Directions: Identify the number that completes the analogy. Apply each operation to the entire number, not to its individual digits.

145 : 326 :: ? : 540 :: 381 : 798

The correct answer is 252.

Step-by-step Explanation:

To solve this number analogy, we need to determine the common mathematical operation applied to the first number in each pair to obtain the second number.

Let's analyze the first pair: 145 : 326

$145\times 2+36=290+36=326$

Now, let's verify if the same pattern applies to the third pair: 381 : 798

$381\times 2+36=762+36=798$

The established pattern for the analogy is:

$(\text{First Number}\times 2)+36=\text{Second Number}$

We can now apply this rule to find the missing number ($?$) in the second pair: ? : 540

$(?\times 2)+36=540$

Subtract 36 from both sides:

$?\times 2=540-36$

$?\times 2=504$

Divide by 2 to get the missing number:

$?=\frac{504}{2}=252$

Therefore, the number that completes the analogy is 252.