Select the option that is related to the third number in the same way as the second number is related to the first number. $36: 109:: 25: $
Explanation:
The given analogy is $36 : 109 :: 25 : ?$. We need to identify the relationship between the first pair and apply it to the second. Upon careful observation, the pattern for the first pair is $x : (x \times 3 + 1)$. For $36 : 109$, we have $36 \times 3 = 108$, and $108 + 1 = 109$. This rule holds for the first pair. Now, we apply the same rule to the third number, $25$: $25 \times 3 = 75$, and $75 + 1 = 76$. Thus, the missing number is $76$. Let's analyze the options: A) $70$: This would imply $25 \times 3 - 5 = 70$, inconsistent. B) $72$: This would imply $25 \times 3 - 3 = 72$, inconsistent. C) $75$: This would imply $25 \times 3 = 75$, inconsistent with the $+1$ in the first pair. D) $76$: This option perfectly matches the derived pattern of multiplying by $3$ and then adding $1$.