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The sum of two numbers is 1056 and their HCF is 66, Find the Number of such pairs.
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- 6
- 2
- 4
- 8
- None of the above
Correct Option: C
Let the numbers be 66a and 66b, where a and b are co-primes.
According to the question,
66a + 66b = 1056
⇒ 66(a + b) = 1056
⇒ (a + b) = 1056/66 = 16
∴ Possible values of a and b are
(a = 1, b = 15), (a = 3, b = 13).
(a = 5, b = 11 ), (a = 7, b = 9)
∴ Numbers are
(66 x 1, 66 x 15), (66 x 3, 66 x 13),
(66 x 5, 66 x 11), (66 x 7, 66 x 9).
∴ Possible number of pairs = 4
