Q. The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above condition is
✅ Correct Answer: (A)
4
Explanation: Let the required numbers be 33a and 33b.
Then 33a +33b= 528 => a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
Therefore, Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4
Explanation by: Bijay Kumar
Let the required numbers be 33a and 33b.
Then 33a +33b= 528 => a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
Therefore, Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4
Then 33a +33b= 528 => a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
Therefore, Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4