15: No clear pattern.

Step 16: Since 85 - 68 = 17 (prime), and 17 is a prime number, and the previous prime added was 13 and 5, the next prime added could be 17.

Step 17: Therefore, 68 is related to 85.

Answer: 85

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