Three numbers which are co-prime to each other are such that the product of…
2024
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
- A.
75
- B.
21
- C.
85
- D.
12
Attempted by 2 students.
Show answer & explanation
Correct answer: C
To find the sum of these three numbers, let's call them a, b, and c.
Step-by-Step Calculation
1. Set up the equations based on the products:
Product of the first two: a × b = 551
Product of the last two: b × c = 1073
2. Find the middle number (b): Since b is a factor of both 551 and 1073, the middle number must be the Highest Common Factor (H.C.F.) of these two products.
To find the H.C.F. of 551 and 1073, we use the division method:
1073 ÷ 551 = 1 with a remainder of 522
551 ÷ 522 = 1 with a remainder of 29
522 ÷ 29 = 18 exactly (with a remainder of 0)
The H.C.F. is 29. Thus, b = 29.
3. Find the other two numbers (a and c):
a = 551 ÷ 29 = 19
c = 1073 ÷ 29 = 37
4. Calculate the sum:
Sum = a + b + c = 19 + 29 + 37 = 85.