Select the option that is related to the third number in the same way as the second number is related to the first number.
52 : 91 : : 72 : ?

The correct option is 126.

To find the missing number in the analogy 52 : 91 : : 72 : ?, we need to determine the mathematical relationship between the first pair of numbers (52 and 91) and apply the same relationship to the second pair.

Let's analyze the relationship between the first pair, 52 and 91:
Both numbers are multiples of 13:
$52=13\times 4$
$91=13\times 7$
Therefore, the ratio of the first number to the second number is 4 : 7.

Now, we apply this same ratio (4 : 7) to the third number (72) to find the fourth number:
First, express 72 as a multiple of 4:
$72=18\times 4$
Following the 4 : 7 ratio, we multiply the common factor (18) by 7:
$18\times 7=126$

Thus, the number related to 72 in the same way is 126.