$42:20::64:\_$

This question involves identifying the relationship between the numbers in the first pair (42 and 20) and then applying the same logic to the second pair (64 and the missing number).

Step 1: Look at the transformation of 42 to 20:

1. Divide 42 by 2: 42 ÷ 2 = 21

2. Subtract 1 from the result: 21 - 1 = 20

Step 2: Apply the same operation to 64:

1. Divide 64 by 2: 64 ÷ 2 = 32

2. Subtract 1 from the result: 32 - 1 = 31

Answer: The missing number is 31.

Correct Option: a. 31