The HCF of two numbers is 12 and their sum is 384. How many such pairs of…
2018
The HCF of two numbers is 12 and their sum is 384. How many such pairs of numbers are possible?
- A.
9
- B.
8
- C.
7
- D.
4
Attempted by 35 students.
Show answer & explanation
Correct answer: B
Let the two numbers be 12x and 12y, because their HCF is 12. Then x and y must be coprime.
Given: 12x + 12y = 384
So, 12(x + y) = 384, which gives x + y = 32.
Now count the positive coprime unordered pairs with sum 32:
(1, 31), (3, 29), (5, 27), (7, 25), (9, 23), (11, 21), (13, 19), and (15, 17).
There are 8 such pairs. Therefore, the correct answer is 8.