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Q. The sum of two numbers is 684 and their HCF is 57. Find all possible pairs of such numbers.

(A) (57, 627) (285, 399)
(B) (37, 575) (270, 390)
(C) (45, 495) (30, 330)
(D) (45, 575) (280, 890)

Correct Answer - Option(A)
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Explanation by: Admin

Since, HCF of two numbers = 57
Hence, numbers are multiples of 57
Let, the numbers be 57x and 57y, where x and y are prime to each other.
According to the sum,
57x + 57y = 684
Or, x + y = 12
Hence, required possible pair of values of x and y which are prime to each other are (1, 11) and (5, 7).
Thus, required pairs of numbers are,
{57 × 1 = 57 and 57 × 11 = 627}

{57 × 5 = 285 and 57 × 7 = 399}

Q. The sum of two numbers is 684 and their HCF is 57. Find all possible pairs of such numbers.

Explanation by: Admin

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