Select the option in which the number set shares the same relationship as that shared by the given number set.

(17, 24, 45)

The correct option is (12, 19, 40).

Step-by-step Explanation:

First, let us analyze the relationship between the numbers in the given set:
(17, 24, 45)

Let the three numbers in the set be represented as a, b, and c respectively.

Let us find the difference between the consecutive numbers:

1. The difference between the second number and the first number ($b-a$):
$24-17=7$

2. The difference between the third number and the second number ($c-b$):
$45-24=21$

We observe that the differences between consecutive terms are +7 and +21. Note that the second difference is three times the first difference:
$7\times 3=21$

Now, let us apply this same logic to the correct option (12, 19, 40):

1. The difference between the second and first numbers:
$19-12=7$

2. The difference between the third and second numbers:
$40-19=21$

Since the differences in the set (12, 19, 40) are also +7 and +21, it shares the exact same relationship as the given set.