Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
9 : 74 :: 8: ? :: 7 : 42

Let's analyze the given numerical pairs to figure out the mathematical relationship:
Pair 3: 7:42

7×(7−1)=7×6=42
Alternatively: 7
2
−7=49−7=42

Pair 1: 9:74
Let's check if the same logic works: 9
2
−9=72

=74.
Let's try another logic:

9×8+2=74
For 7:42: 7×6+0=42. This does not align.

Let's try adding something related to the square:

9
2
−7=74

7
2
−7=42
Wow! In both cases, subtracting 7 from the square of the number gives the result? Wait:
9
2
−7=81−7=74. (Correct)
7
2
−7=49−7=42. (Correct)

Thus, the mathematical rule for the relationship is:

Number→(Number)
2
−7
Let's apply this logic to the middle term where the number is 8:

8
2
−7=64−7=57