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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

A
4
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B
6
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C
9
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D
3
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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.

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