2018 · Q38
Three numbers which are co-prime to each other, are such that the product of the first two is 286 and that of the last two is 770. What is the sum of the three numbers?
Elementary MathematicsNumber System
- A85
- B80
- C75
- D70
Explanation
The middle number divides both 286 = 2 × 11 × 13 and 770 = 2 × 5 × 7 × 11, so it is gcd(286, 770) = 22. The numbers are 286/22 = 13, 22 and 770/22 = 35 — pairwise coprime — summing to 70, option (D).