There are three numbers which are co-prime to one other such that the product of the first two is 357 and that of the last two is 609. What is the sum of the three numbers?

Correct option is B

Given:

Let the three co-prime numbers be A, B, and C.

​$$A \cdot B = 357 \\ B \cdot C = 609$$​​

Solution:

the prime factorization of 357 and 609:

​$$357 = 3 \cdot 7 \cdot 17$$

$$609 = 3 \cdot 7 \cdot 29$$

​​​From these factorizations, we can deduce the values of A, B, and C:

​$$A= 17$$

​​$$B = 3 \cdot 7 = 21$$​​

​$$C=29$$​​

Therefore, the sum of the three numbers is $$17+21+29=\bf 67$$​​