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Question
The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is
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Solution
The correct option is A 4
Let us consider, P and Q are the numbers whose HCF is H, then, H should divide both P and Q.
P=H×p,
Q=H×q.
where p,q are integers prime to each other.
Let the required numbers be 33p and 33q.
Then 33p+33q=528=>p+q=16.
Now co-primes with sum 16 are (1,15);(3,13);(5,11);and(7,9).
Four pairs of such numbers are possible (33,495);(99,429);(165,363)and(231,297)
The number of such pairs is 4.
Let us consider, P and Q are the numbers whose HCF is H, then, H should divide both P and Q.
P=H×p,
Q=H×q.
where p,q are integers prime to each other.
Then 33p+33q=528=>p+q=16.
Now co-primes with sum 16 are (1,15);(3,13);(5,11);and(7,9).
Four pairs of such numbers are possible (33,495);(99,429);(165,363)and(231,297)
The number of such pairs is 4.
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