Multiple choice

HCF of two numbers is 15 and their sum is 150. If both the numbers are greater than 15, then those numbers are

  1. 45, 105

  2. 60, 90

  3. 55, 95

  4. 30, 120
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A Correct answer
Explanation

Let the numbers be 15x and 15y, where x and y are coprime. 15x + 15y = 150 implies x + y = 10. Possible pairs (x, y) are (1, 9), (3, 7). If (1, 9), numbers are 15 and 135. If (3, 7), numbers are 45 and 105. Since both must be greater than 15, 45 and 105 is the correct pair.

AI explanation

Since the highest common factor of the two numbers is 15, let the numbers be 15x and 15y where x and y are coprime. Their sum is 15x + 15y = 150, which simplifies to x + y = 10. Checking the pairs of coprime factors that sum to 10, the only valid pair greater than 1 is 3 and 7, making the numbers 15(3) = 45 and 15(7) = 105. The result is 45, 105.

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