Question

The sum of two positive numbers is 384 and their HCF is 24. How many pairs of such numbers can be formed?
1. 8
2. 3
3. 5
4. 4

Answer 1

Correct Answer - Option 4 : 4

Given:

Sum of two positive numbers = 384 

HCF of two positive numbers = 24 

Calculation:

Let the two numbers be a and b respectively. 

Now, 24a + 24b = 384

⇒ 24(a + b) = 384

⇒ a + b = 384/24 = 16

⇒ a + b = 16

For a = 1, b = 15 [1 × 24 + 15 × 24 = 384]

For a = 3, b = 13 [3 × 24 + 13 × 24 = 384]

For a = 5, b = 11 [5 × 24 + 11 × 24 = 384]

For a = 7, b = 9  [7 × 24 + 9 × 24 = 384]

∴ The number of such pairs is 4.